Notes

== Repeating decimals part I (vinculum mode) ==
11.1886{{overline|8099173553719008264462}}
10.06981{{overline|2892561983471074380165}}
6.71320{{overline|8595041322314049586776}}
4.47547{{overline|2396694214876033057851}}
4.027925{{overline|1570247933884297520661}}

11.18868095{{overline|930232558139534883720}}
10.069812863{{overline|372093023255813953488}}
6.71320857{{overline|558139534883720930232}}
4.4754723{{overline|837209302325581395348}}
4.02792514{{overline|534883720930232558139}}

== Repeating decimals part II (vinculum mode) ==
111.886{{overline|8099173553719008264462}}
100.6981{{overline|2892561983471074380165}}
67.1320{{overline|8595041322314049586776}}
44.7547{{overline|2396694214876033057851}}
40.27925{{overline|1570247933884297520661}}

111.8868095{{overline|930232558139534883720}}
100.69812863{{overline|372093023255813953488}}
67.1320857{{overline|558139534883720930232}}
44.754723{{overline|837209302325581395348}}
40.2792514{{overline|534883720930232558139}}

== Repeating decimals part I (dot mode) ==
11.1886{{overset|.|8}}09917355371900826446{{overset|.|2}}
10.06981{{overset|.|2}}89256198347107438016{{overset|.|5}}
6.71320{{overset|.|8}}59504132231404958677{{overset|.|6}}
4.47547{{overset|.|2}}39669421487603305785{{overset|.|1}}
4.027925{{overset|.|1}}57024793388429752066{{overset|.|1}}

11.18868095{{overset|.|9}}3023255813953488372{{overset|.|0}}
10.069812863{{overset|.|3}}7209302325581395348{{overset|.|8}}
6.71320857{{overset|.|5}}5813953488372093023{{overset|.|2}}
4.4754723{{overset|.|8}}3720930232558139534{{overset|.|8}}
4.02792514{{overset|.|5}}3488372093023255813{{overset|.|9}}

== Repeating decimals part II (dot mode) ==
111.886{{overset|.|8}}09917355371900826446{{overset|.|2}}
100.6981{{overset|.|2}}89256198347107438016{{overset|.|5}}
67.1320{{overset|.|8}}59504132231404958677{{overset|.|6}}
44.7547{{overset|.|2}}39669421487603305785{{overset|.|1}}
40.27925{{overset|.|1}}57024793388429752066{{overset|.|1}}

111.8868095{{overset|.|9}}3023255813953488372{{overset|.|0}}
100.69812863{{overset|.|3}}7209302325581395348{{overset|.|8}}
67.1320857{{overset|.|5}}5813953488372093023{{overset|.|2}}
44.754723{{overset|.|8}}3720930232558139534{{overset|.|8}}
40.2792514{{overset|.|5}}3488372093023255813{{overset|.|9}}

== Live Japan-United States Meeting/Tour ==
===Table containing information focusing on the Live Japan-United States Meeting/Tour===
{| class="wikitable sortable"
|-
! Meeting/tour
! Description
! Inauguration date (date of first live event held)
! Monthly live event count
! Annual live event count
! Annual phase count
! Age status (Japanese-American stars/personalities)
|-
| Live Japan-United States Meeting/Tour
| Licensed famous Japanese-American live meeting/tour containing multiple live events featuring Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal as Japanese-American stars/personalities on Wednesdays and weekends everywhere in multiple American and Japanese cities or urban areas
| {{start date and age|2022|4|13}}
| 12 to 14 live events every month starting in May 2022
| 156 or 157 live events every year starting in May 2022
| Two phases per year (one containing 55 live events and the other containing 101 or 102 live events)
| Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal getting older in later live events
|}
===Table focusing on live events and phases===
{| class="wikitable sortable"
|-
! Phase
! Release date
! Live event count
! Date (first live event held)
! Date (final live event held)
! Duration
! Status
|-
| Phase #1 (Live Japan-United States Meeting/Tour) || {{start date and age|2022|4|13}} || 55 live Wednesday and weekend events (live events #1-55) || {{start date and age|2022|4|13}} || {{start date and age|2022|8|17}} || About four months || rowspan="2" | Featuring Shadow at age 37, Silver at age 35, Mighty at age 37, Sonic at age 36, Ray at age 30, Tails at age 29, Knuckles at age 36, Amy at age 32, Tangle at age 35, Rouge at age 38, Blaze at age 35, Sally at age 36, Marine at age 28, Mina at age 37 and Tikal at age 35
|-
| Phase #2 (Live Japan-United States Meeting/Tour) || {{start date and age|2022|8|20}} || 101 live Wednesday and weekend events (live events #56-156) || {{start date and age|2022|8|20}} || {{start date and age|2023|4|9}} || Nearly eight months
|-
| Phase #3 (Live Japan-United States Meeting/Tour) || {{start date and age|2023|4|12}} || 55 live Wednesday and weekend events (live events #157-211) || {{start date and age|2023|4|12}} || {{start date and age|2023|8|16}} || About four months || rowspan="2" | Featuring Shadow at age 38, Silver at age 36, Mighty at age 38, Sonic at age 37, Ray at age 31, Tails at age 30, Knuckles at age 37, Amy at age 33, Tangle at age 36, Rouge at age 39, Blaze at age 36, Sally at age 37, Marine at age 29, Mina at age 38 and Tikal at age 36
|-
| Phase #4 (Live Japan-United States Meeting/Tour) || {{start date and age|2023|8|19}} || 104 live Wednesday and weekend events (live events #212-315) || {{start date and age|2023|8|19}} || {{start date and age|2024|4|14}} || Nearly eight months
|-
| Phase #5 (Live Japan-United States Meeting/Tour) || {{start date and age|2024|4|17}} || 55 live Wednesday and weekend events (live events #316-370) || {{start date and age|2024|4|17}} || {{start date and age|2024|8|21}} || About four months || Featuring or scheduled to feature Shadow at age 39, Silver at age 37, Mighty at age 39, Sonic at age 38, Ray at age 32, Tails at age 31, Knuckles at age 38, Amy at age 34, Tangle at age 37, Rouge at age 40, Blaze at age 37, Sally at age 38, Marine at age 30, Mina at age 39 and Tikal at age 37
|-
| Phase #6 (Live Japan-United States Meeting/Tour) || {{start date and age|2024|8|24}} || 101 live Wednesday and weekend events (live events #371-471) || {{start date and age|2024|8|24}} || {{start date and age|2025|4|13}} || Nearly eight months || Scheduled to feature Shadow at age 39, Silver at age 37, Mighty at age 39, Sonic at age 38, Ray at age 32, Tails at age 31, Knuckles at age 38, Amy at age 34, Tangle at age 37, Rouge at age 40, Blaze at age 37, Sally at age 38, Marine at age 30, Mina at age 39 and Tikal at age 37
|-
| Phase #7 (Live Japan-United States Meeting/Tour) || {{start date and age|2025|4|16}} || 55 live Wednesday and weekend events (live events #472-526) || {{start date and age|2025|4|16}} || {{start date and age|2025|8|20}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 40, Silver at age 38, Mighty at age 40, Sonic at age 39, Ray at age 33, Tails at age 32, Knuckles at age 39, Amy at age 35, Tangle at age 38, Rouge at age 41, Blaze at age 38, Sally at age 39, Marine at age 31, Mina at age 40 and Tikal at age 38
|-
| Phase #8 (Live Japan-United States Meeting/Tour) || {{start date and age|2025|8|23}} || 101 live Wednesday and weekend events (live events #527-627) || {{start date and age|2025|8|23}} || {{start date and age|2026|4|12}} || Nearly eight months
|-
| Phase #9 (Live Japan-United States Meeting/Tour) || {{start date and age|2026|4|15}} || 55 live Wednesday and weekend events (live events #628-682) || {{start date and age|2026|4|15}} || {{start date and age|2026|8|19}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 41, Silver at age 39, Mighty at age 41, Sonic at age 40, Ray at age 34, Tails at age 33, Knuckles at age 40, Amy at age 36, Tangle at age 39, Rouge at age 42, Blaze at age 39, Sally at age 40, Marine at age 32, Mina at age 41 and Tikal at age 39
|-
| Phase #10 (Live Japan-United States Meeting/Tour) || {{start date and age|2026|8|22}} || 101 live Wednesday and weekend events (live events #683-783) || {{start date and age|2026|8|22}} || {{start date and age|2027|4|11}} || Nearly eight months
|-
| Phase #11 (Live Japan-United States Meeting/Tour) || {{start date and age|2027|4|14}} || 55 live Wednesday and weekend events (live events #784-838) || {{start date and age|2027|4|14}} || {{start date and age|2027|8|18}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 42, Silver at age 40, Mighty at age 42, Sonic at age 41, Ray at age 35, Tails at age 34, Knuckles at age 41, Amy at age 37, Tangle at age 40, Rouge at age 43, Blaze at age 40, Sally at age 41, Marine at age 33, Mina at age 42 and Tikal at age 40
|-
| Phase #12 (Live Japan-United States Meeting/Tour) || {{start date and age|2027|8|21}} || 101 live Wednesday and weekend events (live events #839-939) || {{start date and age|2027|8|21}} || {{start date and age|2028|4|9}} || Nearly eight months
|-
| Phase #13 (Live Japan-United States Meeting/Tour) || {{start date and age|2028|4|12}} || 55 live Wednesday and weekend events (live events #940-994) || {{start date and age|2028|4|12}} || {{start date and age|2028|8|16}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 43, Silver at age 41, Mighty at age 43, Sonic at age 42, Ray at age 35, Tails at age 34, Knuckles at age 42, Amy at age 38, Tangle at age 41, Rouge at age 44, Blaze at age 41, Sally at age 42, Marine at age 34, Mina at age 43 and Tikal at age 41
|-
| Phase #14 (Live Japan-United States Meeting/Tour) || {{start date and age|2028|8|19}} || 101 live Wednesday and weekend events (live events #995-1,095) || {{start date and age|2028|8|19}} || {{start date and age|2029|4|8}} || Nearly eight months
|-
| Phase #15 (Live Japan-United States Meeting/Tour) || {{start date and age|2029|4|11}} || 55 live Wednesday and weekend events (live events #1,096-1,150) || {{start date and age|2029|4|11}} || {{start date and age|2029|8|15}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 44, Silver at age 42, Mighty at age 44, Sonic at age 43, Ray at age 37, Tails at age 36, Knuckles at age 43, Amy at age 39, Tangle at age 42, Rouge at age 45, Blaze at age 42, Sally at age 43, Marine at age 35, Mina at age 44 and Tikal at age 42
|-
| Phase #16 (Live Japan-United States Meeting/Tour) || {{start date and age|2029|8|18}} || 104 live Wednesday and weekend events (live events #1,151-1,254) || {{start date and age|2029|8|18}} || {{start date and age|2030|4|14}} || Nearly eight months
|-
| Phase #17 (Live Japan-United States Meeting/Tour) || {{start date and age|2030|4|17}} || 55 live Wednesday and weekend events (live events #1,255-1,309) || {{start date and age|2030|4|17}} || {{start date and age|2030|8|21}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 45, Silver at age 43, Mighty at age 45, Sonic at age 44, Ray at age 38, Tails at age 37, Knuckles at age 44, Amy at age 40, Tangle at age 43, Rouge at age 46, Blaze at age 43, Sally at age 44, Marine at age 36, Mina at age 45 and Tikal at age 43
|-
| Phase #18 (Live Japan-United States Meeting/Tour) || {{start date and age|2030|8|24}} || 101 live Wednesday and weekend events (live events #1,310-1,410) || {{start date and age|2030|8|24}} || {{start date and age|2031|4|13}} || Nearly eight months
|-
| Phase #19 (Live Japan-United States Meeting/Tour) || {{start date and age|2031|4|16}} || 55 live Wednesday and weekend events (live events #1,411-1,465) || {{start date and age|2031|4|16}} || {{start date and age|2031|8|20}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 46, Silver at age 44, Mighty at age 46, Sonic at age 45, Ray at age 39, Tails at age 38, Knuckles at age 45, Amy at age 41, Tangle at age 44, Rouge at age 47, Blaze at age 44, Sally at age 45, Marine at age 37, Mina at age 46 and Tikal at age 44
|-
| Phase #20 (Live Japan-United States Meeting/Tour) || {{start date and age|2031|8|23}} || 101 live Wednesday and weekend events (live events #1,466-1,566) || {{start date and age|2031|8|23}} || {{start date and age|2032|4|11}} || Nearly eight months
|-
| Phase #21 (Live Japan-United States Meeting/Tour) || {{start date and age|2032|4|14}} || 55 live Wednesday and weekend events (live events #1,567-1,621) || {{start date and age|2032|4|14}} || {{start date and age|2032|8|18}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 47, Silver at age 45, Mighty at age 47, Sonic at age 46, Ray at age 40, Tails at age 39, Knuckles at age 46, Amy at age 42, Tangle at age 45, Rouge at age 48, Blaze at age 45, Sally at age 46, Marine at age 38, Mina at age 47 and Tikal at age 45
|-
| Phase #22 (Live Japan-United States Meeting/Tour) || {{start date and age|2032|8|21}} || 101 live Wednesday and weekend events (live events #1,622-1,722) || {{start date and age|2032|8|21}} || {{start date and age|2033|4|10}} || Nearly eight months
|-
| Phase #23 (Live Japan-United States Meeting/Tour) || {{start date and age|2033|4|13}} || 55 live Wednesday and weekend events (live events #1,723-1,777) || {{start date and age|2033|4|13}} || {{start date and age|2033|8|17}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 48, Silver at age 46, Mighty at age 48, Sonic at age 47, Ray at age 41, Tails at age 40, Knuckles at age 47, Amy at age 43, Tangle at age 46, Rouge at age 49, Blaze at age 46, Sally at age 47, Marine at age 39, Mina at age 48 and Tikal at age 46
|-
| Phase #24 (Live Japan-United States Meeting/Tour) || {{start date and age|2033|8|20}} || 101 live Wednesday and weekend events (live events #1,778-1,878) || {{start date and age|2033|8|20}} || {{start date and age|2034|4|9}} || Nearly eight months
|-
| Phase #25 (Live Japan-United States Meeting/Tour) || {{start date and age|2034|4|12}} || 55 live Wednesday and weekend events (live events #1,879-1,933) || {{start date and age|2034|4|12}} || {{start date and age|2034|8|16}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 49, Silver at age 47, Mighty at age 49, Sonic at age 48, Ray at age 42, Tails at age 41, Knuckles at age 48, Amy at age 44, Tangle at age 47, Rouge at age 50, Blaze at age 47, Sally at age 48, Marine at age 40, Mina at age 49 and Tikal at age 47
|-
| Phase #26 (Live Japan-United States Meeting/Tour) || {{start date and age|2034|8|19}} || 101 live Wednesday and weekend events (live events #1,934-2,034) || {{start date and age|2034|8|19}} || {{start date and age|2035|4|8}} || Nearly eight months
|-
| Phase #27 (Live Japan-United States Meeting/Tour) || {{start date and age|2035|4|11}} || 55 live Wednesday and weekend events (live events #2,035-2,089) || {{start date and age|2035|4|11}} || {{start date and age|2035|8|15}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 50, Silver at age 48, Mighty at age 50, Sonic at age 49, Ray at age 43, Tails at age 42, Knuckles at age 49, Amy at age 45, Tangle at age 48, Rouge at age 51, Blaze at age 48, Sally at age 49, Marine at age 41, Mina at age 50 and Tikal at age 48
|-
| Phase #28 (Live Japan-United States Meeting/Tour) || {{start date and age|2035|8|18}} || 104 live Wednesday and weekend events (live events #2,090-2,193)|| {{start date and age|2035|8|18}} || {{start date and age|2036|4|13}} || Nearly eight months
|-
| Phase #29 (Live Japan-United States Meeting/Tour) || {{start date and age|2036|4|16}} || 55 live Wednesday and weekend events (live events #2,194-2,248) || {{start date and age|2036|4|16}} || {{start date and age|2036|8|20}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 51, Silver at age 49, Mighty at age 51, Sonic at age 50, Ray at age 44, Tails at age 43, Knuckles at age 50, Amy at age 46, Tangle at age 49, Rouge at age 52, Blaze at age 49, Sally at age 50, Marine at age 42, Mina at age 51 and Tikal at age 49
|-
| Phase #30 (Live Japan-United States Meeting/Tour) || {{start date and age|2036|8|23}} || 101 live Wednesday and weekend events (live events #2,249-2,349)|| {{start date and age|2036|8|23}} || {{start date and age|2037|4|12}} || Nearly eight months
|-
| Phase #31 (Live Japan-United States Meeting/Tour) || {{start date and age|2037|4|15}} || 55 live Wednesday and weekend events (live events #2,350-2,404) || {{start date and age|2037|4|15}} || {{start date and age|2037|8|19}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 52, Silver at age 50, Mighty at age 52, Sonic at age 51, Ray at age 45, Tails at age 44, Knuckles at age 51, Amy at age 47, Tangle at age 50, Rouge at age 53, Blaze at age 50, Sally at age 51, Marine at age 43, Mina at age 52 and Tikal at age 50
|-
| Phase #32 (Live Japan-United States Meeting/Tour) || {{start date and age|2037|8|22}} || 101 live Wednesday and weekend events (live events #2,405-2,505)|| {{start date and age|2037|8|22}} || {{start date and age|2038|4|11}} || Nearly eight months
|-
| Phase #33 (Live Japan-United States Meeting/Tour) || {{start date and age|2038|4|14}} || 55 live Wednesday and weekend events (live events #2,506-2,560) || {{start date and age|2038|4|14}} || {{start date and age|2038|8|18}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 53, Silver at age 51, Mighty at age 53, Sonic at age 52, Ray at age 46, Tails at age 45, Knuckles at age 52, Amy at age 48, Tangle at age 51, Rouge at age 54, Blaze at age 51, Sally at age 52, Marine at age 44, Mina at age 53 and Tikal at age 51
|-
| Phase #34 (Live Japan-United States Meeting/Tour) || {{start date and age|2038|8|21}} || 101 live Wednesday and weekend events (live events #2,561-2,661)|| {{start date and age|2038|8|21}} || {{start date and age|2039|4|10}} || Nearly eight months
|-
| Phase #35 (Live Japan-United States Meeting/Tour) || {{start date and age|2039|4|13}} || 55 live Wednesday and weekend events (live events #2,662-2,716) || {{start date and age|2039|4|13}} || {{start date and age|2039|8|17}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 54, Silver at age 52, Mighty at age 54, Sonic at age 53, Ray at age 47, Tails at age 46, Knuckles at age 53, Amy at age 49, Tangle at age 52, Rouge at age 55, Blaze at age 52, Sally at age 53, Marine at age 45, Mina at age 54 and Tikal at age 52
|-
| Phase #36 (Live Japan-United States Meeting/Tour) || {{start date and age|2039|8|20}} || 101 live Wednesday and weekend events (live events #2,717-2,817)|| {{start date and age|2039|8|20}} || {{start date and age|2040|4|8}} || Nearly eight months
|-
| Phase #37 (Live Japan-United States Meeting/Tour) || {{start date and age|2040|4|11}} || 55 live Wednesday and weekend events (live events #2,818-2,872) || {{start date and age|2040|4|11}} || {{start date and age|2040|8|15}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 55, Silver at age 53, Mighty at age 55, Sonic at age 54, Ray at age 48, Tails at age 47, Knuckles at age 54, Amy at age 50, Tangle at age 53, Rouge at age 56, Blaze at age 53, Sally at age 54, Marine at age 46, Mina at age 55 and Tikal at age 53
|-
| Phase #38 (Live Japan-United States Meeting/Tour) || {{start date and age|2040|8|18}} || 104 live Wednesday and weekend events (live events #2,873-2,976)|| {{start date and age|2040|8|18}} || {{start date and age|2041|4|14}} || Nearly eight months
|-
| Phase #39 (Live Japan-United States Meeting/Tour) || {{start date and age|2041|4|17}} || 55 live Wednesday and weekend events (live events #2,977-3,031) || {{start date and age|2041|4|17}} || {{start date and age|2041|8|21}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 56, Silver at age 54, Mighty at age 56, Sonic at age 55, Ray at age 49, Tails at age 48, Knuckles at age 55, Amy at age 51, Tangle at age 54, Rouge at age 57, Blaze at age 54, Sally at age 55, Marine at age 47, Mina at age 56 and Tikal at age 54
|-
| Phase #40 (Live Japan-United States Meeting/Tour) || {{start date and age|2041|8|24}} || 104 live Wednesday and weekend events (live events #3,032-3,132)|| {{start date and age|2041|8|24}} || {{start date and age|2042|4|13}} || Nearly eight months
|-
| Phase #41 (Live Japan-United States Meeting/Tour) || {{start date and age|2042|4|16}} || 55 live Wednesday and weekend events (live events #3,133-3,187) || {{start date and age|2042|4|16}} || {{start date and age|2042|8|20}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 57, Silver at age 55, Mighty at age 57, Sonic at age 56, Ray at age 50, Tails at age 49, Knuckles at age 56, Amy at age 52, Tangle at age 55, Rouge at age 58, Blaze at age 55, Sally at age 56, Marine at age 48, Mina at age 57 and Tikal at age 55
|-
| Phase #42 (Live Japan-United States Meeting/Tour) || {{start date and age|2042|8|23}} || 101 live Wednesday and weekend events (live events #3,188-3,288)|| {{start date and age|2042|8|23}} || {{start date and age|2043|4|12}} || Nearly eight months
|-
| Phase #43 (Live Japan-United States Meeting/Tour) || {{start date and age|2043|4|15}} || 55 live Wednesday and weekend events (live events #3,289-3,343) || {{start date and age|2043|4|15}} || {{start date and age|2043|8|19}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 58, Silver at age 56, Mighty at age 58, Sonic at age 57, Ray at age 51, Tails at age 50, Knuckles at age 57, Amy at age 53, Tangle at age 56, Rouge at age 59, Blaze at age 56, Sally at age 57, Marine at age 49, Mina at age 58 and Tikal at age 56
|-
| Phase #44 (Live Japan-United States Meeting/Tour) || {{start date and age|2043|8|22}} || 101 live Wednesday and weekend events (live events #3,344-3,444)|| {{start date and age|2043|8|22}} || {{start date and age|2044|4|10}} || Nearly eight months
|-
| Phase #45 (Live Japan-United States Meeting/Tour) || {{start date and age|2044|4|13}} || 55 live Wednesday and weekend events (live events #3,445-3,499) || {{start date and age|2044|4|13}} || {{start date and age|2044|8|17}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 59, Silver at age 57, Mighty at age 59, Sonic at age 58, Ray at age 52, Tails at age 51, Knuckles at age 58, Amy at age 54, Tangle at age 57, Rouge at age 60, Blaze at age 57, Sally at age 58, Marine at age 50, Mina at age 59 and Tikal at age 57
|-
| Phase #46 (Live Japan-United States Meeting/Tour) || {{start date and age|2044|8|20}} || 101 live Wednesday and weekend events (live events #3,500-3,600)|| {{start date and age|2044|8|20}} || {{start date and age|2045|4|9}} || Nearly eight months
|-
| Phase #47 (Live Japan-United States Meeting/Tour) || {{start date and age|2045|4|12}} || 55 live Wednesday and weekend events (live events #3,601-3,655) || {{start date and age|2045|4|12}} || {{start date and age|2045|8|16}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 60, Silver at age 58, Mighty at age 60, Sonic at age 59, Ray at age 53, Tails at age 52, Knuckles at age 59, Amy at age 55, Tangle at age 58, Rouge at age 61, Blaze at age 58, Sally at age 59, Marine at age 51, Mina at age 60 and Tikal at age 58
|-
| Phase #48 (Live Japan-United States Meeting/Tour) || {{start date and age|2045|8|19}} || 101 live Wednesday and weekend events (live events #3,656-3,756)|| {{start date and age|2045|8|19}} || {{start date and age|2046|4|8}} || Nearly eight months
|-
| Phase #49 (Live Japan-United States Meeting/Tour) || {{start date and age|2046|4|11}} || 55 live Wednesday and weekend events (live events #3,757-3,811) || {{start date and age|2046|4|11}} || {{start date and age|2046|8|15}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 61, Silver at age 59, Mighty at age 61, Sonic at age 60, Ray at age 54, Tails at age 53, Knuckles at age 60, Amy at age 56, Tangle at age 59, Rouge at age 62, Blaze at age 59, Sally at age 60, Marine at age 52, Mina at age 61 and Tikal at age 59
|-
| Phase #50 (Live Japan-United States Meeting/Tour) || {{start date and age|2046|8|18}} || 104 live Wednesday and weekend events (live events #3,812-3,915)|| {{start date and age|2046|8|18}} || {{start date and age|2047|4|14}} || Nearly eight months
|}

== Live Japan-United States Documentary ==
===Table containing information focusing on the Live Japan-United States Documentary===
{| class="wikitable sortable"
|-
! Documentary
! Description
! Debut date (date of first episode released)
! Monthly episode count
! Annual episode count
! Annual edition count
! Age status (Japanese-American stars/personalities)
|-
| Live Japan-United States Documentary
| Licensed famous Japanese-American live documentary containing multiple episodes released indefinitely on Wednesdays and weekends and featuring Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal as Japanese-American stars/personalities everywhere in multiple American and Japanese cities or urban areas
| {{start date and age|2022|4|13}}
| 12 to 14 episodes every month starting in May 2022
| 156 or 157 episodes every year starting in May 2022
| Two editions per year (one containing 55 episodes and the other containing 101 or 102 episodes)
| Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal getting older in later live events
|}
===Table focusing on editions and episodes and their release dates===
{| class="wikitable sortable"
|-
! Edition
! Release date
! Episode count
! Date (first episode released)
! Date (final episode released)
! Duration
! Status
|-
| Edition #1 (Live Japan-United States Documentary) || {{start date and age|2022|4|13}} || 55 episodes released on Wednesdays and weekends (episodes #1-55) || {{start date and age|2022|4|13}} || {{start date and age|2022|8|17}} || About four months || rowspan="2" | Featuring Shadow at age 37, Silver at age 35, Mighty at age 37, Sonic at age 36, Ray at age 30, Tails at age 29, Knuckles at age 36, Amy at age 32, Tangle at age 35, Rouge at age 38, Blaze at age 35, Sally at age 36, Marine at age 28, Mina at age 37 and Tikal at age 35
|-
| Edition #2 (Live Japan-United States Documentary) || {{start date and age|2022|8|20}} || 101 episodes released on Wednesdays and weekends (episodes #56-156) || {{start date and age|2022|8|20}} || {{start date and age|2023|4|9}} || Nearly eight months
|-
| Edition #3 (Live Japan-United States Documentary) || {{start date and age|2023|4|12}} || 55 episodes released on Wednesdays and weekends (episodes #157-211) || {{start date and age|2023|4|12}} || {{start date and age|2023|8|16}} || About four months || rowspan="2" | Featuring Shadow at age 38, Silver at age 36, Mighty at age 38, Sonic at age 37, Ray at age 31, Tails at age 30, Knuckles at age 37, Amy at age 33, Tangle at age 36, Rouge at age 39, Blaze at age 36, Sally at age 37, Marine at age 29, Mina at age 38 and Tikal at age 36
|-
| Edition #4 (Live Japan-United States Documentary) || {{start date and age|2023|8|19}} || 104 episodes released on Wednesdays and weekends (episodes #212-315) || {{start date and age|2023|8|19}} || {{start date and age|2024|4|14}} || Nearly eight months
|-
| Edition #5 (Live Japan-United States Documentary) || {{start date and age|2024|4|17}} || 55 episodes released or scheduled to be released on Wednesdays and weekends (episodes #316-370) || {{start date and age|2024|4|17}} || {{start date and age|2024|8|21}} || About four months || Featuring or scheduled to feature Shadow at age 39, Silver at age 37, Mighty at age 39, Sonic at age 38, Ray at age 32, Tails at age 31, Knuckles at age 38, Amy at age 34, Tangle at age 37, Rouge at age 40, Blaze at age 37, Sally at age 38, Marine at age 30, Mina at age 39 and Tikal at age 37
|-
| Edition #6 (Live Japan-United States Documentary) || {{start date and age|2024|8|24}} || 101 episodes scheduled to be released on Wednesdays and weekends (episodes #371-471) || {{start date and age|2024|8|24}} || {{start date and age|2025|4|13}} || Nearly eight months || Scheduled to feature Shadow at age 39, Silver at age 37, Mighty at age 39, Sonic at age 38, Ray at age 32, Tails at age 31, Knuckles at age 38, Amy at age 34, Tangle at age 37, Rouge at age 40, Blaze at age 37, Sally at age 38, Marine at age 30, Mina at age 39 and Tikal at age 37
|-
| Edition #7 (Live Japan-United States Documentary) || {{start date and age|2025|4|16}} || 55 episodes scheduled to be released on Wednesdays and weekends (episodes #472-526) || {{start date and age|2025|4|16}} || {{start date and age|2025|8|20}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 40, Silver at age 38, Mighty at age 40, Sonic at age 39, Ray at age 33, Tails at age 32, Knuckles at age 39, Amy at age 35, Tangle at age 38, Rouge at age 41, Blaze at age 38, Sally at age 39, Marine at age 31, Mina at age 40 and Tikal at age 38
|-
| Edition #8 (Live Japan-United States Documentary) || {{start date and age|2025|8|23}} || 101 episodes scheduled to be released on Wednesdays and weekends (episodes #527-627) || {{start date and age|2025|8|23}} || {{start date and age|2026|4|12}} || Nearly eight months
|-
| Edition #9 (Live Japan-United States Documentary) || {{start date and age|2026|4|15}} || 55 episodes scheduled to be released on Wednesdays and weekends (episodes #628-682) || {{start date and age|2026|4|15}} || {{start date and age|2026|8|19}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 41, Silver at age 39, Mighty at age 41, Sonic at age 40, Ray at age 34, Tails at age 33, Knuckles at age 40, Amy at age 36, Tangle at age 39, Rouge at age 42, Blaze at age 39, Sally at age 40, Marine at age 32, Mina at age 41 and Tikal at age 39
|-
| Edition #10 (Live Japan-United States Documentary) || {{start date and age|2026|8|22}} || 101 episodes scheduled to be released on Wednesdays and weekends (episodes #683-783) || {{start date and age|2026|8|22}} || {{start date and age|2027|4|11}} || Nearly eight months
|-
| Edition #11 (Live Japan-United States Documentary) || {{start date and age|2027|4|14}} || 55 episodes scheduled to be released on Wednesdays and weekends (episodes #784-838) || {{start date and age|2027|4|14}} || {{start date and age|2027|8|18}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 42, Silver at age 40, Mighty at age 42, Sonic at age 41, Ray at age 35, Tails at age 34, Knuckles at age 41, Amy at age 37, Tangle at age 40, Rouge at age 43, Blaze at age 40, Sally at age 41, Marine at age 33, Mina at age 42 and Tikal at age 40
|-
| Edition #12 (Live Japan-United States Documentary) || {{start date and age|2027|8|21}} || 101 episodes scheduled to be released on Wednesdays and weekends (episodes #839-939) || {{start date and age|2027|8|21}} || {{start date and age|2028|4|9}} || Nearly eight months
|-
| Edition #13 (Live Japan-United States Documentary) || {{start date and age|2028|4|12}} || 55 episodes scheduled to be released on Wednesdays and weekends (episodes #940-994) || {{start date and age|2028|4|12}} || {{start date and age|2028|8|16}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 43, Silver at age 41, Mighty at age 43, Sonic at age 42, Ray at age 35, Tails at age 34, Knuckles at age 42, Amy at age 38, Tangle at age 41, Rouge at age 44, Blaze at age 41, Sally at age 42, Marine at age 34, Mina at age 43 and Tikal at age 41
|-
| Edition #14 (Live Japan-United States Documentary) || {{start date and age|2028|8|19}} || 101 episodes scheduled to be released on Wednesdays and weekends (episodes #995-1,095) || {{start date and age|2028|8|19}} || {{start date and age|2029|4|8}} || Nearly eight months
|-
| Edition #15 (Live Japan-United States Documentary) || {{start date and age|2029|4|11}} || 55 episodes scheduled to be released on Wednesdays and weekends (episodes #1,096-1,150) || {{start date and age|2029|4|11}} || {{start date and age|2029|8|15}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 44, Silver at age 42, Mighty at age 44, Sonic at age 43, Ray at age 37, Tails at age 36, Knuckles at age 43, Amy at age 39, Tangle at age 42, Rouge at age 45, Blaze at age 42, Sally at age 43, Marine at age 35, Mina at age 44 and Tikal at age 42
|-
| Edition #16 (Live Japan-United States Documentary) || {{start date and age|2029|8|18}} || 104 episodes scheduled to be released on Wednesdays and weekends (episodes #1,151-1,254) || {{start date and age|2029|8|18}} || {{start date and age|2030|4|14}} || Nearly eight months
|-
| Edition #17 (Live Japan-United States Documentary) || {{start date and age|2030|4|17}} || 55 episodes scheduled to be released on Wednesdays and weekends (episodes #1,255-1,309) || {{start date and age|2030|4|17}} || {{start date and age|2030|8|21}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 45, Silver at age 43, Mighty at age 45, Sonic at age 44, Ray at age 38, Tails at age 37, Knuckles at age 44, Amy at age 40, Tangle at age 43, Rouge at age 46, Blaze at age 43, Sally at age 44, Marine at age 36, Mina at age 45 and Tikal at age 43
|-
| Edition #18 (Live Japan-United States Documentary) || {{start date and age|2030|8|24}} || 101 episodes scheduled to be released on Wednesdays and weekends (episodes #1,310-1,410) || {{start date and age|2030|8|24}} || {{start date and age|2031|4|13}} || Nearly eight months
|-
| Edition #19 (Live Japan-United States Documentary) || {{start date and age|2031|4|16
}} || 55 episodes scheduled to be released on Wednesdays and weekends (episodes #1,411-1,465) || {{start date and age|2031|4|16}} || {{start date and age|2031|8|20}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 46, Silver at age 44, Mighty at age 46, Sonic at age 45, Ray at age 39, Tails at age 38, Knuckles at age 45, Amy at age 41, Tangle at age 44, Rouge at age 47, Blaze at age 44, Sally at age 45, Marine at age 37, Mina at age 46 and Tikal at age 44
|-
| Edition #20 (Live Japan-United States Documentary) || {{start date and age|2031|8|23}} || 101 episodes scheduled to be released on Wednesdays and weekends (episodes #1,466-1,566) || {{start date and age|2031|8|23}} || {{start date and age|2032|4|11}} || Nearly eight months
|-
| Edition #21 (Live Japan-United States Documentary) || {{start date and age|2032|4|14}} || 55 episodes scheduled to be released on Wednesdays and weekends (episodes #1,567-1,621) || {{start date and age|2032|4|14}} || {{start date and age|2032|8|18}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 47, Silver at age 45, Mighty at age 47, Sonic at age 46, Ray at age 40, Tails at age 39, Knuckles at age 46, Amy at age 42, Tangle at age 45, Rouge at age 48, Blaze at age 45, Sally at age 46, Marine at age 38, Mina at age 47 and Tikal at age 45
|-
| Edition #22 (Live Japan-United States Documentary) || {{start date and age|2032|8|21}} || 101 episodes scheduled to be released on Wednesdays and weekends (episodes #1,622-1,722) || {{start date and age|2032|8|21}} || {{start date and age|2033|4|10}} || Nearly eight months
|-
| Edition #23 (Live Japan-United States Documentary) || {{start date and age|2033|4|13}} || 55 episodes scheduled to be released on Wednesdays and weekends (episodes #1,723-1,777) || {{start date and age|2033|4|13}} || {{start date and age|2033|8|17}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 48, Silver at age 46, Mighty at age 48, Sonic at age 47, Ray at age 41, Tails at age 40, Knuckles at age 47, Amy at age 43, Tangle at age 46, Rouge at age 49, Blaze at age 46, Sally at age 47, Marine at age 39, Mina at age 48 and Tikal at age 46
|-
| Edition #24 (Live Japan-United States Documentary) || {{start date and age|2033|8|20}} || 101 episodes scheduled to be released on Wednesdays and weekends (episodes #1,778-1,878) || {{start date and age|2033|8|20}} || {{start date and age|2034|4|9}} || Nearly eight months
|-
| Edition #25 (Live Japan-United States Documentary) || {{start date and age|2034|4|12}} || 55 episodes scheduled to be released on Wednesdays and weekends (episodes #1,879-1,933) || {{start date and age|2034|4|12}} || {{start date and age|2034|8|16}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 49, Silver at age 47, Mighty at age 49, Sonic at age 48, Ray at age 42, Tails at age 41, Knuckles at age 48, Amy at age 44, Tangle at age 47, Rouge at age 50, Blaze at age 47, Sally at age 48, Marine at age 40, Mina at age 49 and Tikal at age 47
|-
| Edition #26 (Live Japan-United States Documentary) || {{start date and age|2034|8|19}} || 101 episodes scheduled to be released on Wednesdays and weekends (episodes #1,934-2,034) || {{start date and age|2034|8|19}} || {{start date and age|2035|4|8}} || Nearly eight months
|-
| Edition #27 (Live Japan-United States Documentary) || {{start date and age|2035|4|11}} || 55 episodes scheduled to be released on Wednesdays and weekends (episodes #2,035-2,089) || {{start date and age|2035|4|11}} || {{start date and age|2035|8|15}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 50, Silver at age 48, Mighty at age 50, Sonic at age 49, Ray at age 43, Tails at age 42, Knuckles at age 49, Amy at age 45, Tangle at age 48, Rouge at age 51, Blaze at age 48, Sally at age 49, Marine at age 41, Mina at age 50 and Tikal at age 48
|-
| Edition #28 (Live Japan-United States Documentary) || {{start date and age|2035|8|18}} || 104 episodes scheduled to be released on Wednesdays and weekends (episodes #2,090-2,193)|| {{start date and age|2035|8|18}} || {{start date and age|2036|4|13}} || Nearly eight months
|-
| Edition #29 (Live Japan-United States Documentary) || {{start date and age|2036|4|16}} || 55 episodes scheduled to be released on Wednesdays and weekends (episodes #2,194-2,248) || {{start date and age|2036|4|16}} || {{start date and age|2036|8|20}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 51, Silver at age 49, Mighty at age 51, Sonic at age 50, Ray at age 44, Tails at age 43, Knuckles at age 50, Amy at age 46, Tangle at age 49, Rouge at age 52, Blaze at age 49, Sally at age 50, Marine at age 42, Mina at age 51 and Tikal at age 49
|-
| Edition #30 (Live Japan-United States Documentary) || {{start date and age|2036|8|23}} || 101 episodes scheduled to be released on Wednesdays and weekends (episodes #2,249-2,349)|| {{start date and age|2036|8|23}} || {{start date and age|2037|4|12}} || Nearly eight months
|-
| Edition #31 (Live Japan-United States Documentary) || {{start date and age|2037|4|15}} || 55 episodes scheduled to be released on Wednesdays and weekends (episodes #2,350-2,404) || {{start date and age|2037|4|15}} || {{start date and age|2037|8|19}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 52, Silver at age 50, Mighty at age 52, Sonic at age 51, Ray at age 45, Tails at age 44, Knuckles at age 51, Amy at age 47, Tangle at age 50, Rouge at age 53, Blaze at age 50, Sally at age 51, Marine at age 43, Mina at age 52 and Tikal at age 50
|-
| Edition #32 (Live Japan-United States Documentary) || {{start date and age|2037|8|22}} || 101 episodes scheduled to be released on Wednesdays and weekends (episodes #2,405-2,505)|| {{start date and age|2037|8|22}} || {{start date and age|2038|4|11}} || Nearly eight months
|-
| Edition #33 (Live Japan-United States Documentary) || {{start date and age|2038|4|14}} || 55 episodes scheduled to be released on Wednesdays and weekends (episodes #2,506-2,560) || {{start date and age|2038|4|14}} || {{start date and age|2038|8|18}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 53, Silver at age 51, Mighty at age 53, Sonic at age 52, Ray at age 46, Tails at age 45, Knuckles at age 52, Amy at age 48, Tangle at age 51, Rouge at age 54, Blaze at age 51, Sally at age 52, Marine at age 44, Mina at age 53 and Tikal at age 51
|-
| Edition #34 (Live Japan-United States Documentary) || {{start date and age|2038|8|21}} || 101 episodes scheduled to be released on Wednesdays and weekends (episodes #2,561-2,661)|| {{start date and age|2038|8|21}} || {{start date and age|2039|4|10}} || Nearly eight months
|-
| Edition #35 (Live Japan-United States Documentary) || {{start date and age|2039|4|13}} || 55 episodes scheduled to be released on Wednesdays and weekends (episodes #2,662-2,716) || {{start date and age|2039|4|13}} || {{start date and age|2039|8|17}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 54, Silver at age 52, Mighty at age 54, Sonic at age 53, Ray at age 47, Tails at age 46, Knuckles at age 53, Amy at age 49, Tangle at age 52, Rouge at age 55, Blaze at age 52, Sally at age 53, Marine at age 45, Mina at age 54 and Tikal at age 52
|-
| Edition #36 (Live Japan-United States Documentary) || {{start date and age|2039|8|20}} || 101 episodes scheduled to be released on Wednesdays and weekends (episodes #2,717-2,817)|| {{start date and age|2039|8|20}} || {{start date and age|2040|4|8}} || Nearly eight months
|-
| Edition #37 (Live Japan-United States Documentary) || {{start date and age|2040|4|11}} || 55 episodes scheduled to be released on Wednesdays and weekends (episodes #2,818-2,872) || {{start date and age|2040|4|11}} || {{start date and age|2040|8|15}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 55, Silver at age 53, Mighty at age 55, Sonic at age 54, Ray at age 48, Tails at age 47, Knuckles at age 54, Amy at age 50, Tangle at age 53, Rouge at age 56, Blaze at age 53, Sally at age 54, Marine at age 46, Mina at age 55 and Tikal at age 53
|-
| Edition #38 (Live Japan-United States Documentary) || {{start date and age|2040|8|18}} || 104 episodes scheduled to be released on Wednesdays and weekends (episodes #2,873-2,976)|| {{start date and age|2040|8|18}} || {{start date and age|2041|4|14}} || Nearly eight months
|-
| Edition #39 (Live Japan-United States Documentary) || {{start date and age|2041|4|17}} || 55 episodes scheduled to be released on Wednesdays and weekends (episodes #2,977-3,031) || {{start date and age|2041|4|17}} || {{start date and age|2041|8|21}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 56, Silver at age 54, Mighty at age 56, Sonic at age 55, Ray at age 49, Tails at age 48, Knuckles at age 55, Amy at age 51, Tangle at age 54, Rouge at age 57, Blaze at age 54, Sally at age 55, Marine at age 47, Mina at age 56 and Tikal at age 54
|-
| Edition #40 (Live Japan-United States Documentary) || {{start date and age|2041|8|24}} || 101 episodes scheduled to be released on Wednesdays and weekends (episodes #3,032-3,132)|| {{start date and age|2041|8|24}} || {{start date and age|2042|4|13}} || Nearly eight months
|-
| Edition #41 (Live Japan-United States Documentary) || {{start date and age|2042|4|16}} || 55 episodes scheduled to be released on Wednesdays and weekends (episodes #3,133-3,187) || {{start date and age|2042|4|16}} || {{start date and age|2042|8|20}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 57, Silver at age 55, Mighty at age 57, Sonic at age 56, Ray at age 50, Tails at age 49, Knuckles at age 56, Amy at age 52, Tangle at age 55, Rouge at age 58, Blaze at age 55, Sally at age 56, Marine at age 48, Mina at age 57 and Tikal at age 55
|-
| Edition #42 (Live Japan-United States Documentary) || {{start date and age|2042|8|23}} || 101 episodes scheduled to be released on Wednesdays and weekends (episodes #3,188-3,288)|| {{start date and age|2042|8|23}} || {{start date and age|2043|4|12}} || Nearly eight months
|-
| Edition #43 (Live Japan-United States Documentary) || {{start date and age|2043|4|15}} || 55 episodes scheduled to be released on Wednesdays and weekends (episodes #3,289-3,343) || {{start date and age|2043|4|15}} || {{start date and age|2043|8|19}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 58, Silver at age 56, Mighty at age 58, Sonic at age 57, Ray at age 51, Tails at age 50, Knuckles at age 57, Amy at age 53, Tangle at age 56, Rouge at age 59, Blaze at age 56, Sally at age 57, Marine at age 49, Mina at age 58 and Tikal at age 56
|-
| Edition #44 (Live Japan-United States Documentary) || {{start date and age|2043|8|22}} || 101 episodes scheduled to be released on Wednesdays and weekends (episodes #3,344-3,444)|| {{start date and age|2043|8|22}} || {{start date and age|2044|4|10}} || Nearly eight months
|-
| Edition #45 (Live Japan-United States Documentary) || {{start date and age|2044|4|13}} || 55 episodes scheduled to be released on Wednesdays and weekends (episodes #3,445-3,499) || {{start date and age|2044|4|13}} || {{start date and age|2044|8|17}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 59, Silver at age 57, Mighty at age 59, Sonic at age 58, Ray at age 52, Tails at age 51, Knuckles at age 58, Amy at age 54, Tangle at age 57, Rouge at age 60, Blaze at age 57, Sally at age 58, Marine at age 50, Mina at age 59 and Tikal at age 57
|-
| Edition #46 (Live Japan-United States Documentary) || {{start date and age|2044|8|20}} || 101 episodes scheduled to be released on Wednesdays and weekends (episodes #3,500-3,600)|| {{start date and age|2044|8|20}} || {{start date and age|2045|4|9}} || Nearly eight months
|-
| Edition #47 (Live Japan-United States Documentary) || {{start date and age|2045|4|12}} || 55 episodes scheduled to be released on Wednesdays and weekends (episodes #3,601-3,655) || {{start date and age|2045|4|12}} || {{start date and age|2045|8|16}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 60, Silver at age 58, Mighty at age 60, Sonic at age 59, Ray at age 53, Tails at age 52, Knuckles at age 59, Amy at age 55, Tangle at age 58, Rouge at age 61, Blaze at age 58, Sally at age 59, Marine at age 51, Mina at age 60 and Tikal at age 58
|-
| Edition #48 (Live Japan-United States Documentary) || {{start date and age|2045|8|19}} || 101 episodes scheduled to be released on Wednesdays and weekends (episodes #3,656-3,756)|| {{start date and age|2045|8|19}} || {{start date and age|2046|4|8}} || Nearly eight months
|-
| Edition #49 (Live Japan-United States Documentary) || {{start date and age|2046|4|11}} || 55 episodes scheduled to be released on Wednesdays and weekends (episodes #3,757-3,811) || {{start date and age|2046|4|11}} || {{start date and age|2046|8|15}} || About four months || rowspan="2" | Scheduled to feature Shadow at age 61, Silver at age 59, Mighty at age 61, Sonic at age 60, Ray at age 54, Tails at age 53, Knuckles at age 60, Amy at age 56, Tangle at age 59, Rouge at age 62, Blaze at age 59, Sally at age 60, Marine at age 52, Mina at age 61 and Tikal at age 59
|-
| Edition #50 (Live Japan-United States Documentary) || {{start date and age|2046|8|18}} || 104 episodes scheduled to be released on Wednesdays and weekends (episodes #3,812-3,915)|| {{start date and age|2046|8|18}} || {{start date and age|2047|4|14}} || Nearly eight months
|}

== Japanese-American star/personality statistics ==
===Table focusing on Japanese-American stars/personalities===

{|class="wikitable sortable"
!Star/personality name
!Gender
!Born
!Country of birth
!Country of raising
!Countries led
!Nationality
!Country of residence
!Country of travel
!Height
!Known or identified by
!First seen
!Live debut date
!Appearance status
!Net worth
!Age status
|-
| Shadow || rowspan="7" | Male || {{birth date and age|1985|4|9}} || rowspan="15" | {{flagicon|USA}} United States || rowspan="15" | {{flagicon|JPN}} Japan || rowspan="15" | {{flagicon|USA}} United States<br>{{flagicon|JPN}} Japan || rowspan="15" | Japanese-American || rowspan="15" | {{flagicon|USA}} United States || rowspan="15" | {{flagicon|JPN}} Japan || rowspan="4" | 6’ 3” || 200+ million in the United States and Japan || rowspan="15" colspan="2" | {{start date and age|2022|4|13}} || rowspan="15" | Appearing indefinitely<br>Continuing to appear for many years in obedience to the announcement on June 8, 2022 || USD$6.4 billion || rowspan="15" | Getting older on later days or in later periods, months or years
|-
| Silver || {{birth date and age|1987|4|9}} || 190+ million in the United States and Japan || USD$6.2 billion
|-
| Mighty || {{birth date and age|1985|4|13}} || 180+ million in the United States and Japan || USD$6 billion
|-
| Sonic || {{birth date and age|1986|4|13}} || 170+ million in the United States and Japan || USD$5.8 billion
|-
| Ray || {{birth date and age|1992|4|11}} || rowspan="3" | 6’ 4” || 160+ million in the United States and Japan || USD$5.6 billion
|-
| Tails || {{birth date and age|1993|4|11}} || 150+ million in the United States and Japan || USD$5.4 billion
|-
| Knuckles || {{birth date and age|1986|4|13}} || 140+ million in the United States and Japan || USD$5.2 billion
|-
| Amy || rowspan="8" | Female || {{birth date and age|1990|4|13}} || rowspan="2" | 5’ 1” || 205+ million in the United States and Japan || USD$6.5 billion
|-
| Tangle || {{birth date and age|1987|4|13}} || 195+ million in the United States and Japan || USD$6.3 billion
|-
| Rouge || {{birth date and age|1984|4|11}} || rowspan="2" | 5’ || 185+ million in the United States and Japan || USD$6.1 billion
|-
| Blaze || {{birth date and age|1987|4|11}} || 175+ million in the United States and Japan || USD$5.9 billion
|-
| Sally || {{birth date and age|1986|4|9}} || rowspan="2" | 5’ 1” || 165+ million in the United States and Japan || USD$5.7 billion
|-
| Marine || {{birth date and age|1994|4|9}} || 155+ million in the United States and Japan || USD$5.5 billion
|-
| Mina || {{birth date and age|1985|4|9}} || rowspan="2" | 5’ || 145+ million in the United States and Japan || USD$5.3 billion
|-
| Tikal || {{birth date and age|1987|4|9}} || 135+ million in the United States and Japan || USD$5.1 billion
|}

== Ages of Japanese-American stars/personalities in previous, current and future years ==
=== Table focusing on ages of Japanese-American stars/personalities in previous, current and future years ===
{| class="wikitable sortable"
!Star/personality name
!Age in mid-2022
!Age in mid-2023
!Age in mid-2024
!Age in mid-2025
!Age in mid-2026
!Age in mid-2027
!Age in mid-2028
!Age in mid-2029
!Age in mid-2030
!Age in mid-2031
!Age in mid-2032
!Age in mid-2033
!Age in mid-2034
!Age in mid-2035
!Age in mid-2036
!Age in mid-2037
!Age in mid-2038
!Age in mid-2039
!Age in mid-2040
!Age in mid-2041
!Age in mid-2042
!Age in mid-2043
!Age in mid-2044
!Age in mid-2045
!Age in mid-2046
|-
| Shadow || 37 || 38 || 39 || 40 || 41 || 42 || 43 || 44 || 45 || 46 || 47 || 48 || 49 || 50 || 51 || 52 || 53 || 54 || 55 || 56 || 57 || 58 || 59 || 60 || 61
|-
| Silver || 35 || 36 || 37 || 38 || 39 || 40 || 41 || 42 || 43 || 44 || 45 || 46 || 47 || 48 || 49 || 50 || 51 || 52 || 53 || 54 || 55 || 56 || 57 || 58 || 59
|-
| Mighty || 37 || 38 || 39 || 40 || 41 || 42 || 43 || 44 || 45 || 46 || 47 || 48 || 49 || 50 || 51 || 52 || 53 || 54 || 55 || 56 || 57 || 58 || 59 || 60 || 61
|-
| Sonic || 36 || 37 || 38 || 39 || 40 || 41 || 42 || 43 || 44 || 45 || 46 || 47 || 48 || 49 || 50 || 51 || 52 || 53 || 54 || 55 || 56 || 57 || 58 || 59 || 60
|-
| Ray || 30 || 31 || 32 || 33 || 34 || 35 || 36 || 37 || 38 || 39 || 40 || 41 || 42 || 43 || 44 || 45 || 46 || 47 || 48 || 49 || 50 || 51 || 52 || 53 || 54
|-
| Tails || 29 || 30 || 31 || 32 || 33 || 34 || 35 || 36 || 37 || 38 || 39 || 40 || 41 || 42 || 43 || 44 || 45 || 46 || 47 || 48 || 49 || 50 || 51 || 52 || 53
|-
| Knuckles || 36 || 37 || 38 || 39 || 40 || 41 || 42 || 43 || 44 || 45 || 46 || 47 || 48 || 49 || 50 || 51 || 52 || 53 || 54 || 55 || 56 || 57 || 58 || 59 || 60
|-
| Amy || 32 || 33 || 34 || 35 || 36 || 37 || 38 || 39 || 40 || 41 || 42 || 43 || 44 || 45 || 46 || 47 || 48 || 49 || 50 || 51 || 52 || 53 || 54 || 55 || 56
|-
| Tangle || 35 || 36 || 37 || 38 || 39 || 40 || 41 || 42 || 43 || 44 || 45 || 46 || 47 || 48 || 49 || 50 || 51 || 52 || 53 || 54 || 55 || 56 || 57 || 58 || 59
|-
| Rouge || 38 || 39 || 40 || 41 || 42 || 43 || 44 || 45 || 46 || 47 || 48 || 49 || 50 || 51 || 52 || 53 || 54 || 55 || 56 || 57 || 58 || 59 || 60 || 61 || 62
|-
| Blaze || 35 || 36 || 37 || 38 || 39 || 40 || 41 || 42 || 43 || 44 || 45 || 46 || 47 || 48 || 49 || 50 || 51 || 52 || 53 || 54 || 55 || 56 || 57 || 58 || 59
|-
| Sally || 36 || 37 || 38 || 39 || 40 || 41 || 42 || 43 || 44 || 45 || 46 || 47 || 48 || 49 || 50 || 51 || 52 || 53 || 54 || 55 || 56 || 57 || 58 || 59 || 60
|-
| Marine || 28 || 29 || 30 || 31 || 32 || 33 || 34 || 35 || 36 || 37 || 38 || 39 || 40 || 41 || 42 || 43 || 44 || 45 || 46 || 47 || 48 || 49 || 50 || 51 || 52
|-
| Mina || 37 || 38 || 39 || 40 || 41 || 42 || 43 || 44 || 45 || 46 || 47 || 48 || 49 || 50 || 51 || 52 || 53 || 54 || 55 || 56 || 57 || 58 || 59 || 60 || 61
|-
| Tikal || 35 || 36 || 37 || 38 || 39 || 40 || 41 || 42 || 43 || 44 || 45 || 46 || 47 || 48 || 49 || 50 || 51 || 52 || 53 || 54 || 55 || 56 || 57 || 58 || 59
|}

== Car motion (in yards) ==
American and Japanese cars containing Shadow (age 37), Silver (age 35), Mighty (age 37), Sonic (age 36), Ray (age 30), Tails (age 29), Knuckles (age 36), Amy (age 32), Tangle (age 35), Rouge (age 38), Blaze (age 35), Sally (age 36), Marine (age 28), Mina (age 37) and Tikal (age 35) as their famous drivers traveled {{sfrac|–1,125''t'' – 225 + 25(10''t'' + 3){{sqrt|30''t'' + 9}}|74.0664}} yd in first 36 seconds as their displacement in multiple live events held in multiple American and Japanese cities/urban areas in May/June 2022. What was their velocity? And what was their acceleration?

Given, ''s'' = {{sfrac|–1,125''t'' – 225 + 25(10''t'' + 3){{sqrt|30''t'' + 9}}|74.0664}} yd for 0 <= ''t'' <= 36 s

''v'' = {{sfrac|d''s''|d''t''}}

''v'' = {{sfrac|–375+125{{sqrt|30''t'' + 9}}|24.6888}} yd/s

American and Japanese cars containing Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal as their famous drivers traveled at {{sfrac|–375+125{{sqrt|30''t'' + 9}}|24.6888}} yd/s in first 36 seconds in multiple live events held in multiple American and Japanese cities/urban areas in May/June 2022, i.e. their velocity increased at a decreasing rate.

''a'' = {{sfrac|d''v''|d''t''}}; {{sfrac|d²''s''|d''t''²}}

''a'' = {{sfrac|625{{sqrt|30''t'' + 9}}|24.6888(10''t'' + 3)}} yd/s²

American and Japanese cars containing Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal as their famous drivers accelerated at {{sfrac|625{{sqrt|30''t'' + 9}}|24.6888(10''t'' + 3)}} yd/s² in first 36 seconds in multiple live events held in multiple American and Japanese cities/urban areas in May/June 2022, i.e. their acceleration decreased.

== Car motion (in feet) ==
American and Japanese cars containing Shadow (age 37), Silver (age 35), Mighty (age 37), Sonic (age 36), Ray (age 30), Tails (age 29), Knuckles (age 36), Amy (age 32), Tangle (age 35), Rouge (age 38), Blaze (age 35), Sally (age 36), Marine (age 28), Mina (age 37) and Tikal (age 35) as their famous drivers traveled {{sfrac|–1,125''t'' – 225 + 25(10''t'' + 3){{sqrt|30''t'' + 9}}|24.6888}} ft in first 36 seconds as their displacement in multiple live events held in multiple American and Japanese cities/urban areas in May/June 2022. What was their velocity? And what was their acceleration?

Given, ''s'' = {{sfrac|–1,125''t'' – 225 + 25(10''t'' + 3){{sqrt|30''t'' + 9}}|24.6888}} ft for 0 <= ''t'' <= 36 s

''v'' = {{sfrac|d''s''|d''t''}}

''v'' = {{sfrac|–375+125{{sqrt|30''t'' + 9}}|8.2296}} ft/s

American and Japanese cars containing Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal as their famous drivers traveled at {{sfrac|–375+125{{sqrt|30''t'' + 9}}|8.2296}} ft/s in first 36 seconds in multiple live events held in multiple American and Japanese cities/urban areas in May/June 2022, i.e. their velocity increased at a decreasing rate.

''a'' = {{sfrac|d''v''|d''t''}}; {{sfrac|d²''s''|d''t''²}}

''a'' = {{sfrac|625{{sqrt|30''t'' + 9}}|8.2296(10''t'' + 3)}} ft/s²

American and Japanese cars containing Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal as their famous drivers accelerated at {{sfrac|625{{sqrt|30''t'' + 9}}|8.2296(10''t'' + 3)}} ft/s² in first 36 seconds in multiple live events held in multiple American and Japanese cities/urban areas in May/June 2022, i.e. their acceleration decreased.

== Motion of American and Japanese cars in first 36 seconds (yards) ==
===Table focusing on the motion of American and Japanese cars containing Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal as their famous drivers in first 36 seconds in multiple American and Japanese cities/urban areas in May/June 2022, where ''s'' = {{sfrac|–1,125''t'' – 225 + 25(10''t'' + 3){{sqrt|30''t'' + 9}}|74.0664}} yd, ''v'' = {{sfrac|–375+125{{sqrt|30''t'' + 9}}|24.6888}} yd/s and ''a'' = {{sfrac|625{{sqrt|30''t'' + 9}}|24.6888(10''t'' + 3)}} yd/s²===
{|class="wikitable sortable"
!Time (''t'', in seconds)!!Displacement (''s'', in yards)!!Velocity (''v'', in yards per second)!!Acceleration (''a'', in yards per second squared)
|-
|colspan="3"|0||25.3
|-
|0.9||7.6||15.2||12.7
|-
|2.4||42.5||30.4||8.4
|-
|4.5||123||45.6||6.3
|-
|7.2||267.3||60.8||5.1
|-
|10.5||493.6||75.9||4.2
|-
|14.4||820.2||91.1||3.6
|-
|18.9||1,265||106.3||3.2
|-
|24||1,847||121.5||2.8
|-
|29.7||2,584||136.7||2.5
|-
|36||3,493||151.9||2.3
|}

== Motion of American and Japanese cars in first 36 seconds (feet) ==
===Table focusing on the motion of American and Japanese cars containing Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal as their famous drivers in first 36 seconds in multiple American and Japanese cities/urban areas in May/June 2022, where ''s'' = {{sfrac|–1,125''t'' – 225 + 25(10''t'' + 3){{sqrt|30''t'' + 9}}|24.6888}} ft, ''v'' = {{sfrac|–375+125{{sqrt|30''t'' + 9}}|8.2296}} ft/s and ''a'' = {{sfrac|625{{sqrt|30''t'' + 9}}|8.2296(10''t'' + 3)}} ft/s²===
{|class="wikitable sortable"
!Time (''t'', in seconds)!!Displacement (''s'', in feet)!!Velocity (''v'', in feet per second)!!Acceleration (''a'', in feet per second squared)
|-
|colspan="3"|0||75.9
|-
|0.9||22.8||45.6||38
|-
|2.4||127.6||91.1||25.3
|-
|4.5||369.1||136.7||19
|-
|7.2||802||182.3||15.2
|-
|10.5||1,481||227.8||12.7
|-
|14.4||2,461||273.4||10.8
|-
|18.9||3,796||319||9.5
|-
|24||5,541||364.5||8.4
|-
|29.7||7,751||410.1||7.6
|-
|36||10,480||455.7||6.9
|}

== Multiple racing car crashes on the racetrack close to Apple Park on May 14, 2022, only minor injuries triggered ==
On May 14, 2022, racing cars containing Shadow (age 37), Silver (age 35), Mighty (age 37), Sonic (age 36), Ray (age 30), Tails (age 29), Knuckles (age 36), Amy (age 32), Tangle (age 35), Rouge (age 38), Blaze (age 35), Sally (age 36), Marine (age 28), Mina (age 37) and Tikal (age 35) and 25 other Japanese-American racing stars as their famous drivers crashed at speeds ranging between 80 mph and 120 mph on the racetrack close to Apple Park. Two racing cars containing Shadow and Silver crashed into each other. Two racing cars containing Mighty and Sonic crashed into each other. Two racing cars containing Ray and Tails crashed into each other. Two racing cars containing Mina and Tikal crashed into each other. Two racing cars containing Rouge and Blaze crashed into each other. Two racing cars containing Sally and Marine crashed into each other. 20 other racing cars containing 20 other Japanese-American stars crashed into each other. Eight other racing cars containing Knuckles, Amy and Tangle and five other Japanese-American stars crashed.

Luckily, Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal and 25 other Japanese-American stars were not seriously injured after being involved in multiple racing car crashes on the racetrack close to Apple Park. Shadow, Silver, Mighty, Sonic, Ray, Tails, Mina, Tikal, Rouge, Blaze, Sally and Marine and 20 other Japanese-American racing stars escaped after the impact by ceasing to be buckled, i.e. removing their seat belts. Emergency crew members were called directly to the racetrack close to Apple Park. Knuckles, Amy and Tangle and five other Japanese-American racing stars were trapped inside for some time as they remained buckled after the impact, i.e. they kept having seat belts worn. Shadow, Silver, Mighty, Sonic, Ray, Tails, Mina, Tikal, Rouge, Blaze, Sally and Marine and 20 other Japanese-American racing stars were outside damaged racing cars for some time before being moved directly to ambulances. Knuckles, Amy and Tangle and five other Japanese-American racing stars were inside damaged racing cars for some time before being moved directly to ambulances as well.

Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal and 25 other Japanese-American stars were sent directly to hospitals close to Apple Park for treatment after multiple racing car crashes on the racetrack close to Apple Park, where they were listed in good condition. Though not seriously injured after being involved in multiple racing car crashes close to Apple Park, they were in hospitals close to Apple Park for only one day while in good condition. A day later, on May 15, 2022, Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal and 25 other Japanese-American stars finally left hospitals the day after multiple racing car crashes on the racetrack close to Apple Park. On that day, the racetrack close to Apple Park was finally cleaned up. Damaged racing cars were finally removed on that day.

== Acceleration times for very high-performance cars ==
===Table focusing on acceleration times for very high-performance American and Japanese cars containing Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal as their famous drivers, though designed in May 2022===
{|class="wikitable sortable"
!Acceleration type!!Time required (in seconds)
|-
|0-31 mph||0.9
|-
|0-62 mph||2.4
|-
|0-93 mph||4.5
|-
|0-124 mph||7.2
|-
|0-155 mph||10.5
|-
|0-186 mph||14.4
|-
|0-217 mph||18.9
|-
|0-249 mph||24
|-
|0-280 mph||29.7
|-
|0-311 mph||36
|-
|31-62 mph||1.5
|-
|31-93 mph||3.6
|-
|31-124 mph||6.3
|-
|31-155 mph||9.6
|-
|31-186 mph||13.5
|-
|31-217 mph||18
|-
|31-249 mph||23.1
|-
|31-280 mph||28.8
|-
|31-311 mph||35.1
|-
|62-93 mph||2.1
|-
|62-124 mph||4.8
|-
|62-155 mph||8.1
|-
|62-186 mph||12
|-
|62-217 mph||16.5
|-
|62-249 mph||21.6
|-
|62-280 mph||27.3
|-
|62-311 mph||33.6
|-
|93-124 mph||2.7
|-
|93-155 mph||6
|-
|93-186 mph||9.9
|-
|93-217 mph||14.4
|-
|93-249 mph||19.5
|-
|93-280 mph||25.2
|-
|93-311 mph||31.5
|-
|124-155 mph||3.3
|-
|124-186 mph||7.2
|-
|124-217 mph||11.7
|-
|124-249 mph||16.8
|-
|124-280 mph||22.5
|-
|124-311 mph||28.8
|-
|155-186 mph||3.9
|-
|155-217 mph||8.4
|-
|155-249 mph||13.5
|-
|155-280 mph||19.2
|-
|155-311 mph||25.5
|-
|186-217 mph||4.5
|-
|186-249 mph||9.6
|-
|186-280 mph||15.3
|-
|186-311 mph||21.6
|-
|217-249 mph||5.1
|-
|217-280 mph||10.8
|-
|217-311 mph||17.1
|-
|249-280 mph||5.7
|-
|249-311 mph||12
|-
|280-311 mph||6.3
|}
===Table focusing on speeds attained by American and Japanese cars containing Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal as their famous drivers, though designed in May 2022===
{|class="wikitable sortable
!Speed type!!Attained in
|-
|31 mph||0.9 second
|-
|62 mph||2.4 seconds
|-
|93 mph||4.5 seconds
|-
|124 mph||7.2 seconds
|-
|155 mph||10.5 seconds
|-
|186 mph||14.4 seconds
|-
|217 mph||18.9 seconds
|-
|249 mph||24 seconds
|-
|280 mph||29.7 seconds
|-
|311 mph||36 seconds as the top speed
|}
===Table focusing on speeds attained by American and Japanese cars designed in May 2022 to accelerate to 62 mph im 2.4 seconds, travel at speeds up to 311 mph and be rated 2,000+ BHP by their power, though containing Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal as their famous drivers===
{|class="wikitable sortable"
!Acceleration (0-62 mph)!!Top speed!!Power
|-
|2.4 seconds||311 mph||2,000+ BHP
|}
===Table focusing on the United States-Japan Super Car Collection===
{|class="wikitable sortable"
!Collection!!Created!!Description!!Famous driver #1!!Famous driver #2!!Famous driver #3!!Famous driver #4!!Famous driver #5!!Famous driver #6!!Famous driver #7!!Famous driver #8!!Famous driver #9!!Famous driver #10!!Famous driver #11!!Famous driver #12!!Famous driver #13!!Famous driver #14!!Famous driver #15
|-
|United States-Japan Super Car Collection||{{start date and age|2022|5}}<br>{{start date and age|2022|6}}||Collection containing or featuring very high-performance American and Japanese cars able to attain 31 mph in 0.9 second, 62 mph in 2.4 seconds, 93 mph in 4.5 seconds, 124 mph in 7.2 seconds, 155 mph in 10.5 seconds, 186 mph in 14.4 seconds, 217 mph in 18.9 seconds, 249 mph in 24 seconds, 280 mph in 29.7 seconds and 311 mph in 36 seconds as their top speed and rated 2,000+ BHP by their power||Shadow||Silver||Mighty||Sonic||Ray||Tails||Knuckles||Amy||Tangle||Rouge||Blaze||Sally||Marine||Mina||Tikal
|}

== Companies, car companies and cities/urban areas by country ==
===Table focusing on cities/urban areas===
{|class="wikitable sortable"
!City/urban area!!Country!!Famous explorer #1!!Famous explorer #2!!Famous explorer #3!!Famous explorer #4!!Famous explorer #5!!Famous explorer #6!!Famous explorer #7!!Famous explorer #8!!Famous explorer #9!!Famous explorer #10!!Famous explorer #11!!Famous explorer #12!!Famous explorer #13!!Famous explorer #14!!Famous explorer #15
|-
|New York City||{{flagicon|USA}} United States||Shadow (since May 2022)||Silver (since May 2022)||Mighty (since May 2022)||Sonic (since May 2022)||Ray (since May 2022)||Tails (since May 2022)||Knuckles (since May 2022)||Amy (since May 2022)||Tangle (since May 2022)||Rouge (since May 2022)||Blaze (since May 2022)||Sally (since May 2022)||Marine (since May 2022)||Mina (since May 2022)||Tikal (since May 2022)
|-
|Tokyo||{{flagicon|JPN}} Japan||Shadow (since June 2022)||Silver (since June 2022)||Mighty (since June 2022)||Sonic (since June 2022)||Ray (since June 2022)||Tails (since June 2022)||Knuckles (since June 2022)||Amy (since June 2022)||Tangle (since June 2022)||Rouge (since June 2022)||Blaze (since June 2022)||Sally (since June 2022)||Marine (since June 2022)||Mina (since June 2022)||Tikal (since June 2022)
|-
|Los Angeles||{{flagicon|USA}} United States||Shadow (since May 2022)||Silver (since May 2022)||Mighty (since May 2022)||Sonic (since May 2022)||Ray (since May 2022)||Tails (since May 2022)||Knuckles (since May 2022)||Amy (since May 2022)||Tangle (since May 2022)||Rouge (since May 2022)||Blaze (since May 2022)||Sally (since May 2022)||Marine (since May 2022)||Mina (since May 2022)||Tikal (since May 2022)
|-
|Yokohama||{{flagicon|JPN}} Japan||Shadow (since June 2022)||Silver (since June 2022)||Mighty (since June 2022)||Sonic (since June 2022)||Ray (since June 2022)||Tails (since June 2022)||Knuckles (since June 2022)||Amy (since June 2022)||Tangle (since June 2022)||Rouge (since June 2022)||Blaze (since June 2022)||Sally (since June 2022)||Marine (since June 2022)||Mina (since June 2022)||Tikal (since June 2022)
|-
|Chicago||{{flagicon|USA}} United States||Shadow (since May 2022)||Silver (since May 2022)||Mighty (since May 2022)||Sonic (since May 2022)||Ray (since May 2022)||Tails (since May 2022)||Knuckles (since May 2022)||Amy (since May 2022)||Tangle (since May 2022)||Rouge (since May 2022)||Blaze (since May 2022)||Sally (since May 2022)||Marine (since May 2022)||Mina (since May 2022)||Tikal (since May 2022)
|-
|Osaka||{{flagicon|JPN}} Japan||Shadow (since June 2022)||Silver (since June 2022)||Mighty (since June 2022)||Sonic (since June 2022)||Ray (since June 2022)||Tails (since June 2022)||Knuckles (since June 2022)||Amy (since June 2022)||Tangle (since June 2022)||Rouge (since June 2022)||Blaze (since June 2022)||Sally (since June 2022)||Marine (since June 2022)||Mina (since June 2022)||Tikal (since June 2022)
|-
|Houston||{{flagicon|USA}} United States||Shadow (since May 2022)||Silver (since May 2022)||Mighty (since May 2022)||Sonic (since May 2022)||Ray (since May 2022)||Tails (since May 2022)||Knuckles (since May 2022)||Amy (since May 2022)||Tangle (since May 2022)||Rouge (since May 2022)||Blaze (since May 2022)||Sally (since May 2022)||Marine (since May 2022)||Mina (since May 2022)||Tikal (since May 2022)
|-
|Nagoya||{{flagicon|JPN}} Japan||Shadow (since June 2022)||Silver (since June 2022)||Mighty (since June 2022)||Sonic (since June 2022)||Ray (since June 2022)||Tails (since June 2022)||Knuckles (since June 2022)||Amy (since June 2022)||Tangle (since June 2022)||Rouge (since June 2022)||Blaze (since June 2022)||Sally (since June 2022)||Marine (since June 2022)||Mina (since June 2022)||Tikal (since June 2022)
|-
|Washington, D.C.||{{flagicon|USA}} United States||Shadow (since May 2022)||Silver (since May 2022)||Mighty (since May 2022)||Sonic (since May 2022)||Ray (since May 2022)||Tails (since May 2022)||Knuckles (since May 2022)||Amy (since May 2022)||Tangle (since May 2022)||Rouge (since May 2022)||Blaze (since May 2022)||Sally (since May 2022)||Marine (since May 2022)||Mina (since May 2022)||Tikal (since May 2022)
|-
|Chiba||{{flagicon|JPN}} Japan||Shadow (since June 2022)||Silver (since June 2022)||Mighty (since June 2022)||Sonic (since June 2022)||Ray (since June 2022)||Tails (since June 2022)||Knuckles (since June 2022)||Amy (since June 2022)||Tangle (since June 2022)||Rouge (since June 2022)||Blaze (since June 2022)||Sally (since June 2022)||Marine (since June 2022)||Mina (since June 2022)||Tikal (since June 2022)
|}
===Table focusing on companies===
{|class="wikitable sortable"
!Company!!Country!!Star #1!!Star #2!!Star #3!!Star #4!!Star #5!!Star #6!!Star #7!!Star #8!!Star #9!!Star #10!!Star #11!!Star #12!!Star #13!!Star #14!!Star #15
|-
|Apple Inc.||{{flagicon|USA}} United States||rowspan="4"|Shadow (since May 2022)||rowspan="4"|Silver (since May 2022)||rowspan="4"|Mighty (since May 2022)||rowspan="4"|Sonic (since May 2022)||rowspan="4"|Ray (since May 2022)||rowspan="4"|Tails (since May 2022)||rowspan="4"|Knuckles (since May 2022)||rowspan="4"|Amy (since May 2022)||rowspan="4"|Tangle (since May 2022)||rowspan="4"|Rouge (since May 2022)||rowspan="4"|Blaze (since May 2022)||rowspan="4"|Sally (since May 2022)||rowspan="4"|Marine (since May 2022)||rowspan="4"|Mina (since May 2022)||rowspan="4"|Tikal (since May 2022)
|-
|Capcom||{{flagicon|JPN}} Japan
|-
|Costco||{{flagicon|USA}} United States
|-
|Vaio||{{flagicon|JPN}} Japan
|}
===Table focusing on car companies===
{|class="wikitable sortable"
!Car company!!Country!!Star #1!!Star #2!!Star #3!!Star #4!!Star #5!!Star #6!!Star #7!!Star #8!!Star #9!!Star #10!!Star #11!!Star #12!!Star #13!!Star #14!!Star #15
|-
|Cadillac||rowspan="4"|{{flagicon|USA}} United States||rowspan="4"|Shadow (since May 2022)||rowspan="4"|Silver (since May 2022)||rowspan="4"|Mighty (since May 2022)||rowspan="4"|Sonic (since May 2022)||rowspan="4"|Ray (since May 2022)||rowspan="4"|Tails (since May 2022)||rowspan="4"|Knuckles (since May 2022)||rowspan="4"|Amy (since May 2022)||rowspan="4"|Tangle (since May 2022)||rowspan="4"|Rouge (since May 2022)||rowspan="4"|Blaze (since May 2022)||rowspan="4"|Sally (since May 2022)||rowspan="4"|Marine (since May 2022)||rowspan="4"|Mina (since May 2022)||rowspan="4"|Tikal (since May 2022)
|-
|Chevrolet
|-
|Dodge
|-
|Ford
|-
|Honda||rowspan="4"|{{flagicon|JPN}} Japan||rowspan="4"|Shadow (since June 2022)||rowspan="4"|Silver (since June 2022)||rowspan="4"|Mighty (since June 2022)||rowspan="4"|Sonic (since June 2022)||rowspan="4"|Ray (since June 2022)||rowspan="4"|Tails (since June 2022)||rowspan="4"|Knuckles (since June 2022)||rowspan="4"|Amy (since June 2022)||rowspan="4"|Tangle (since June 2022)||rowspan="4"|Rouge (since June 2022)||rowspan="4"|Blaze (since June 2022)||rowspan="4"|Sally (since June 2022)||rowspan="4"|Marine (since June 2022)||rowspan="4"|Mina (since June 2022)||rowspan="4"|Tikal (since June 2022)
|-
|Mitsubishi
|-
|Nissan
|-
|Toyota
|}

== Tables containing information focusing on quadratic functions ==
===Table focusing on ''y'' = 4''x''² – 16''x'' + 15===
{|class="wikitable sortable"
!''x''!!''y''
|-
|{{sfrac|3|2}}||0
|-
|2||–1
|-
|{{sfrac|5|2}}||0
|}
===Table focusing on ''y'' = 15''x''² – 16''x'' + 4===
{|class="wikitable sortable"
!''x''!!''y''
|-
|{{sfrac|2|5}}||0
|-
|{{sfrac|8|15}}||–{{sfrac|4|15}}
|-
|{{sfrac|2|3}}||0
|}
===Table focusing on ''y'' = 6''x''² – 19''x'' + 15===
{|class="wikitable sortable"
!''x''!!''y''
|-
|{{sfrac|3|2}}||0
|-
|{{sfrac|19|12}}||–{{sfrac|1|24}}
|-
|{{sfrac|5|3}}||0
|}
===Table focusing on ''y'' = 15''x''² – 19''x'' + 6===
{|class="wikitable sortable"
!''x''!!''y''
|-
|{{sfrac|3|5}}||0
|-
|{{sfrac|19|30}}||–{{sfrac|1|60}}
|-
|{{sfrac|2|3}}||0
|}
===Table focusing on ''y'' = 6''x''² – 25''x'' + 25===
{|class="wikitable sortable"
!''x''!!''y''
|-
|{{sfrac|5|3}}||0
|-
|{{sfrac|25|12}}||–{{sfrac|25|24}}
|-
|{{sfrac|5|2}}||0
|}
===Table focusing on ''y'' = 25''x''² – 25''x'' + 6===
{|class="wikitable sortable"
!''x''!!''y''
|-
|{{sfrac|2|5}}||0
|-
|{{sfrac|1|2}}||–{{sfrac|1|4}}
|-
|{{sfrac|3|5}}||0
|}
===Table focusing on ''y'' = 6''x''² – 19''x'' + 10===
{|class="wikitable sortable"
!''x''!!''y''
|-
|{{sfrac|2|3}}||0
|-
|{{sfrac|19|12}}||–{{sfrac|121|24}}
|-
|{{sfrac|5|2}}||0
|}
===Table focusing on ''y'' = 10''x''² – 19''x'' + 6===
{|class="wikitable sortable"
!''x''!!''y''
|-
|{{sfrac|2|5}}||0
|-
|{{sfrac|19|20}}||–{{sfrac|121|40}}
|-
|{{sfrac|3|2}}||0
|}
===Table focusing on ''y'' = 9''x''² – 21''x'' + 10===
{|class="wikitable sortable"
!''x''!!''y''
|-
|{{sfrac|2|3}}||0
|-
|{{sfrac|7|6}}||–{{sfrac|9|4}}
|-
|{{sfrac|5|3}}||0
|}
===Table focusing on ''y'' = 10''x''² – 21''x'' + 9===
{|class="wikitable sortable"
!''x''!!''y''
|-
|{{sfrac|3|5}}||0
|-
|{{sfrac|21|20}}||–{{sfrac|81|40}}
|-
|{{sfrac|3|2}}||0
|}
===Table focusing on ''y'' = 10''x''² – 31''x'' + 15===
{|class="wikitable sortable"
!''x''!!''y''
|-
|{{sfrac|3|5}}||0
|-
|{{sfrac|31|20}}||–{{sfrac|361|40}}
|-
|{{sfrac|5|2}}||0
|}
===Table focusing on ''y'' = 15''x''² – 31''x'' + 10===
{|class="wikitable sortable"
!''x''!!''y''
|-
|{{sfrac|2|5}}||0
|-
|{{sfrac|31|30}}||–{{sfrac|361|60}}
|-
|{{sfrac|5|3}}||0
|}
===Table focusing on ''y'' = 6''x''² – 13''x'' + 6===
{|class="wikitable sortable"
!''x''!!''y''
|-
|{{sfrac|2|3}}||0
|-
|{{sfrac|13|12}}||–{{sfrac|25|24}}
|-
|{{sfrac|3|2}}||0
|}
===Table focusing on ''y'' = 10''x''² – 29''x'' + 10===
{|class="wikitable sortable"
!''x''!!''y''
|-
|{{sfrac|2|5}}||0
|-
|{{sfrac|29|20}}||–{{sfrac|441|40}}
|-
|{{sfrac|5|2}}||0
|}
===Table focusing on ''y'' = 15''x''² – 34''x'' + 15===
{|class="wikitable sortable"
!''x''!!''y''
|-
|{{sfrac|3|5}}||0
|-
|{{sfrac|17|15}}||–{{sfrac|64|15}}
|-
|{{sfrac|5|3}}||0
|}

== Tables containing information focusing on quadratic expressions and their forms, coefficients and minimum values ==
===Table focusing on different forms of quadratic expressions===
{|class="wikitable sortable"
!Quadratic expression!!Vertex form!!Factorized form
|-
|4''x''² – 16''x'' + 15||(2''x'' – 4)² – 1||(2''x'' – 3)(2''x'' – 5)
|-
|15''x''² – 16''x'' + 4||{{sfrac|(15''x'' – 8)² – 4|15}}||(5''x'' – 2)(3''x'' – 2)
|-
|6''x''² – 19''x'' + 15||{{sfrac|(12''x'' – 19)² – 1|24}}||(2''x'' – 3)(3''x'' – 5)
|-
|15''x''² – 19''x'' + 6||{{sfrac|(30''x'' – 19)² – 1|60}}||(5''x'' – 3)(3''x'' – 2)
|-
|6''x''² – 25''x'' + 25||{{sfrac|(12''x'' – 25)² – 25|24}}||(3''x'' – 5)(2''x'' – 5)
|-
|25''x''² – 25''x'' + 6||{{sfrac|(10''x'' – 5)² – 1|4}}||(5''x'' – 2)(5''x'' – 3)
|-
|6''x''² – 19''x'' + 10||{{sfrac|(12''x'' – 19)² – 121|24}}||(3''x'' – 2)(2''x'' – 5)
|-
|10''x''² – 19''x'' + 6||{{sfrac|(20''x'' – 19)² – 121|40}}||(5''x'' – 2)(2''x'' – 3)
|-
|9''x''² – 21''x'' + 10||{{sfrac|(6''x'' – 7)² – 9|4}}||(3''x'' – 2)(3''x'' – 5)
|-
|10''x''² – 21''x'' + 9||{{sfrac|(20''x'' – 21)² – 81|40}}||(5''x'' – 3)(2''x'' – 3)
|-
|10''x''² – 31''x'' + 15||{{sfrac|(20''x'' – 31)² – 361|40}}||(5''x'' – 3)(2''x'' – 5)
|-
|15''x''² – 31''x'' + 10||{{sfrac|(30''x'' – 31)² – 361|60}}||(5''x'' – 2)(3''x'' – 5)
|-
|6''x''² – 13''x'' + 6||{{sfrac|(12''x'' – 13)² – 25|24}}||(3''x'' – 2)(2''x'' – 3)
|-
|10''x''² – 29''x'' + 10||{{sfrac|(20''x'' – 29)² – 441|40}}||(5''x'' – 2)(2''x'' – 5)
|-
|15''x''² – 34''x'' + 15||{{sfrac|(15''x'' – 17)² – 64|15}}||(5''x'' – 3)(3''x'' – 5)
|}
===Table focusing on coefficients of quadratic expressions===
{|class="wikitable sortable"
!Quadratic expression!!''a'' (''x''²-coefficient)!!''b'' (''x''-coefficient)!!''c'' (constant coefficient)
|-
|4''x''² – 16''x'' + 15||4||rowspan="2"|–16||15
|-
|15''x''² – 16''x'' + 4||15||4
|-
|6''x''² – 19''x'' + 15||6||rowspan="2"|–19||15
|-
|15''x''² – 19''x'' + 6||15||6
|-
|6''x''² – 25''x'' + 25||6||rowspan="2"|–25||25
|-
|25''x''² – 25''x'' + 6||25||6
|-
|6''x''² – 19''x'' + 10||6||rowspan="2"|–19||10
|-
|10''x''² – 19''x'' + 6||10||6
|-
|9''x''² – 21''x'' + 10||9||rowspan="2"|–21||10
|-
|10''x''² – 21''x'' + 9||rowspan="2"|10||9
|-
|10''x''² – 31''x'' + 15||rowspan="2"|–31||15
|-
|15''x''² – 31''x'' + 10||15||10
|-
|6''x''² – 13''x'' + 6||6||–13||6
|-
|10''x''² – 29''x'' + 10||10||–29||10
|-
|15''x''² – 34''x'' + 15||15||–34||15
|}
===Table focusing on minimum values of quadratic expressions===
{|class="wikitable sortable"
!Quadratic expression!!Minimum value
|-
|4''x''² – 16''x'' + 15||–1
|-
|15''x''² – 16''x'' + 4||–{{sfrac|4|15}}
|-
|6''x''² – 19''x'' + 15||–{{sfrac|1|24}}
|-
|15''x''² – 19''x'' + 6||–{{sfrac|1|60}}
|-
|6''x''² – 25''x'' + 25||–{{sfrac|25|24}}
|-
|25''x''² – 25''x'' + 6||–{{sfrac|1|4}}
|-
|6''x''² – 19''x'' + 10||–{{sfrac|121|24}}
|-
|10''x''² – 19''x'' + 6||–{{sfrac|121|40}}
|-
|9''x''² – 21''x'' + 10||–{{sfrac|9|4}}
|-
|10''x''² – 21''x'' + 9||–{{sfrac|81|40}}
|-
|10''x''² – 31''x'' + 15||–{{sfrac|361|40}}
|-
|15''x''² – 31''x'' + 10||–{{sfrac|361|60}}
|-
|6''x''² – 13''x'' + 6||–{{sfrac|25|24}}
|-
|10''x''² – 29''x'' + 10||–{{sfrac|441|40}}
|-
|15''x''² – 34''x'' + 15||–{{sfrac|64|15}}
|}
===Table focusing on the ability of quadratic expressions to be factorized and methods for checking/using them===
{|class="wikitable sortable"
!Quadratic expression!!Able to be factorized!!Checking/usage date!!Checked/used by
|-
|4''x''² – 16''x'' + 15||rowspan="15" {{Yes}}||rowspan="15"|{{start date and age|2022|6|23}}<br>{{start date and age|2022|6|24}}<br>{{start date and age|2022|6|25}}<br>{{start date and age|2022|6|26}}<br>{{start date and age|2022|6|27}}<br>{{start date and age|2022|6|28}}||Shadow (37 by age at that time)
|-
|15''x''² – 16''x'' + 4||Silver (35 by age at that time)
|-
|6''x''² – 19''x'' + 15||Mighty (37 by age at that time)
|-
|15''x''² – 19''x'' + 6||Sonic (36 by age at that time)
|-
|6''x''² – 25''x'' + 25||Ray (30 by age at that time)
|-
|25''x''² – 25''x'' + 6||Tails (29 by age at that time)
|-
|6''x''² – 19''x'' + 10||Mina (37 by age at that time)
|-
|10''x''² – 19''x'' + 6||Tikal (35 by age at that time)
|-
|9''x''² – 21''x'' + 10||Rouge (38 by age at that time)
|-
|10''x''² – 21''x'' + 9||Blaze (35 by age at that time)
|-
|10''x''² – 31''x'' + 15||Sally (36 by age at that time)
|-
|15''x''² – 31''x'' + 10||Marine (28 by age at that time)
|-
|6''x''² – 13''x'' + 6||Amy (32 by age at that time)
|-
|10''x''² – 29''x'' + 10||Tangle (35 by age at that time)
|-
|15''x''² – 34''x'' + 15||Knuckles (36 by age at that time)
|}
===Table focusing on ''b''² and 4''ac'' for quadratic expressions===
{|class="wikitable sortable"
!Quadratic expression!!''b''²!!4''ac''!!Difference (''b''² – 4''ac'')
|-
|4''x''² – 16''x'' + 15||rowspan="2"|256||rowspan="2"|240||rowspan="2"|16 (which is a perfect square)
|-
|15''x''² – 16''x'' + 4
|-
|6''x''² – 19''x'' + 15||rowspan="2"|361||rowspan="2"|360||rowspan="2"|1 (which is a perfect square)
|-
|15''x''² – 19''x'' + 6
|-
|6''x''² – 25''x'' + 25||rowspan="2"|625||rowspan="2"|600||rowspan="2"|25 (which is a perfect square)
|-
|25''x''² – 25''x'' + 6
|-
|6''x''² – 19''x'' + 10||rowspan="2"|361||rowspan="2"|240||rowspan="2"|121 (which is a perfect square)
|-
|10''x''² – 19''x'' + 6
|-
|9''x''² – 21''x'' + 10||rowspan="2"|441||rowspan="2"|360||rowspan="2"|81 (which is a perfect square)
|-
|10''x''² – 21''x'' + 9
|-
|10''x''² – 31''x'' + 15||rowspan="2"|961||rowspan="2"|600||rowspan="2"|361 (which is a perfect square)
|-
|15''x''² – 31''x'' + 10
|-
|6''x''² – 13''x'' + 6||169||144||25 (which is a perfect square)
|-
|10''x''² – 29''x'' + 10||841||400||441 (which is a perfect square)
|-
|15''x''² – 34''x'' + 15||1,156||900||256 (which is a perfect square)
|}
===Table focusing on quadratic expressions changing===
{|class="wikitable sortable"
!Quadratic expression!!Decreasing for!!Having a minimum stationary value at!!Increasing for
|-
|4''x''² – 16''x'' + 15||''x'' < 2||''x'' = 2||''x'' > 2
|-
|15''x''² – 16''x'' + 4||''x'' < {{sfrac|8|15}}||''x'' = {{sfrac|8|15}}||''x'' > {{sfrac|8|15}}
|-
|6''x''² – 19''x'' + 15||''x'' < {{sfrac|19|12}}||''x'' = {{sfrac|19|12}}||''x'' > {{sfrac|19|12}}
|-
|15''x''² – 19''x'' + 6||''x'' < {{sfrac|19|30}}||''x'' = {{sfrac|19|30}}||''x'' > {{sfrac|19|30}}
|-
|6''x''² – 25''x'' + 25||''x'' < {{sfrac|25|12}}||''x'' = {{sfrac|25|12}}||''x'' > {{sfrac|25|12}}
|-
|25''x''² – 25''x'' + 6||''x'' < {{sfrac|1|2}}||''x'' = {{sfrac|1|2}}||''x'' > {{sfrac|1|2}}
|-
|6''x''² – 19''x'' + 10||''x'' < {{sfrac|19|12}}||''x'' = {{sfrac|19|12}}||''x'' > {{sfrac|19|12}}
|-
|10''x''² – 19''x'' + 6||''x'' < {{sfrac|19|20}}||''x'' = {{sfrac|19|20}}||''x'' > {{sfrac|19|20}}
|-
|9''x''² – 21''x'' + 10||''x'' < {{sfrac|7|6}}||''x'' = {{sfrac|7|6}}||''x'' > {{sfrac|7|6}}
|-
|10''x''² – 21''x'' + 9||''x'' < {{sfrac|21|20}}||''x'' = {{sfrac|21|20}}||''x'' > {{sfrac|21|20}}
|-
|10''x''² – 31''x'' + 15||''x'' < {{sfrac|31|20}}||''x'' = {{sfrac|31|20}}||''x'' > {{sfrac|31|20}}
|-
|15''x''² – 31''x'' + 10||''x'' < {{sfrac|31|30}}||''x'' = {{sfrac|31|30}}||''x'' > {{sfrac|31|30}}
|-
|6''x''² – 13''x'' + 6||''x'' < {{sfrac|13|12}}||''x'' = {{sfrac|13|12}}||''x'' > {{sfrac|13|12}}
|-
|10''x''² – 29''x'' + 10||''x'' < {{sfrac|29|20}}||''x'' = {{sfrac|29|20}}||''x'' > {{sfrac|29|20}}
|-
|15''x''² – 34''x'' + 15||''x'' < {{sfrac|17|15}}||''x'' = {{sfrac|17|15}}||''x'' > {{sfrac|17|15}}
|}
===Table focusing on values of quadratic expressions===
{|class="wikitable sortable"
!Quadratic expression!!Negative for!!Zero at!!Positive for
|-
|4''x''² – 16''x'' + 15||{{sfrac|3|2}} < ''x'' < {{sfrac|5|2}} ||''x'' = {{sfrac|3|2}}<br>''x'' = {{sfrac|5|2}}||''x'' < {{sfrac|3|2}}<br>''x'' > {{sfrac|5|2}}
|-
|15''x''² – 16''x'' + 4||{{sfrac|2|5}} < ''x'' < {{sfrac|2|3}} ||''x'' = {{sfrac|2|5}}<br>''x'' = {{sfrac|2|3}}||''x'' < {{sfrac|2|5}}<br>''x'' > {{sfrac|2|3}}
|-
|6''x''² – 19''x'' + 15||{{sfrac|3|2}} < ''x'' < {{sfrac|5|3}} ||''x'' = {{sfrac|3|2}}<br>''x'' = {{sfrac|5|3}}||''x'' < {{sfrac|3|2}}<br>''x'' > {{sfrac|5|3}}
|-
|15''x''² – 19''x'' + 6||{{sfrac|3|5}} < ''x'' < {{sfrac|2|3}} ||''x'' = {{sfrac|3|5}}<br>''x'' = {{sfrac|2|3}}||''x'' < {{sfrac|3|5}}<br>''x'' > {{sfrac|2|3}}
|-
|6''x''² – 25''x'' + 25||{{sfrac|5|3}} < ''x'' < {{sfrac|5|2}} ||''x'' = {{sfrac|5|3}}<br>''x'' = {{sfrac|5|2}}||''x'' < {{sfrac|5|3}}<br>''x'' > {{sfrac|5|2}}
|-
|25''x''² – 25''x'' + 6||{{sfrac|2|5}} < ''x'' < {{sfrac|3|5}} ||''x'' = {{sfrac|2|5}}<br>''x'' = {{sfrac|3|5}}||''x'' < {{sfrac|2|5}}<br>''x'' > {{sfrac|3|5}}
|-
|6''x''² – 19''x'' + 10||{{sfrac|2|3}} < ''x'' < {{sfrac|5|2}} ||''x'' = {{sfrac|2|3}}<br>''x'' = {{sfrac|5|2}}||''x'' < {{sfrac|2|3}}<br>''x'' > {{sfrac|5|2}}
|-
|10''x''² – 19''x'' + 6||{{sfrac|2|5}} < ''x'' < {{sfrac|3|2}} ||''x'' = {{sfrac|2|5}}<br>''x'' = {{sfrac|3|2}}||''x'' < {{sfrac|2|5}}<br>''x'' > {{sfrac|3|2}}
|-
|9''x''² – 21''x'' + 10||{{sfrac|2|3}} < ''x'' < {{sfrac|5|3}} ||''x'' = {{sfrac|2|3}}<br>''x'' = {{sfrac|5|3}}||''x'' < {{sfrac|2|3}}<br>''x'' > {{sfrac|5|3}}
|-
|10''x''² – 21''x'' + 9||{{sfrac|3|5}} < ''x'' < {{sfrac|3|2}} ||''x'' = {{sfrac|3|5}}<br>''x'' = {{sfrac|3|2}}||''x'' < {{sfrac|3|5}}<br>''x'' > {{sfrac|3|2}}
|-
|10''x''² – 31''x'' + 15||{{sfrac|3|5}} < ''x'' < {{sfrac|5|2}} ||''x'' = {{sfrac|3|5}}<br>''x'' = {{sfrac|5|2}}||''x'' < {{sfrac|3|5}}<br>''x'' > {{sfrac|5|2}}
|-
|15''x''² – 31''x'' + 10||{{sfrac|2|5}} < ''x'' < {{sfrac|5|3}} ||''x'' = {{sfrac|2|5}}<br>''x'' = {{sfrac|5|3}}||''x'' < {{sfrac|2|5}}<br>''x'' > {{sfrac|5|3}}
|-
|6''x''² – 13''x'' + 6||{{sfrac|2|3}} < ''x'' < {{sfrac|3|2}} ||''x'' = {{sfrac|2|3}}<br>''x'' = {{sfrac|3|2}}||''x'' < {{sfrac|2|3}}<br>''x'' > {{sfrac|3|2}}
|-
|10''x''² – 29''x'' + 10||{{sfrac|2|5}} < ''x'' < {{sfrac|5|2}} ||''x'' = {{sfrac|2|5}}<br>''x'' = {{sfrac|5|2}}||''x'' < {{sfrac|2|5}}<br>''x'' > {{sfrac|5|2}}
|-
|15''x''² – 34''x'' + 15||{{sfrac|3|5}} < ''x'' < {{sfrac|5|3}} ||''x'' = {{sfrac|3|5}}<br>''x'' = {{sfrac|5|3}}||''x'' < {{sfrac|3|5}}<br>''x'' > {{sfrac|5|3}}
|}

== Tables focusing on star design group seals and star flags ==
===Table focusing on star design group seals===
{|class="wikitable sortable"
!Design group seal name!!Description!!First adopted!!First sold to the American market!!First sold to the Japanese market!!Units/copies sold
|-
|SS design pair seal||Japanese-American design pair seal containing or featuring Shadow and Silver as grown men||{{start date and age|2022|4|16}}||colspan="2"|{{start date and age|2022|4|23}}<br>{{start date and age|2022|4|30}}||40+ million to American and Japanese markets in late June or early summer 2022
|-
|MSRT design quartet seal||Japanese-American design quartet seal containing or featuring Mighty, Sonic, Ray and Tails as grown men||{{start date and age|2022|4|17}}||colspan="2"|{{start date and age|2022|4|24}}<br>{{start date and age|2022|5|1}}||40+ million to American and Japanese markets in late June or early summer 2022
|-
|KAT design group seal||Japanese-American design group seal containing or featuring Knuckles, Amy and Tangle as grown-ups||{{start date and age|2022|4|20}}||colspan="2"|{{start date and age|2022|4|27}}<br>{{start date and age|2022|5|4}}||40+ million to American and Japanese markets in late June or early summer 2022
|-
|RBSM design quartet seal||Japanese-American design quartet seal containing or featuring Rouge, Blaze, Sally and Marine as grown women||{{start date and age|2022|4|23}}||colspan="2"|{{start date and age|2022|4|30}}<br>{{start date and age|2022|5|7}}||40+ million to American and Japanese markets in late June or early summer 2022
|-
|MT design pair seal||Japanese-American design pair seal containing or featuring Mina and Tikal as grown women||{{start date and age|2022|4|24}}||colspan="2"|{{start date and age|2022|5|1}}<br>{{start date and age|2022|5|8}}||40+ million to American and Japanese markets in late June or early summer 2022
|}
===Other table focusing on star design group seals===
{|class="wikitable sortable"
!Design group seal name!!Selling status
|-
|SS design group seal||Sold to American and Japanese markets since April 23, 2022 or maybe since April 30, 2022<br>Continuing to be sold to American and Japanese markets for many years in obedience to the announcement on June 8, 2022
|-
|MSRT design group seal||Sold to American and Japanese markets since April 24, 2022 or maybe since May 1, 2022<br>Continuing to be sold to American and Japanese markets for many years in obedience to the announcement on June 8, 2022
|-
|KAT design group seal||Sold to American and Japanese markets since April 27, 2022 or maybe since May 4, 2022<br>Continuing to be sold to American and Japanese markets for many years in obedience to the announcement on June 8, 2022
|-
|RBSM design group seal||Sold to American and Japanese markets since April 30, 2022 or maybe since May 7, 2022<br>Continuing to be sold to American and Japanese markets for many years in obedience to the announcement on June 8, 2022
|-
|MT design group seal||Sold to American and Japanese markets since May 1, 2022 or maybe since May 8, 2022<br>Continuing to be sold to American and Japanese markets for many years in obedience to the announcement on June 8, 2022
|}
===Table focusing on star flags===
{|class="wikitable sortable"
!Flag name!!Description!!First adopted!!First sold to the American market!!First sold to the Japanese market!!Units/copies sold!!Height-to-width proportion!!Width-to-height proportion
|-
|SS flag||Japanese-American flag containing the SS design pair seal or featuring Shadow and Silver as grown men||{{start date and age|2022|4|16}}||colspan="2"|{{start date and age|2022|4|23}}<br>{{start date and age|2022|4|30}}||40+ million to American and Japanese markets in late June or early summer 2022||rowspan="5"|3 : 5 (0.6)||rowspan="5"|5 : 3 (1.{{overline|6}})
|-
|MSRT flag||Japanese-American flag containing the MSRT design quartet seal or featuring Mighty, Sonic, Ray and Tails as grown men||{{start date and age|2022|4|17}}||colspan="2"|{{start date and age|2022|4|24}}<br>{{start date and age|2022|5|1}}||40+ million to American and Japanese markets in late June or early summer 2022
|-
|KAT flag||Japanese-American flag containing the KAT design group seal or featuring Knuckles, Amy and Tangle as grown-ups||{{start date and age|2022|4|20}}||colspan="2"|{{start date and age|2022|4|27}}<br>{{start date and age|2022|5|4}}||40+ million to American and Japanese markets in late June or early summer 2022
|-
|RBSM flag||Japanese-American flag containing the RBSM design quartet seal or featuring Rouge, Blaze, Sally and Marine as grown women||{{start date and age|2022|4|23}}||colspan="2"|{{start date and age|2022|4|30}}<br>{{start date and age|2022|5|7}}||40+ million to American and Japanese markets in late June or early summer 2022
|-
|MT flag||Japanese-American flag containing the MT design pair seal or featuring Mina and Tikal as grown women||{{start date and age|2022|4|24}}||colspan="2"|{{start date and age|2022|5|1}}<br>{{start date and age|2022|5|8}}||40+ million to American and Japanese markets in late June or early summer 2022
|}
===Other table focusing on star flags===
{|class="wikitable sortable"
!Flag name!!Selling status
|-
|SS flag||Sold to American and Japanese markets since April 23, 2022 or maybe since April 30, 2022<br>Continuing to be sold to American and Japanese markets for many years in obedience to the announcement on June 8, 2022
|-
|MSRT flag||Sold to American and Japanese markets since April 24, 2022 or maybe since May 1, 2022<br>Continuing to be sold to American and Japanese markets for many years in obedience to the announcement on June 8, 2022
|-
|KAT flag||Sold to American and Japanese markets since April 27, 2022 or maybe since May 4, 2022<br>Continuing to be sold to American and Japanese markets for many years in obedience to the announcement on June 8, 2022
|-
|RBSM flag||Sold to American and Japanese markets since April 30, 2022 or maybe since May 7, 2022<br>Continuing to be sold to American and Japanese markets for many years in obedience to the announcement on June 8, 2022
|-
|MT flag||Sold to American and Japanese markets since May 1, 2022 or maybe since May 8, 2022<br>Continuing to be sold to American and Japanese markets for many years in obedience to the announcement on June 8, 2022
|}

== Japanese-American star groups ==
===Table focusing on Japanese-American star groups===
{|class="wikitable sortable"
!Star group name!!Description!!Created!!Based in
|-
|Famous SS Pair||Famous Japanese-American male pair containing or featuring Shadow and Silver either as grown men or in the advanced stage||rowspan="5"|{{start date and age|2022|4|13}}||rowspan="5"|{{flagicon|USA}} United States<br>{{flagicon|JPN}} Japan
|-
|Famous MSRT Quartet||Famous Japanese-American male quartet containing or featuring Mighty, Sonic, Ray and Tails either as grown men or in the advanced stage
|-
|Famous KAT Group||Famous Japanese-American group containing or featuring Knuckles, Amy and Tangle either as grown-ups or in the advanced stage
|-
|Famous RBSM Quartet||Famous Japanese-American female quartet containing or featuring Rouge, Blaze, Sally and Marine either as grown women or in the advanced stage
|-
|Famous MT Pair||Famous Japanese-American female pair containing or featuring Mina and Tikal either as grown women or in the advanced stage
|}

== American planes containing Japanese parts ==
===Table focusing on American planes containing Japanese parts===
{|class="wikitable sortable"
!Plane!!Produced!!First flight date!!Mass (in tons)!!Cost!!Operators!!Occupied by or containing!!Capacity!!Top speed
|-
|Big plane||rowspan="2"|{{start date and age|2022|4|13}} in New York City||rowspan="2"|{{start date and age|2022|4|20}} to Tokyo||8||USD$24 million||colspan="2"|Shadow, Silver, Mighty, Sonic, Ray, Tails, Mina, Tikal, Rouge, Blaze, Sally and Marine||12 (Shadow, Silver, Mighty, Sonic, Ray, Tails, Mina, Tikal, Rouge, Blaze, Sally and Marine)||rowspan="2"|621 mph
|-
|Little plane||2||USD$6 million||colspan="2"|Knuckles, Amy and Tangle||3 (Knuckles, Amy and Tangle)
|}
===Table focusing on American planes on their first flight to Tokyo on April 20, 2022, though produced in New York City a week earlier, on April 13, 2022===
{|class="wikitable sortable"
!Plane!!Height above/over the ground!!Kinetic energy (in calories)!!Gravitational potential energy (in calories)!!Total mechanical energy (in calories)
|-
|Big plane||About 3.1 miles above/over the ground while on the first flight to Tokyo on April 20, 2022, though created in New York City a week earlier, on April 13, 2022, and occupied by or containing Shadow, Silver, Mighty, Sonic, Ray, Tails, Mina, Tikal, Rouge, Blaze, Sally and Marine||Nearly 73.8 million||About 151 million||Nearly 225 million
|-
|Little plane||About 1.2 miles above/over the ground while on the first flight to Tokyo on April 20, 2022, though created in New York City a week earlier, on April 13, 2022, and occupied by or containing Knuckles, Amy and Tangle||About 18.4 million||About 15.1 million||Nearly 33.6 million
|}

== Tables focusing on the United States and Japan ==
===Table containing some late June or early summer 2022 analysis focusing on gender, age, urbanization and Internet usage===
{|class="wikitable sortable"
!Country!!Two-letter country code!!Three-letter country code!!Capital!!Biggest and most populous city!!Capital as the biggest and most populous city!!Male population (2022)!!Male population percentage (2022)!!Female population (2022)!!Female population percentage (2022)!!Urban population (2022)!!Urbanization rate (2022)!!Rural population (2022)!!Rural population percentage (2022)!!Child population (2022)!!Child population percentage (2022)!!Adult population (2022)!!Adult population percentage (2022)!!Elderly population (2022)!!Elderly population percentage (2022)!!Median age (2022)!!Population difference by gender (2022)!!Gender proportion (2022)!!Internet user population (2022)!!Internet usage rate (2022)!!Dependency proportion (2022)
|-
|{{flagicon|USA}} United States||US||USA||Washington, D.C.||New York City||{{No}}||167.4 million||49.5%||170.4 million||50.5%||281.6 million||83.3%||56.3 million||16.7%||69.8 million||20.6%||210 million||62.1%||58.1 million||17.2%||40.4||3.1 million||0.982 (54 men to 55 women)||253.4 million||75%||0.609 (39 children and senior citizens to 64 adults)
|-
|{{flagicon|JPN}} Japan||JP||JPN||colspan="2"|Tokyo||{{Yes}}||61.4 million||48.8%||64.4 million||51.2%||116.5 million||92.6%||9.3 million||7.4%||17.4 million||13.8%||69.9 million||55.6%||38.4 million||30.5%||49.2||3 million||0.954 (21 men to 22 women)||109.2 million||86.8%||0.797 (51 children and senior citizens to 64 adults)
|-
|}
===Gender and age table (late June or early summer 2022)===
{|class="wikitable sortable"
!Country!!Male child population (2022)!!Male child population percentage (2022)!!Female child population (2022)!!Female child population percentage (2022)!!Male adult population (2022)!!Male adult population percentage (2022)!!Female adult population (2022)!!Female adult population percentage (2022)!!Male elderly population (2022)!!Male elderly population percentage (2022)!!Female elderly population (2022)!!Female elderly population percentage (2022)!!Child population difference (2022)!!Adult population difference (2022)!!Elderly population difference (2022)!!Child gender proportion (2022)!!Adult gender proportion (2022)!!Elderly gender proportion (2022)!!Male median age (2022)!!Female median age (2022)!!Median age difference (2022)!!Male dependency proportion (2022)!!Female dependency proportion (2022)
|-
|{{flagicon|USA}} United States||36 million||10.7%||33.8 million||10%||105 million||31.1%||105 million||31.1%||26.4 million||7.8%||31.7 million||9.4%||2.2 million||40,000||5.3 million||1.07 (16 boys to 15 girls)||1 (one man to one woman)||0.833 (five men to six women)||40||40.8||0.8||0.594 (19 boys and elderly men to 32 men)||0.624 (five girls and elderly women to eight women)
|-
|{{flagicon|JPN}} Japan||9 million||7.1%||8.4 million||6.7%||35.9 million||28.6%||34 million||27.1%||16.5 million||13.1%||21.9 million||17.4%||560,000||1.8 million||5.5 million||1.07 (16 boys to 15 girls)||1.05 (21 men to 20 women)||0.75 (three men to four women)||48||50.4||2.4||0.709 (17 boys and elderly men to 24 men)||0.886 (31 girls and elderly women to 35 women)
|}
===Gender and urbanization table (late June or early summer 2022)===
{|class="wikitable sortable"
!Country!!Male urban population (2022)!!Male urbanization rate (2022)!!Female urban population (2022)!!Female urbanization rate (2022)!!Male rural population (2022)!!Male rural population percentage (2022)!!Female rural population (2022)!!Female rural population percentage (2022)
|-
|{{flagicon|USA}} United States||139.5 million||41.3%||142 million||42.1%||27.9 million||8.3%||28.4 million||8.4%
|-
|{{flagicon|JPN}} Japan||56.9 million||45.2%||59.6 million||47.4%||4.5 million||3.6%||4.8 million||3.8%
|}
===Gender and Internet usage table (late June or early summer 2022)===
{|class="wikitable sortable"
!Country!!Male Internet user population (2022)!!Male Internet usage rate (2022)!!Female Internet user population (2022)!!Female Internet usage rate (2022)
|-
|{{flagicon|USA}} United States||125.6 million||37.1%||127.8 million||37.9%
|-
|{{flagicon|JPN}} Japan||53.3 million||42.4%||55.9 million||44.4%
|}
===Age and urbanization table (late June or early summer 2022)===
{|class="wikitable sortable"
!Country!!Urban child population (2022)!!Urban child population percentage (2022)!!Rural child population (2022)!!Rural child population percentage (2022)!!Urban adult population (2022)!!Urban adult population percentage (2022)!!Rural adult population (2022)!!Rural adult population percentage (2022)!!Urban elderly population (2022)!!Urban elderly population percentage (2022)!!Rural elderly population (2022)!!Rural elderly population percentage (2022)
|-
|{{flagicon|USA}} United States||58.2 million||17.2%||11.6 million||3.4%||175 million||51.7%||35 million||10.3%||48.4 million||14.3%||9.7 million||2.9%
|-
|{{flagicon|JPN}} Japan||16.1 million||12.8%||1.3 million||1%||64.7 million||51.5%||5.2 million||4.1%||35.6 million||28.3%||2.8 million||2.3%
|}
===Age and Internet usage table (late June or early summer 2022)===
{|class="wikitable sortable"
!Country!!Child Internet user population (2022)!!Child Internet usage rate (2022)!!Adult Internet user population (2022)!!Adult Internet usage rate (2022)!!Elderly Internet user population (2022)!!Elderly Internet usage rate (2022)
|-
|{{flagicon|USA}} United States||52.3 million||15.5%||157.5 million||46.6%||43.6 million||12.9%
|-
|{{flagicon|JPN}} Japan||15.1 million||12%||60.8 million||48.3%||33.3 million||26.5%
|}
===Urbanization and Internet usage table (late June or early summer 2022)===
{|class="wikitable sortable"
!Country!!Urban Internet user population (2022)!!Urban Internet usage rate (2022)!!Rural Internet user population (2022)!!Rural Internet usage rate (2022)
|-
|{{flagicon|USA}} United States||211.2 million||62.5%||42.2 million||12.5%
|-
|{{flagicon|JPN}} Japan||101.1 million||80.4%||8.1 million||6.4%
|}
===Table containing some late June or early summer 2022 analysis focusing on income and debt===
{|class="wikitable sortable"
!Country!!Gross domestic product (2022)!!Gross domestic product per capita (2022)!!Gross national income (2022)!!Gross national income per capita (2022)!!Debt (2022)!!Debt per capita (2022)!!Flow of money (2022)!!Flow of money per capita (2022)!!Debt-to-GDP proportion (2022)!!Debt-to-GNI proportion (2022)
|-
{{flagicon|USA}} United States||USD$24.5 trillion||USD$72,500||USD$25.3 trillion||USD$74,900||USD$33.6 trillion||USD$99,500||USD$816 billion||USD$2,400||1.4||1.3
|-
|{{flagicon|JPN}} Japan||USD$5.5 trillion||USD$43,700||USD$5.7 trillion||USD$45,300||USD$13.7 trillion||USD$109,000||USD$184 billion||USD$1,500||2.5||2.4
|}

== Top-anthro-star-or-personality list ==
===Table focusing on the top-anthro-star-or-personality list===
{|class="wikitable sortable"
!List name!!Description!!First produced!!Update status!!Monthly update count!!Yearly update count!!Countries of availability!!Age status (Japanese-American stars/personalities)
|-
|Top-anthro-star-or-personality list||Licensed list containing or featuring Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal as top anthro stars or personalities, AKA most famous anthro citizens||{{start date and age|2022|4|13}} in the United States and Japan||Receiving live Wednesday and weekend updates indefinitely starting on April 16, 2022||12 to 14 live Wednesday and weekend updates every month starting in May 2022||156 or 157 live Wednesday and weekend updates every year starting in May 2022||{{flagicon|USA}} United States<br>{{flagicon|JPN}} Japan||Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal getting older in later versions
|}
===Table focusing on top-anthro-star-or-personality list versions===
{|class="wikitable sortable"
!Version!!Release date!!Description
|-
|Version 1.0||{{start date and age|2022|4|13}}||First version featuring Shadow at age 37, Silver at age 35, Mighty at age 37, Sonic at age 36, Ray at age 30, Tails at age 29, Knuckles at age 36, Amy at age 32, Tangle at age 35, Rouge at age 38, Blaze at age 35, Sally at age 36, Marine at age 28, Mina at age 37 and Tikal at age 35
|-
|Version 2.0||{{start date and age|2023|4|12}}||157th version featuring Shadow at age 38, Silver at age 36, Mighty near age 38, Sonic near age 37, Ray at age 31, Tails at age 30, Knuckles near age 37, Amy near age 33, Tangle near age 36, Rouge at age 39, Blaze at age 36, Sally at age 37, Marine at age 29, Mina at age 38 and Tikal at age 36
|-
|Version 3.0||{{start date and age|2024|4|17}}||316th version featuring Shadow at age 39, Silver at age 37, Mighty at age 39, Sonic at age 38, Ray at age 32, Tails at age 31, Knuckles at age 38, Amy at age 34, Tangle at age 37, Rouge at age 40, Blaze at age 37, Sally at age 38, Marine at age 30, Mina at age 39 and Tikal at age 37
|-
|Version 4.0||{{start date and age|2025|4|16}}||472nd version scheduled to feature Shadow at age 40, Silver at age 38, Mighty at age 40, Sonic at age 39, Ray at age 33, Tails at age 32, Knuckles at age 39, Amy at age 35, Tangle at age 38, Rouge at age 41, Blaze at age 38, Sally at age 39, Marine at age 31, Mina at age 40 and Tikal at age 38
|-
|Version 5.0||{{start date and age|2026|4|15}}||628th version scheduled to feature Shadow at age 41, Silver at age 49, Mighty at age 41, Sonic at age 40, Ray at age 34, Tails at age 33, Knuckles at age 40, Amy at age 36, Tangle at age 39, Rouge at age 42, Blaze at age 39, Sally at age 40, Marine at age 32, Mina at age 41 and Tikal at age 39
|-
|Version 6.0||{{start date and age|2027|4|14}}||784th version scheduled to feature Shadow at age 42, Silver at age 40, Mighty at age 42, Sonic at age 41, Ray at age 35, Tails at age 34, Knuckles at age 41, Amy at age 37, Tangle at age 40, Rouge at age 43, Blaze at age 40, Sally at age 41, Marine at age 33, Mina at age 42 and Tikal at age 40
|-
|Version 7.0||{{start date and age|2028|4|12}}||940th version scheduled to feature Shadow at age 43, Silver at age 41, Mighty near age 43, Sonic near age 42, Ray at age 36, Tails at age 35, Knuckles near age 42, Amy near age 38, Tangle near age 41, Rouge at age 44, Blaze at age 41, Sally at age 42, Marine at age 34, Mina at age 43 and Tikal at age 41
|-
|Version 8.0||{{start date and age|2029|4|11}}||1,096th version scheduled to feature Shadow at age 44, Silver at age 42, Mighty near age 44, Sonic near age 43, Ray at age 37, Tails at age 36, Knuckles near age 43, Amy near age 39, Tangle near age 42, Rouge at age 45, Blaze at age 42, Sally at age 43, Marine at age 35, Mina at age 44 and Tikal at age 42
|-
|Version 9.0||{{start date and age|2030|4|17}}||1,255th version scheduled to feature Shadow at age 45, Silver at age 43, Mighty at age 45, Sonic at age 44, Ray at age 38, Tails at age 37, Knuckles at age 44, Amy at age 40, Tangle at age 43, Rouge at age 46, Blaze at age 43, Sally at age 44, Marine at age 36, Mina at age 45 and Tikal at age 43
|-
|Version 10.0||{{start date and age|2031|4|16}}||1,411th version scheduled to feature Shadow at age 46, Silver at age 44, Mighty at age 46, Sonic at age 45, Ray at age 39, Tails at age 38, Knuckles at age 45, Amy at age 41, Tangle at age 44, Rouge at age 47, Blaze at age 44, Sally at age 45, Marine at age 37, Mina at age 46 and Tikal at age 44
|-
|Version 11.0||{{start date and age|2032|4|14}}||1,567th version scheduled to feature Shadow at age 47, Silver at age 45, Mighty at age 47, Sonic at age 46, Ray at age 40, Tails at age 39, Knuckles at age 46, Amy at age 42, Tangle at age 45, Rouge at age 48, Blaze at age 45, Sally at age 46, Marine at age 38, Mina at age 47 and Tikal at age 45
|-
|Version 12.0||{{start date and age|2033|4|13}}||1,723rd version and 11th anniversary version scheduled to feature Shadow at age 48, Silver at age 46, Mighty at age 48, Sonic at age 47, Ray at age 41, Tails at age 40, Knuckles at age 47, Amy at age 43, Tangle at age 46, Rouge at age 49, Blaze at age 46, Sally at age 47, Marine at age 39, Mina at age 48 and Tikal at age 46
|-
|Version 13.0||{{start date and age|2034|4|12}}||1,879th version scheduled to feature Shadow at age 49, Silver at age 47, Mighty near age 49, Sonic near age 48, Ray at age 42, Tails at age 41, Knuckles near age 48, Amy near age 44, Tangle near age 47, Rouge at age 50, Blaze at age 47, Sally at age 48, Marine at age 40, Mina at age 49 and Tikal at age 47
|-
|Version 14.0||{{start date and age|2035|4|11}}||2,035th version scheduled to feature Shadow at age 50, Silver at age 48, Mighty near age 50, Sonic near age 49, Ray at age 43, Tails at age 42, Knuckles near age 49, Amy near age 45, Tangle near age 48, Rouge at age 51, Blaze at age 48, Sally at age 49, Marine at age 41, Mina at age 50 and Tikal at age 48
|-
|Version 15.0||{{start date and age|2036|4|16}}||2,194th version scheduled to feature Shadow at age 51, Silver at age 49, Mighty at age 51, Sonic at age 50, Ray at age 44, Tails at age 43, Knuckles at age 50, Amy at age 46, Tangle at age 49, Rouge at age 52, Blaze at age 49, Sally at age 50, Marine at age 42, Mina at age 51 and Tikal at age 49
|-
|Version 16.0||{{start date and age|2037|4|15}}||2,350th version scheduled to feature Shadow at age 52, Silver at age 50, Mighty at age 52, Sonic at age 51, Ray at age 45, Tails at age 44, Knuckles at age 51, Amy at age 47, Tangle at age 50, Rouge at age 53, Blaze at age 50, Sally at age 51, Marine at age 43, Mina at age 52 and Tikal at age 50
|-
|Version 17.0||{{start date and age|2038|4|14}}||2,506th version scheduled to feature Shadow at age 53, Silver at age 51, Mighty at age 53, Sonic at age 52, Ray at age 46, Tails at age 45, Knuckles at age 52, Amy at age 48, Tangle at age 51, Rouge at age 54, Blaze at age 51, Sally at age 52, Marine at age 44, Mina at age 53 and Tikal at age 51
|-
|Version 18.0||{{start date and age|2039|4|13}}||2,662nd version and 17th anniversary version scheduled to feature Shadow at age 54, Silver at age 52, Mighty at age 54, Sonic at age 53, Ray at age 47, Tails at age 46, Knuckles at age 53, Amy at age 49, Tangle at age 52, Rouge at age 55, Blaze at age 52, Sally at age 53, Marine at age 45, Mina at age 54 and Tikal at age 52
|-
|Version 19.0||{{start date and age|2040|4|11}}||2,818th version scheduled to feature Shadow at age 55, Silver at age 53, Mighty near age 55, Sonic near age 54, Ray at age 48, Tails at age 47, Knuckles near age 54, Amy near age 50, Tangle near age 53, Rouge at age 56, Blaze at age 53, Sally at age 54, Marine at age 46, Mina at age 55 and Tikal at age 53
|-
|Version 20.0||{{start date and age|2041|4|17}}||2,977th version scheduled to feature Shadow at age 56, Silver at age 54, Mighty at age 56, Sonic at age 55, Ray at age 49, Tails at age 48, Knuckles at age 55, Amy at age 51, Tangle at age 54, Rouge at age 57, Blaze at age 54, Sally at age 55, Marine at age 47, Mina at age 56 and Tikal at age 54
|-
|Version 21.0||{{start date and age|2042|4|16}}||3,133rd version scheduled to feature Shadow at age 57, Silver at age 55, Mighty at age 57, Sonic at age 56, Ray at age 50, Tails at age 49, Knuckles at age 56, Amy at age 52, Tangle at age 55, Rouge at age 58, Blaze at age 55, Sally at age 56, Marine at age 48, Mina at age 57 and Tikal at age 55
|-
|Version 22.0||{{start date and age|2043|4|15}}||3,289th version scheduled to feature Shadow at age 58, Silver at age 56, Mighty at age 58, Sonic at age 57, Ray at age 51, Tails at age 50, Knuckles at age 57, Amy at age 53, Tangle at age 56, Rouge at age 59, Blaze at age 56, Sally at age 57, Marine at age 49, Mina at age 58 and Tikal at age 56
|-
|Version 23.0||{{start date and age|2044|4|13}}||3,445th version and 22nd anniversary version scheduled to feature Shadow at age 59, Silver at age 57, Mighty at age 59, Sonic at age 58, Ray at age 52, Tails at age 51, Knuckles at age 58, Amy at age 54, Tangle at age 57, Rouge at age 60, Blaze at age 57, Sally at age 58, Marine at age 50, Mina at age 59 and Tikal at age 57
|-
|Version 24.0||{{start date and age|2045|4|12}}||3,601st version scheduled to feature Shadow at age 60, Silver at age 58, Mighty near age 60, Sonic near age 59, Ray at age 53, Tails at age 52, Knuckles near age 59, Amy near age 55, Tangle near age 58, Rouge at age 61, Blaze at age 58, Sally at age 59, Marine at age 51, Mina at age 60 and Tikal at age 58
|-
|Version 25.0||{{start date and age|2046|4|11}}||3,757th version scheduled to feature Shadow at age 61, Silver at age 59, Mighty near age 61, Sonic near age 60, Ray at age 54, Tails at age 53, Knuckles near age 60, Amy near age 56, Tangle near age 59, Rouge at age 62, Blaze at age 59, Sally at age 60, Marine at age 52, Mina at age 61 and Tikal at age 59
|}

== Lookalikes of Japanese-American stars/personalities ==
===Tables focusing on lookalike capacities of Japanese-American stars/personalities in the United States and Japan===
{|class="wikitable sortable"
!Star/personality name!!Lookalike population!!% of lookalikes as OCs!!% of lookalikes as canonical characters
|-
|Shadow||About three and a half million in the United States and Japan||rowspan="15"|0%||rowspan="15"|100%
|-
|Silver||Nearly three and a half million in the United States and Japan
|-
|Mighty||About 3.4 million in the United States and Japan
|-
|Sonic||Nearly 3.4 million in the United States and Japan
|-
|Ray||About 3.3 million in the United States and Japan
|-
|Tails||Nearly 3.3 million in the United States and Japan
|-
|Knuckles||About 3.2 million in the United States and Japan
|-
|Amy||Nearly 3.2 million in the United States and Japan
|-
|Tangle||About 3.1 million in the United States and Japan
|-
|Rouge||Nearly 3.1 million in the United States and Japan
|-
|Blaze||About three million in the United States and Japan
|-
|Sally||Nearly three million million in the United States and Japan
|-
|Marine||About 2.9 million in the United States and Japan
|-
|Mina||Nearly 2.9 million in the United States and Japan
|-
|Tikal||About 2.8 million in the United States and Japan
|}

== Gameplay ==
===Table focusing on highest scores acquired by Japanese-American stars or personalities===
{|class="wikitable sortable
!Star/personality name!!Total score!!Life count!!Difficulty size!!Stages!!Total time taken!!Date submitted!!Age upon finishing the whole game
|-
|Shadow||28.2 million||rowspan="6"|290||rowspan="15"|''Very very hard''||rowspan="15"|1-35 (incl. secret stages)||rowspan="15"|1 day||{{start date and age|2022|5|7}}||37
|-
|Silver||28 million||{{start date and age|2022|5|8}}||35
|-
|Mighty||27.9 million||{{start date and age|2022|5|11}}||37
|-
|Sonic||27.7 million||{{start date and age|2022|5|14}}||36
|-
|Ray||27.6 million||{{start date and age|2022|5|15}}||30
|-
|Tails||27.4 million||{{start date and age|2022|5|18}}||29
|-
|Knuckles||27.3 million||rowspan="7"|280||{{start date and age|2022|5|21}}||36
|-
|Amy||27.1 million||{{start date and age|2022|5|22}}||32
|-
|Tangle||27 million||{{start date and age|2022|5|25}}||35
|-
|Rouge||26.8 million||{{start date and age|2022|5|28}}||38
|-
|Blaze||26.7 million||{{start date and age|2022|5|29}}||35
|-
|Sally||26.5 million||{{start date and age|2022|6|1}}||36
|-
|Marine||26.4 million||{{start date and age|2022|6|4}}||28
|-
|Mina||26.2 million||rowspan="2"|270||{{start date and age|2022|6|5}}||37
|-
|Tikal||26.1 million||{{start date and age|2022|6|8}}||35
|}
===Table focusing on gameplay lengths of Japanese-American stars/personalities===
{|class="wikitable sortable"
!Star/personality name!!Gameplay start date!!Gameplay end date!!Gameplay duration
|-
|Shadow||{{start date and age|2022|4|13}}||{{start date and age|2022|5|7}}||24 days
|-
|Silver||{{start date and age|2022|4|16}}||{{start date and age|2022|5|8}}||22 days
|-
|Mighty||{{start date and age|2022|4|17}}||{{start date and age|2022|5|11}}||rowspan="2"|24 days
|-
|Sonic||{{start date and age|2022|4|20}}||{{start date and age|2022|5|14}}
|-
|Ray||{{start date and age|2022|4|23}}||{{start date and age|2022|5|15}}||22 days
|-
|Tails||{{start date and age|2022|4|24}}||{{start date and age|2022|5|18}}||rowspan="2"|24 days
|-
|Knuckles||{{start date and age|2022|4|27}}||{{start date and age|2022|5|21}}
|-
|Amy||{{start date and age|2022|4|30}}||{{start date and age|2022|5|22}}||22 days
|-
|Tangle||{{start date and age|2022|5|1}}||{{start date and age|2022|5|25}}||rowspan="2"|24 days
|-
|Rouge||{{start date and age|2022|5|4}}||{{start date and age|2022|5|28}}
|-
|Blaze||{{start date and age|2022|5|7}}||{{start date and age|2022|5|29}}||22 days
|-
|Sally||{{start date and age|2022|5|8}}||{{start date and age|2022|6|1}}||rowspan="2"|24 days
|-
|Marine||{{start date and age|2022|5|11}}||{{start date and age|2022|6|4}}
|-
|Mina||{{start date and age|2022|5|14}}||{{start date and age|2022|6|5}}||22 days
|-
|Tikal||{{start date and age|2022|5|15}}||{{start date and age|2022|6|8}}||24 days
|}

== Daily live workout goal tables ==

===Daily live workout goal table one===
{|class="wikitable sortable"
!Star/personality!!Date of first daily live workout goal attained!!Date of second daily live workout goal attained!!Date of fifth daily live workout goal attained!!Date of tenth daily live workout goal attained!!Date of 25th daily live workout goal attained!!Date of 50th daily live workout goal attained!!Date of 100th daily live workout goal attained!!Date of 250th daily live workout goal attained!!Date of 500th daily live workout goal attained!!Date of 1,000th daily live workout goal scheduled to be attained!!Date of 2,000th daily live workout goal scheduled to be attained!!Date of 5,000th daily live workout goal scheduled to be attained!!Date of 10,000th daily live workout goal scheduled to be attained
|-
|Shadow||rowspan="15"|{{start date and age|2022|4|13}}||rowspan="15"|{{start date and age|2022|4|14}}||rowspan="15"|{{start date and age|2022|4|17}}||rowspan="15"|{{start date and age|2022|4|22}}||rowspan="15"|{{start date and age|2022|5|7}}||rowspan="15"|{{start date and age|2022|6|1}}||rowspan="15"|{{start date and age|2022|7|21}}||rowspan="15"|{{start date and age|2022|12|18}}||rowspan="15"|{{start date and age|2023|8|25}}||rowspan="15"|{{start date and age|2025|1|6}}||rowspan="15"|{{start date and age|2027|10|3}}||rowspan="15"|{{start date and age|2035|12|20}}||rowspan="15"|{{start date and age|2049|8|28}}
|-
|Silver
|-
|Mighty
|-
|Sonic
|-
|Ray
|-
|Tails
|-
|Knuckles
|-
|Amy
|-
|Tangle
|-
|Rouge
|-
|Blaze
|-
|Sally
|-
|Marine
|-
|Mina
|-
|Tikal
|}

===Daily live workout goal table two===
{|class="wikitable sortable"
!Star/personality!!Age upon attaining the first daily live workout goal!!Age upon attaining the second daily live workout goal!!Age upon attaining the fifth daily live workout goal!!Age upon attaining the tenth daily live workout goal!!Age upon attaining the 25th daily live workout goal!!Age upon attaining the 50th daily live workout goal!!Age upon attaining the 100th daily live workout goal!!Age upon attaining the 250th daily live workout goal!!Age upon attaining the 500th daily live workout goal!!Age upon being scheduled to attain the 1,000th daily live workout goal!!Age upon being scheduled to attain the 2,000th daily live workout goal!!Age upon being scheduled to attain the 5,000th daily live workout goal!!Age upon being scheduled to attain the 10,000th daily live workout goal
|-
|Shadow||colspan="8"|37||38||39||42||50||64
|-
|Silver||colspan="8"|35||36||37||40||48||62
|-
|Mighty||colspan="8"|37||38||39||42||50||64
|-
|Sonic||colspan="8"|36||37||38||41||49||63
|-
|Ray||colspan="8"|30||31||32||35||43||57
|-
|Tails||colspan="8"|29||30||31||34||42||56
|-
|Knuckles||colspan="8"|36||37||38||41||49||63
|-
|Amy||colspan="8"|32||33||34||37||45||59
|-
|Tangle||colspan="8"|35||36||37||40||48||62
|-
|Rouge||colspan="8"|38||39||40||43||51||65
|-
|Blaze||colspan="8"|35||36||37||40||48||62
|-
|Sally||colspan="8"|36||37||38||41||49||63
|-
|Marine||colspan="8"|28||29||30||33||41||55
|-
|Mina||colspan="8"|37||38||39||42||50||64
|-
|Tikal||colspan="8"|35||36||37||40||48||62
|}

===Daily live workout goal table three===
{|class="wikitable sortable"
!Star/personality!!Date of one daily live workout goal attained so far!!Date of two daily live workout goals attained so far!!Date of five daily live workout goals attained so far!!Date of ten daily live workout goals attained so far!!Date of 25 daily live workout goals attained so far!!Date of 50 daily live workout goals attained so far!!Date of 100 daily live workout goals attained so far!!Date of 250 daily live workout goals attained so far!!Date of 500 daily live workout goals attained so far!!Date of 1,000 daily live workout goals scheduled to be attained so far!!Date of 2,000 daily live workout goals scheduled to be attained so far!!Date of 5,000 daily live workout goals scheduled to be attained so far!!Date of 10,000 daily live workout goals scheduled to be attained so far
|-
|Shadow||rowspan="15"|{{start date and age|2022|4|13}}||rowspan="15"|{{start date and age|2022|4|14}}||rowspan="15"|{{start date and age|2022|4|17}}||rowspan="15"|{{start date and age|2022|4|22}}||rowspan="15"|{{start date and age|2022|5|7}}||rowspan="15"|{{start date and age|2022|6|1}}||rowspan="15"|{{start date and age|2022|7|21}}||rowspan="15"|{{start date and age|2022|12|18}}||rowspan="15"|{{start date and age|2023|8|25}}||rowspan="15"|{{start date and age|2025|1|6}}||rowspan="15"|{{start date and age|2027|10|3}}||rowspan="15"|{{start date and age|2035|12|20}}||rowspan="15"|{{start date and age|2049|8|28}}
|-
|Silver
|-
|Mighty
|-
|Sonic
|-
|Ray
|-
|Tails
|-
|Knuckles
|-
|Amy
|-
|Tangle
|-
|Rouge
|-
|Blaze
|-
|Sally
|-
|Marine
|-
|Mina
|-
|Tikal
|}

===Daily live workout goal table four===
{|class="wikitable sortable"
!Star/personality!!Age upon attaining one daily live workout goal so far!!Age upon attaining two daily live workout goals so far!!Age upon attaining five daily live workout goals so far!!Age upon attaining ten daily live workout goals so far!!Age upon attaining 25 daily live workout goals so far!!Age upon attaining 50 daily live workout goals so far!!Age upon attaining 100 daily live workout goals so far!!Age upon attaining 250 daily live workout goals so far!!Age upon attaining 500 daily live workout goals so far!!Age upon being scheduled to attain 1,000 daily live workout goals so far!!Age upon being scheduled to attain 2,000 daily live workout goals so far!!Age upon being scheduled to attain 5,000 daily live workout goals so far!!Age upon being scheduled to attain 10,000 daily live workout goals so far
|-
|Shadow||colspan="8"|37||38||39||42||50||64
|-
|Silver||colspan="8"|35||36||37||40||48||62
|-
|Mighty||colspan="8"|37||38||39||42||50||64
|-
|Sonic||colspan="8"|36||37||38||41||49||63
|-
|Ray||colspan="8"|30||31||32||35||43||57
|-
|Tails||colspan="8"|29||30||31||34||42||56
|-
|Knuckles||colspan="8"|36||37||38||41||49||63
|-
|Amy||colspan="8"|32||33||34||37||45||59
|-
|Tangle||colspan="8"|35||36||37||40||48||62
|-
|Rouge||colspan="8"|38||39||40||43||51||65
|-
|Blaze||colspan="8"|35||36||37||40||48||62
|-
|Sally||colspan="8"|36||37||38||41||49||63
|-
|Marine||colspan="8"|28||29||30||33||41||55
|-
|Mina||colspan="8"|37||38||39||42||50||64
|-
|Tikal||colspan="8"|35||36||37||40||48||62
|}

== Live meeting or tour event tables ==
===Live meeting or tour event table one===
{|class="wikitable sortable"
!Star/personality!!Date of appearance in some first live events of licensed Japanese-American live star meetings/tours!!Date of appearance in some second live events of licensed Japanese-American live star meetings/tours!!Date of appearance in some fifth live events of licensed Japanese-American live star meetings/tours!!Date of appearance in some tenth live events of licensed Japanese-American live star meetings/tours!!Date of appearance in some 25th live events of licensed Japanese-American live star meetings/tours!!Date of appearance in some 50th live events of licensed Japanese-American live star meetings/tours!!Date of appearance in some 100th live events of licensed Japanese-American live star meetings/tours!!Date of appearance in some 250th live events of licensed Japanese-American live star meetings/tours!!Date of appearance in some 500th live events of licensed Japanese-American live star meetings/tours!!Date of appearance in some 1,000th live events of licensed Japanese-American live star meetings/tours!!Date of appearance in some 2,000th live events of licensed Japanese-American live star meetings/tours!!Date of appearance in some 5,000th live events of licensed Japanese-American live star meetings/tours
|-
|Shadow||rowspan="15"|{{start date and age|2022|4|13}}||rowspan="15"|{{start date and age|2022|4|16}}||rowspan="15"|{{start date and age|2022|4|23}}||rowspan="15"|{{start date and age|2022|5|4}}||rowspan="15"|{{start date and age|2022|6|8}}||rowspan="15"|{{start date and age|2022|8|6}}||rowspan="15"|{{start date and age|2022|11|30}}||rowspan="15"|{{start date and age|2023|11|15}}||rowspan="15"|{{start date and age|2025|6|21}}||rowspan="15"|{{start date and age|2028|8|30}}||rowspan="15"|{{start date and age|2035|1|20}}||rowspan="15"|{{start date and age|2054|3|21}}
|-
|Silver
|-
|Mighty
|-
|Sonic
|-
|Ray
|-
|Tails
|-
|Knuckles
|-
|Amy
|-
|Tangle
|-
|Rouge
|-
|Blaze
|-
|Sally
|-
|Marine
|-
|Mina
|-
|Tikal
|}

===Live meeting or tour event table two===
{|class="wikitable sortable"
!Star/personality!!Age upon appearance in some first live events of licensed Japanese-American live star meetings/tours!!Age upon appearance in some second live events of licensed Japanese-American live star meetings/tours!!Age upon appearance in some fifth live events of licensed Japanese-American live star meetings/tours!!Age upon appearance in some tenth live events of licensed Japanese-American live star meetings/tours!!Age upon appearance in some 25th live events of licensed Japanese-American live star meetings/tours!!Age upon appearance in some 50th live events of licensed Japanese-American live star meetings/tours!!Age upon appearance in some 100th live events of licensed Japanese-American live star meetings/tours!!Age upon appearance in some 250th live events of licensed Japanese-American live star meetings/tours!!Age upon appearance in some 500th live events of licensed Japanese-American live star meetings/tours!!Age upon appearance in some 1,000th live events of licensed Japanese-American live star meetings/tours!!Age upon appearance in some 2,000th live events of licensed Japanese-American live star meetings/tours!!Age upon appearance in some 5,000th live events of licensed Japanese-American live star meetings/tours
|-
|Shadow||colspan="7"|37||38||40||43||49||68
|-
|Silver||colspan="7"|35||36||38||41||47||66
|-
|Mighty||colspan="7"|37||38||40||43||49||68
|-
|Sonic||colspan="7"|36||37||39||42||48||67
|-
|Ray||colspan="7"|30||31||33||36||42||61
|-
|Tails||colspan="7"|29||30||32||35||41||60
|-
|Knuckles||colspan="7"|36||37||39||42||48||67
|-
|Amy||colspan="7"|32||33||35||38||44||63
|-
|Tangle||colspan="7"|35||36||38||41||47||66
|-
|Rouge||colspan="7"|38||39||41||44||50||69
|-
|Blaze||colspan="7"|35||36||38||41||47||66
|-
|Sally||colspan="7"|36||37||39||42||48||67
|-
|Marine||colspan="7"|28||29||31||34||40||59
|-
|Mina||colspan="7"|37||38||40||43||49||68
|-
|Tikal||colspan="7"|35||36||38||41||47||66
|}

===Live meeting or tour event table three===
{|class="wikitable sortable"
!Star/personality!!Date of appearance in one live event so far of some licensed Japanese-American live star meetings/tours!!Date of appearance in two live events so far of some licensed Japanese-American live star meetings/tours!!Date of appearance in five live events so far of some licensed Japanese-American live star meetings/tours!!Date of appearance in ten live events so far of some licensed Japanese-American live star meetings/tours!!Date of appearance in 25 live events so far of some licensed Japanese-American live star meetings/tours!!Date of appearance in 50 live events so far of some licensed Japanese-American live star meetings/tours!!Date of appearance in 100 live events so far of some licensed Japanese-American live star meetings/tours!!Date of appearance in 250 live events so far of some licensed Japanese-American live star meetings/tours!!Date of appearance in 500 live events so far of some licensed Japanese-American live star meetings/tours!!Date of appearance in 1,000 live events so far of some licensed Japanese-American live star meetings/tours!!Date of appearance in 2,000 live events so far of some licensed Japanese-American live star meetings/tours!!Date of appearance in 5,000 live events so far of some licensed Japanese-American live star meetings/tours
|-
|Shadow||rowspan="15"|{{start date and age|2022|4|13}}||rowspan="15"|{{start date and age|2022|4|16}}||rowspan="15"|{{start date and age|2022|4|23}}||rowspan="15"|{{start date and age|2022|5|4}}||rowspan="15"|{{start date and age|2022|6|8}}||rowspan="15"|{{start date and age|2022|8|6}}||rowspan="15"|{{start date and age|2022|11|30}}||rowspan="15"|{{start date and age|2023|11|15}}||rowspan="15"|{{start date and age|2025|6|21}}||rowspan="15"|{{start date and age|2028|8|30}}||rowspan="15"|{{start date and age|2035|1|20}}||rowspan="15"|{{start date and age|2054|3|21}}
|-
|Silver
|-
|Mighty
|-
|Sonic
|-
|Ray
|-
|Tails
|-
|Knuckles
|-
|Amy
|-
|Tangle
|-
|Rouge
|-
|Blaze
|-
|Sally
|-
|Marine
|-
|Mina
|-
|Tikal
|}

===Live meeting or tour event table four===
{|class="wikitable sortable"
!Star/personality!!Age upon appearance in one live event so far of some licensed Japanese-American live star meetings/tours!!Age upon appearance in two live events so far of some licensed Japanese-American live star meetings/tours!!Age upon appearance in five live events so far of some licensed Japanese-American live star meetings/tours!!Age upon appearance in ten live events so far of some licensed Japanese-American live star meetings/tours!!Age upon appearance in 25 live events so far of some licensed Japanese-American live star meetings/tours!!Age upon appearance in 50 live events so far of some licensed Japanese-American live star meetings/tours!!Age upon appearance in 100 live events so far of some licensed Japanese-American live star meetings/tours!!Age upon appearance in 250 live events so far of some licensed Japanese-American live star meetings/tours!!Age upon appearance in 500 live events so far of some licensed Japanese-American live star meetings/tours!!Age upon appearance in 1,000 live events so far of some licensed Japanese-American live star meetings/tours!!Age upon appearance in 2,000 live events so far of some licensed Japanese-American live star meetings/tours!!Age upon appearance in 5,000 live events so far of some licensed Japanese-American live star meetings/tours
|-
|Shadow||colspan="7"|37||38||40||43||49||68
|-
|Silver||colspan="7"|35||36||38||41||47||66
|-
|Mighty||colspan="7"|37||38||40||43||49||68
|-
|Sonic||colspan="7"|36||37||39||42||48||67
|-
|Ray||colspan="7"|30||31||33||36||42||61
|-
|Tails||colspan="7"|29||30||32||35||41||60
|-
|Knuckles||colspan="7"|36||37||39||42||48||67
|-
|Amy||colspan="7"|32||33||35||38||44||63
|-
|Tangle||colspan="7"|35||36||38||41||47||66
|-
|Rouge||colspan="7"|38||39||41||44||50||69
|-
|Blaze||colspan="7"|35||36||38||41||47||66
|-
|Sally||colspan="7"|36||37||39||42||48||67
|-
|Marine||colspan="7"|28||29||31||34||40||59
|-
|Mina||colspan="7"|37||38||40||43||49||68
|-
|Tikal||colspan="7"|35||36||38||41||47||66
|}

== Live documentary episode tables ==
===Live documentary episode table one===
{|class="wikitable sortable"
!Star/personality!!Date of appearance in some first episodes of licensed Japanese-American live star documentaries!!Date of appearance in some second episodes of licensed Japanese-American live star documentaries!!Date of appearance in some fifth episodes of licensed Japanese-American live star documentaries!!Date of appearance in some tenth episodes of licensed Japanese-American live star documentaries!!Date of appearance in some 25th episodes of licensed Japanese-American live star documentaries!!Date of appearance in some 50th episodes of licensed Japanese-American live star documentaries!!Date of appearance in some 100th episodes of licensed Japanese-American live star documentaries!!Date of appearance in some 250th episodes of licensed Japanese-American live star documentaries!!Date of appearance in some 500th episodes of licensed Japanese-American live star documentaries!!Date of appearance in some 1,000th episodes of licensed Japanese-American live star documentaries!!Date of appearance in some 2,000th episodes of licensed Japanese-American live star documentaries!!Date of appearance in some 5,000th episodes of licensed Japanese-American live star documentaries
|-
|Shadow||rowspan="15"|{{start date and age|2022|4|13}}||rowspan="15"|{{start date and age|2022|4|16}}||rowspan="15"|{{start date and age|2022|4|23}}||rowspan="15"|{{start date and age|2022|5|4}}||rowspan="15"|{{start date and age|2022|6|8}}||rowspan="15"|{{start date and age|2022|8|6}}||rowspan="15"|{{start date and age|2022|11|30}}||rowspan="15"|{{start date and age|2023|11|15}}||rowspan="15"|{{start date and age|2025|6|21}}||rowspan="15"|{{start date and age|2028|8|30}}||rowspan="15"|{{start date and age|2035|1|20}}||rowspan="15"|{{start date and age|2054|3|21}}
|-
|Silver
|-
|Mighty
|-
|Sonic
|-
|Ray
|-
|Tails
|-
|Knuckles
|-
|Amy
|-
|Tangle
|-
|Rouge
|-
|Blaze
|-
|Sally
|-
|Marine
|-
|Mina
|-
|Tikal
|}

===Live documentary episode table two===
{|class="wikitable sortable"
!Star/personality!!Age upon appearance in some first episodes of licensed Japanese-American live star documentaries!!Age upon appearance in some second episodes of licensed Japanese-American live star documentaries!!Age upon appearance in some fifth episodes of licensed Japanese-American live star documentaries!!Age upon appearance in some tenth episodes of licensed Japanese-American live star documentaries!!Age upon appearance in some 25th episodes of licensed Japanese-American live star documentaries!!Age upon appearance in some 50th episodes of licensed Japanese-American live star documentaries!!Age upon appearance in some 100th episodes of licensed Japanese-American live star documentaries!!Age upon appearance in some 250th episodes of licensed Japanese-American live star documentaries!!Age upon appearance in some 500th episodes of licensed Japanese-American live star documentaries!!Age upon appearance in some 1,000th episodes of licensed Japanese-American live star documentaries!!Age upon appearance in some 2,000th episodes of licensed Japanese-American live star documentaries!!Age upon appearance in some 5,000th episodes of licensed Japanese-American live star documentaries
|-
|Shadow||colspan="7"|37||38||40||43||49||68
|-
|Silver||colspan="7"|35||36||38||41||47||66
|-
|Mighty||colspan="7"|37||38||40||43||49||68
|-
|Sonic||colspan="7"|36||37||39||42||48||67
|-
|Ray||colspan="7"|30||31||33||36||42||61
|-
|Tails||colspan="7"|29||30||32||35||41||60
|-
|Knuckles||colspan="7"|36||37||39||42||48||67
|-
|Amy||colspan="7"|32||33||35||38||44||63
|-
|Tangle||colspan="7"|35||36||38||41||47||66
|-
|Rouge||colspan="7"|38||39||41||44||50||69
|-
|Blaze||colspan="7"|35||36||38||41||47||66
|-
|Sally||colspan="7"|36||37||39||42||48||67
|-
|Marine||colspan="7"|28||29||31||34||40||59
|-
|Mina||colspan="7"|37||38||40||43||49||68
|-
|Tikal||colspan="7"|35||36||38||41||47||66
|}

===Live documentary episode table three===
{|class="wikitable sortable"
!Star/personality!!Date of appearance in one episode so far of some licensed Japanese-American live star documentaries!!Date of appearance in two episodes so far of some licensed Japanese-American live star documentaries!!Date of appearance in five episodes so far of some licensed Japanese-American live star documentaries!!Date of appearance in ten episodes so far of some licensed Japanese-American live star documentaries!!Date of appearance in 25 episodes so far of some licensed Japanese-American live star documentaries!!Date of appearance in 50 episodes so far of some licensed Japanese-American live star documentaries!!Date of appearance in 100 episodes so far of some licensed Japanese-American live star documentaries!!Date of appearance in 250 episodes so far of some licensed Japanese-American live star documentaries!!Date of appearance in 500 episodes so far of some licensed Japanese-American live star documentaries!!Date of appearance in 1,000 episodes so far of some licensed Japanese-American live star documentaries!!Date of appearance in 2,000 episodes so far of some licensed Japanese-American live star documentaries!!Date of appearance in 5,000 episodes so far of some licensed Japanese-American live star documentaries
|-
|Shadow||rowspan="15"|{{start date and age|2022|4|13}}||rowspan="15"|{{start date and age|2022|4|16}}||rowspan="15"|{{start date and age|2022|4|23}}||rowspan="15"|{{start date and age|2022|5|4}}||rowspan="15"|{{start date and age|2022|6|8}}||rowspan="15"|{{start date and age|2022|8|6}}||rowspan="15"|{{start date and age|2022|11|30}}||rowspan="15"|{{start date and age|2023|11|15}}||rowspan="15"|{{start date and age|2025|6|21}}||rowspan="15"|{{start date and age|2028|8|30}}||rowspan="15"|{{start date and age|2035|1|20}}||rowspan="15"|{{start date and age|2054|3|21}}
|-
|Silver
|-
|Mighty
|-
|Sonic
|-
|Ray
|-
|Tails
|-
|Knuckles
|-
|Amy
|-
|Tangle
|-
|Rouge
|-
|Blaze
|-
|Sally
|-
|Marine
|-
|Mina
|-
|Tikal
|}

===Live documentary episode table four===
{|class="wikitable sortable"
!Star/personality!!Age upon appearance in one episode so far of some licensed Japanese-American live star documentaries!!Age upon appearance in two episodes so far of some licensed Japanese-American live star documentaries!!Age upon appearance in five episodes so far of some licensed Japanese-American live star documentaries!!Age upon appearance in ten episodes so far of some licensed Japanese-American live star documentaries!!Age upon appearance in 25 episodes so far of some licensed Japanese-American live star documentaries!!Age upon appearance in 50 episodes so far of some licensed Japanese-American live star documentaries!!Age upon appearance in 100 episodes so far of some licensed Japanese-American live star documentaries!!Age upon appearance in 250 episodes so far of some licensed Japanese-American live star documentaries!!Age upon appearance in 500 episodes so far of some licensed Japanese-American live star documentaries!!Age upon appearance in 1,000 episodes so far of some licensed Japanese-American live star documentaries!!Age upon appearance in 2,000 episodes so far of some licensed Japanese-American live star documentaries!!Age upon appearance in 5,000 episodes so far of some licensed Japanese-American live star documentaries
|-
|Shadow||colspan="7"|37||38||40||43||49||68
|-
|Silver||colspan="7"|35||36||38||41||47||66
|-
|Mighty||colspan="7"|37||38||40||43||49||68
|-
|Sonic||colspan="7"|36||37||39||42||48||67
|-
|Ray||colspan="7"|30||31||33||36||42||61
|-
|Tails||colspan="7"|29||30||32||35||41||60
|-
|Knuckles||colspan="7"|36||37||39||42||48||67
|-
|Amy||colspan="7"|32||33||35||38||44||63
|-
|Tangle||colspan="7"|35||36||38||41||47||66
|-
|Rouge||colspan="7"|38||39||41||44||50||69
|-
|Blaze||colspan="7"|35||36||38||41||47||66
|-
|Sally||colspan="7"|36||37||39||42||48||67
|-
|Marine||colspan="7"|28||29||31||34||40||59
|-
|Mina||colspan="7"|37||38||40||43||49||68
|-
|Tikal||colspan="7"|35||36||38||41||47||66
|}

== Live Star Workout Battle tables ==

===Live Star Workout Battle table one===
{|class="wikitable sortable"
!Battle name!!Description!!Inauguration date!!Capacity (regular live events held per battle)!!Capacity (live bonus events held per battle)!!Period (regular live battle events)!!Period (live bonus battle events)!!Age status (Japanese-American stars)
|-
|Live Japan-United States Star Workout Battle||Licensed Japanese-American annual live star workout battle featuring Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal indefinitely as Japanese-American stars everywhere in multiple American and Japanese cities or urban areas on Wednesdays and weekends||{{start date and age|2022|4|13}}||25 regular live workout battle events held per battle occurring every year||Two live bonus workout battle events held per battle occurring every year||Wednesdays and weekends ranging between the second or third Wednesday in April and the first or second Wednesday in June every year||Second or third Saturday and second or third Sunday in June every year||Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal getting older in later live workout battle events
|}

===Live Star Workout Battle table two===
{|class="wikitable sortable
!Battle edition!!Description!!Count of regular live events!!Count of live bonus events!!First regular live event date!!Final regular live event date!!Live bonus event date!!Other live bonus event date
|-
|Live Japan-United States Star Workout Battle 2022||First Live Japan-United States Star Workout Battle edition featuring Shadow at age 37, Silver at age 35, Mighty at age 37, Sonic at age 36, Ray at age 30, Tails at age 29, Knuckles at age 36, Amy at age 32, Tangle at age 35, Rouge at age 38, Blaze at age 35, Sally at age 36, Marine at age 28, Mina at age 37 and Tikal at age 35||25 regular live workout battle events (live workout battle events #1-25)||Two live bonus workout battle events (first and second live bonus workout battle events)||{{start date and age|2022|4|13}}||{{start date and age|2022|6|8}}||{{start date and age|2022|6|11}}||{{start date and age|2022|6|12}}
|-
|Live Japan-United States Star Workout Battle 2023||Second Live Japan-United States Star Workout Battle edition featuring Shadow at age 38, Silver at age 36, Mighty at age 38, Sonic at age 37, Ray at age 31, Tails at age 30, Knuckles at age 37, Amy at age 33, Tangle at age 36, Rouge at age 39, Blaze at age 36, Sally at age 37, Marine at age 29, Mina at age 38 and Tikal at age 36||25 regular live workout battle events (live workout battle events #26-50)||Two live bonus workout battle events (third and fourth live bonus workout battle events)||{{start date and age|2023|4|12}}||{{start date and age|2023|6|7}}||{{start date and age|2023|6|10}}||{{start date and age|2023|6|11}}
|-
|Live Japan-United States Star Workout Battle 2024||Third and current Live Japan-United States Star Workout Battle edition featuring or scheduled to feature Shadow at age 39, Silver at age 37, Mighty at age 39, Sonic at age 38, Ray at age 32, Tails at age 31, Knuckles at age 38, Amy at age 34, Tangle at age 37, Rouge at age 40, Blaze at age 37, Sally at age 38, Marine at age 30, Mina at age 39 and Tikal at age 37||25 regular live workout battle events (live workout battle events #51-75)||Two live bonus workout battle events (fifth and sixth live bonus workout battle events)||{{start date and age|2024|4|17}}||{{start date and age|2024|6|12}}||{{start date and age|2024|6|15}}||{{start date and age|2024|6|16}}
|-
|Live Japan-United States Star Workout Battle 2025||Fourth Live Japan-United States Star Workout Battle edition scheduled to feature Shadow at age 40, Silver at age 38, Mighty at age 40, Sonic at age 39, Ray at age 33, Tails at age 32, Knuckles at age 39, Amy at age 35, Tangle at age 38, Rouge at age 41, Blaze at age 38, Sally at age 39, Marine at age 31, Mina at age 40 and Tikal at age 38||25 regular live workout battle events (live workout battle events #76-100)||Two live bonus workout battle events (seventh and eighth live bonus workout battle events)||{{start date and age|2025|4|16}}||{{start date and age|2025|6|11}}||{{start date and age|2025|6|14}}||{{start date and age|2025|6|15}}
|-
|Live Japan-United States Star Workout Battle 2026||Fifth Live Japan-United States Star Workout Battle edition scheduled to feature Shadow at age 41, Silver at age 39, Mighty at age 41, Sonic at age 40, Ray at age 34, Tails at age 33, Knuckles at age 40, Amy at age 36, Tangle at age 39, Rouge at age 42, Blaze at age 39, Sally at age 40, Marine at age 32, Mina at age 41 and Tikal at age 39||25 regular live workout battle events (live workout battle events #101-125)||Two live bonus workout battle events (ninth and tenth live workout battle bonus events)||{{start date and age|2026|4|15}}||{{start date and age|2026|6|10}}||{{start date and age|2026|6|13}}||{{start date and age|2026|6|14}}
|-
|Live Japan-United States Star Workout Battle 2027||Sixth Live Japan-United States Star Workout Battle edition scheduled to feature Shadow at age 42, Silver at age 40, Mighty at age 42, Sonic at age 41, Ray at age 35, Tails at age 34, Knuckles at age 41, Amy at age 37, Tangle at age 40, Rouge at age 43, Blaze at age 40, Sally at age 41, Marine at age 33, Mina at age 42 and Tikal at age 40||25 regular live workout battle events (live workout battle events #126-150)||Two live bonus workout battle events (11th and 12th live bonus workout battle events)||{{start date and age|2027|4|14}}||{{start date and age|2027|6|9}}||{{start date and age|2027|6|12}}||{{start date and age|2027|6|13}}
|-
|Live Japan-United States Star Workout Battle 2028||Seventh Live Japan-United States Star Workout Battle edition scheduled to feature Shadow at age 43, Silver at age 41, Mighty at age 43, Sonic at age 42, Ray at age 36, Tails at age 35, Knuckles at age 42, Amy at age 38, Tangle at age 41, Rouge at age 44, Blaze at age 41, Sally at age 42, Marine at age 34, Mina at age 43 and Tikal at age 41||25 regular live workout battle events (live workout battle events #151-175)||Two live bonus workout battle events (13th and 14th live bonus workout battle events)||{{start date and age|2028|4|12}}||{{start date and age|2028|6|7}}||{{start date and age|2028|6|10}}||{{start date and age|2028|6|11}}
|-
|Live Japan-United States Star Workout Battle 2029||Eighth Live Japan-United States Star Workout Battle edition scheduled to feature Shadow at age 44, Silver at age 42, Mighty at age 44, Sonic at age 43, Ray at age 37, Tails at age 36, Knuckles at age 43, Amy at age 39, Tangle at age 42, Rouge at age 45, Blaze at age 42, Sally at age 43, Marine at age 35, Mina at age 44 and Tikal at age 42||25 regular live workout battle events (live workout battle events #176-200)||Two live bonus workout battle events (15th and 16th live bonus workout battle events)||{{start date and age|2029|4|11}}||{{start date and age|2029|6|6}}||{{start date and age|2029|6|9}}||{{start date and age|2029|6|10}}
|-
|Live Japan-United States Star Workout Battle 2030||Ninth Live Japan-United States Star Workout Battle edition scheduled to feature Shadow at age 45, Silver at age 43, Mighty at age 45, Sonic at age 44, Ray at age 38, Tails at age 37, Knuckles at age 44, Amy at age 40, Tangle at age 43, Rouge at age 46, Blaze at age 43, Sally at age 44, Marine at age 36, Mina at age 45 and Tikal at age 43||25 regular live workout battle events (live workout battle events #201-225)||Two live bonus workout battle events (17th and 18th live bonus workout battle events)||{{start date and age|2030|4|17}}||{{start date and age|2030|6|12}}||{{start date and age|2030|6|15}}||{{start date and age|2030|6|16}}
|-
|Live Japan-United States Star Workout Battle 2031||Tenth Live Japan-United States Star Workout Battle edition scheduled to feature Shadow at age 46, Silver at age 44, Mighty at age 46, Sonic at age 45, Ray at age 39, Tails at age 38, Knuckles at age 45, Amy at age 41, Tangle at age 44, Rouge at age 47, Blaze at age 44, Sally at age 45, Marine at age 37, Mina at age 46 and Tikal at age 44||25 regular live workout battle events (live workout battle events #226-250)||Two live bonus workout battle events (19th and 20th live bonus workout battle events)||{{start date and age|2031|4|16}}||{{start date and age|2031|6|11}}||{{start date and age|2031|6|14}}||{{start date and age|2031|6|15}}
|-
|Live Japan-United States Star Workout Battle 2032||11th Live Japan-United States Star Workout Battle edition scheduled to feature Shadow at age 47, Silver at age 45, Mighty at age 47, Sonic at age 46, Ray at age 40, Tails at age 39, Knuckles at age 46, Amy at age 42, Tangle at age 45, Rouge at age 48, Blaze at age 45, Sally at age 46, Marine at age 38, Mina at age 47 and Tikal at age 45||25 regular live workout battle events (live workout battle events #251-275)||Two live bonus workout battle events (21st and 22nd live bonus workout battle events)||{{start date and age|2032|4|14}}||{{start date and age|2032|6|9}}||{{start date and age|2032|6|12}}||{{start date and age|2032|6|13}}
|-
|Live Japan-United States Star Workout Battle 2033||12th Live Japan-United States Star Workout Battle edition scheduled to feature Shadow at age 48, Silver at age 46, Mighty at age 48, Sonic at age 47, Ray at age 41, Tails at age 40, Knuckles at age 47, Amy at age 43, Tangle at age 46, Rouge at age 49, Blaze at age 46, Sally at age 47, Marine at age 39, Mina at age 48 and Tikal at age 46||25 regular live workout battle events (live workout battle events #276-300)||Two live bonus workout battle events (23rd and 24th live bonus workout battle events)||{{start date and age|2033|4|13}}||{{start date and age|2033|6|8}}||{{start date and age|2033|6|11}}||{{start date and age|2033|6|12}}
|-
|Live Japan-United States Star Workout Battle 2034||13th Live Japan-United States Star Workout Battle edition scheduled to feature Shadow at age 49, Silver at age 47, Mighty at age 49, Sonic at age 48, Ray at age 42, Tails at age 41, Knuckles at age 48, Amy at age 44, Tangle at age 47, Rouge at age 50, Blaze at age 47, Sally at age 48, Marine at age 40, Mina at age 49 and Tikal at age 47||25 regular live workout battle events (live workout battle events #301-325)||Two live bonus workout battle events (25th and 26th live bonus workout battle events)||{{start date and age|2034|4|12}}||{{start date and age|2034|6|7}}||{{start date and age|2034|6|10}}||{{start date and age|2034|6|11}}
|-
|Live Japan-United States Star Workout Battle 2035||14th Live Japan-United States Star Workout Battle edition scheduled to feature Shadow at age 50, Silver at age 48, Mighty at age 50, Sonic at age 49, Ray at age 43, Tails at age 42, Knuckles at age 49, Amy at age 45, Tangle at age 48, Rouge at age 51, Blaze at age 48, Sally at age 49, Marine at age 41, Mina at age 50 and Tikal at age 48||25 regular live workout battle events (live workout battle events #326-350)||Two live bonus workout battle events (27th and 28th live bonus workout battle events)||{{start date and age|2035|4|11}}||{{start date and age|2035|6|6}}||{{start date and age|2035|6|9}}||{{start date and age|2035|6|10}}
|-
|Live Japan-United States Star Workout Battle 2036||15th Live Japan-United States Star Workout Battle edition scheduled to feature Shadow at age 51, Silver at age 49, Mighty at age 51, Sonic at age 50, Ray at age 44, Tails at age 43, Knuckles at age 50, Amy at age 46, Tangle at age 49, Rouge at age 52, Blaze at age 49, Sally at age 50, Marine at age 42, Mina at age 51 and Tikal at age 49||25 regular live workout battle events (live workout battle events #351-375)||Two live bonus workout battle events (29th and 30th live bonus workout battle events)||{{start date and age|2036|4|16}}||{{start date and age|2036|6|11}}||{{start date and age|2036|6|14}}||{{start date and age|2036|6|15}}
|-
|Live Japan-United States Star Workout Battle 2037||16th Live Japan-United States Star Workout Battle edition scheduled to feature Shadow at age 52, Silver at age 50, Mighty at age 52, Sonic at age 51, Ray at age 45, Tails at age 44, Knuckles at age 51, Amy at age 47, Tangle at age 50, Rouge at age 53, Blaze at age 50, Sally at age 51, Marine at age 43, Mina at age 52 and Tikal at age 50||25 regular live workout battle events (live workout battle events #376-400)||Two live bonus workout battle events (31st and 32nd live bonus workout battle events)||{{start date and age|2037|4|15}}||{{start date and age|2037|6|10}}||{{start date and age|2037|6|13}}||{{start date and age|2037|6|14}}
|-
|Live Japan-United States Star Workout Battle 2038||17th Live Japan-United States Star Workout Battle edition scheduled to feature Shadow at age 53, Silver at age 51, Mighty at age 53, Sonic at age 52, Ray at age 46, Tails at age 45, Knuckles at age 52, Amy at age 48, Tangle at age 51, Rouge at age 54, Blaze at age 51, Sally at age 52, Marine at age 44, Mina at age 53 and Tikal at age 51||25 regular live workout battle events (live workout battle events #401-425)||Two live bonus workout battle events (33rd and 34th live bonus workout battle events)||{{start date and age|2038|4|14}}||{{start date and age|2038|6|9}}||{{start date and age|2038|6|12}}||{{start date and age|2038|6|13}}
|-
|Live Japan-United States Star Workout Battle 2039||18th Live Japan-United States Star Workout Battle edition scheduled to feature Shadow at age 54, Silver at age 52, Mighty at age 54, Sonic at age 53, Ray at age 47, Tails at age 46, Knuckles at age 53, Amy at age 49, Tangle at age 52, Rouge at age 55, Blaze at age 52, Sally at age 53, Marine at age 45, Mina at age 54 and Tikal at age 52||25 regular live workout battle events (live workout battle events #426-450)||Two live bonus workout battle events (35th and 36th live bonus workout battle events)||{{start date and age|2039|4|13}}||{{start date and age|2039|6|8}}||{{start date and age|2039|6|11}}||{{start date and age|2039|6|12}}
|-
|Live Japan-United States Star Workout Battle 2040||19th Live Japan-United States Star Workout Battle edition scheduled to feature Shadow at age 55, Silver at age 53, Mighty at age 55, Sonic at age 54, Ray at age 48, Tails at age 47, Knuckles at age 54, Amy at age 50, Tangle at age 53, Rouge at age 56, Blaze at age 53, Sally at age 54, Marine at age 46, Mina at age 55 and Tikal at age 53||25 regular live workout battle events (live workout battle events #451-475)||Two live bonus workout battle events (37th and 38th live bonus workout battle events)||{{start date and age|2040|4|11}}||{{start date and age|2040|6|6}}||{{start date and age|2040|6|9}}||{{start date and age|2040|6|10}}
|-
|Live Japan-United States Star Workout Battle 2041||20th Live Japan-United States Star Workout Battle edition scheduled to feature Shadow at age 56, Silver at age 54, Mighty at age 56, Sonic at age 55, Ray at age 49, Tails at age 48, Knuckles at age 55, Amy at age 51, Tangle at age 54, Rouge at age 57, Blaze at age 54, Sally at age 55, Marine at age 47, Mina at age 56 and Tikal at age 54||25 regular live workout battle events (live workout battle events #476-500)||Two live bonus workout battle events (39th and 40th live bonus workout battle events)||{{start date and age|2041|4|17}}||{{start date and age|2041|6|12}}||{{start date and age|2041|6|15}}||{{start date and age|2041|6|16}}
|-
|Live Japan-United States Star Workout Battle 2042||21st Live Japan-United States Star Workout Battle edition scheduled to feature Shadow at age 57, Silver at age 55, Mighty at age 57, Sonic at age 56, Ray at age 50, Tails at age 49, Knuckles at age 56, Amy at age 52, Tangle at age 55, Rouge at age 58, Blaze at age 55, Sally at age 56, Marine at age 48, Mina at age 57 and Tikal at age 55||25 regular live workout battle events (live workout battle events #501-525)||Two live bonus workout battle events (41st and 42nd live bonus workout battle events)||{{start date and age|2042|4|16}}||{{start date and age|2042|6|11}}||{{start date and age|2042|6|14}}||{{start date and age|2042|6|15}}
|-
|Live Japan-United States Star Workout Battle 2043||22nd Live Japan-United States Star Workout Battle edition scheduled to feature Shadow at age 58, Silver at age 56, Mighty at age 58, Sonic at age 57, Ray at age 51, Tails at age 50, Knuckles at age 57, Amy at age 53, Tangle at age 56, Rouge at age 59, Blaze at age 56, Sally at age 57, Marine at age 49, Mina at age 58 and Tikal at age 56||25 regular live workout battle events (live workout battle events #526-550)||Two live bonus workout battle events (43rd and 44th live bonus workout battle events)||{{start date and age|2043|4|15}}||{{start date and age|2043|6|10}}||{{start date and age|2043|6|13}}||{{start date and age|2043|6|14}}
|-
|Live Japan-United States Star Workout Battle 2044||23rd Live Japan-United States Star Workout Battle edition scheduled to feature Shadow at age 59, Silver at age 57, Mighty at age 59, Sonic at age 58, Ray at age 52, Tails at age 51, Knuckles at age 58, Amy at age 54, Tangle at age 57, Rouge at age 60, Blaze at age 57, Sally at age 58, Marine at age 50, Mina at age 59 and Tikal at age 57||25 regular live workout battle events (live workout battle events #551-575)||Two live bonus workout battle events (45th and 46th live bonus workout battle events)||{{start date and age|2044|4|13}}||{{start date and age|2044|6|8}}||{{start date and age|2044|6|11}}||{{start date and age|2044|6|12}}
|-
|Live Japan-United States Star Workout Battle 2045||24th Live Japan-United States Star Workout Battle edition scheduled to feature Shadow at age 60, Silver at age 58, Mighty at age 60, Sonic at age 59, Ray at age 53, Tails at age 52, Knuckles at age 59, Amy at age 55, Tangle at age 58, Rouge at age 61, Blaze at age 58, Sally at age 59, Marine at age 51, Mina at age 60 and Tikal at age 58||25 regular live workout battle events (live workout battle events #576-600)||Two live bonus workout battle events (47th and 48th live bonus workout battle events)||{{start date and age|2045|4|12}}||{{start date and age|2045|6|7}}||{{start date and age|2045|6|10}}||{{start date and age|2045|6|11}}
|-
|Live Japan-United States Star Workout Battle 2046||25th Live Japan-United States Star Workout Battle edition scheduled to feature Shadow at age 61, Silver at age 59, Mighty at age 61, Sonic at age 60, Ray at age 54, Tails at age 53, Knuckles at age 60, Amy at age 56, Tangle at age 59, Rouge at age 62, Blaze at age 59, Sally at age 60, Marine at age 52, Mina at age 61 and Tikal at age 59||25 regular live workout battle events (live workout battle events #601-625)||Two live bonus workout battle events (49th and 50th live bonus workout battle events)||{{start date and age|2046|4|11}}||{{start date and age|2046|6|6}}||{{start date and age|2046|6|9}}||{{start date and age|2046|6|10}}
|}

== Live Star Media and Entertainment Contest tables ==

===Live Star Media and Entertainment Contest table one===
{|class="wikitable sortable"
!Contest name!!Description!!Inauguration date!!Capacity (regular live events held per contest)!!Capacity (live bonus events held per contest)!!Period (regular live contest events)!!Period (live bonus contest events)!!Age status (Japanese-American stars)
|-
|Live Japan-United States Star Media and Entertainment Contest||Licensed Japanese-American annual live star media and entertainment contest featuring Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal indefinitely as Japanese-American stars everywhere in multiple American and Japanese cities or urban areas on Wednesdays and weekends||{{start date and age|2022|4|13}}||25 regular live media and entertainment contest events held per contest occurring every year||Two live bonus media and entertainment contest events held per contest occurring every year||Wednesdays and weekends ranging between the second or third Wednesday in April and the first or second Wednesday in June every year||Second or third Saturday and second or third Sunday in June every year||Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal getting older in later live media and entertainment contest events
|}

===Live Star Media and Entertainment Contest table two===
{|class="wikitable sortable
!Contest edition!!Description!!Count of regular live events!!Count of live bonus events!!First regular live event date!!Final regular live event date!!Live bonus event date!!Other live bonus event date
|-
|Live Japan-United States Star Media and Entertainment Contest 2022||First Live Japan-United States Star Media and Entertainment Contest edition featuring Shadow at age 37, Silver at age 35, Mighty at age 37, Sonic at age 36, Ray at age 30, Tails at age 29, Knuckles at age 36, Amy at age 32, Tangle at age 35, Rouge at age 38, Blaze at age 35, Sally at age 36, Marine at age 28, Mina at age 37 and Tikal at age 35||25 regular live media and entertainment contest events (live media and entertainment contest events #1-25)||Two live bonus media and entertainment contest events (first and second live bonus media and entertainment contest events)||{{start date and age|2022|4|13}}||{{start date and age|2022|6|8}}||{{start date and age|2022|6|11}}||{{start date and age|2022|6|12}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2023||Second Live Japan-United States Star Media and Entertainment Contest edition featuring Shadow at age 38, Silver at age 36, Mighty at age 38, Sonic at age 37, Ray at age 31, Tails at age 30, Knuckles at age 37, Amy at age 33, Tangle at age 36, Rouge at age 39, Blaze at age 36, Sally at age 37, Marine at age 29, Mina at age 38 and Tikal at age 36||25 regular live media and entertainment contest events (live media and entertainment contest events #26-50)||Two live bonus media and entertainment contest events (third and fourth live bonus media and entertainment contest events)||{{start date and age|2023|4|12}}||{{start date and age|2023|6|7}}||{{start date and age|2023|6|10}}||{{start date and age|2023|6|11}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2024||Third and current Live Japan-United States Star Media and Entertainment Contest edition featuring or scheduled to feature Shadow at age 39, Silver at age 37, Mighty at age 39, Sonic at age 38, Ray at age 32, Tails at age 31, Knuckles at age 38, Amy at age 34, Tangle at age 37, Rouge at age 40, Blaze at age 37, Sally at age 38, Marine at age 30, Mina at age 39 and Tikal at age 37||25 regular live media and entertainment contest events (live media and entertainment contest events #51-75)||Two live bonus media and entertainment contest events (fifth and sixth live bonus media and entertainment contest events)||{{start date and age|2024|4|17}}||{{start date and age|2024|6|12}}||{{start date and age|2024|6|15}}||{{start date and age|2024|6|16}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2025||Fourth Live Japan-United States Star Media and Entertainment Contest edition scheduled to feature Shadow at age 40, Silver at age 38, Mighty at age 40, Sonic at age 39, Ray at age 33, Tails at age 32, Knuckles at age 39, Amy at age 35, Tangle at age 38, Rouge at age 41, Blaze at age 38, Sally at age 39, Marine at age 31, Mina at age 40 and Tikal at age 38||25 regular live media and entertainment contest events (live media and entertainment contest events #76-100)||Two live bonus media and entertainment contest events (seventh and eighth live bonus media and entertainment contest events)||{{start date and age|2025|4|16}}||{{start date and age|2025|6|11}}||{{start date and age|2025|6|14}}||{{start date and age|2025|6|15}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2026||Fifth Live Japan-United States Star Media and Entertainment Contest edition scheduled to feature Shadow at age 41, Silver at age 39, Mighty at age 41, Sonic at age 40, Ray at age 34, Tails at age 33, Knuckles at age 40, Amy at age 36, Tangle at age 39, Rouge at age 42, Blaze at age 39, Sally at age 40, Marine at age 32, Mina at age 41 and Tikal at age 39||25 regular live media and entertainment contest events (live media and entertainment contest events #101-125)||Two live bonus media and entertainment contest events (ninth and tenth live bonus media and entertainment contest events)||{{start date and age|2026|4|15}}||{{start date and age|2026|6|10}}||{{start date and age|2026|6|13}}||{{start date and age|2026|6|14}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2027||Sixth Live Japan-United States Star Media and Entertainment Contest edition scheduled to feature Shadow at age 42, Silver at age 40, Mighty at age 42, Sonic at age 41, Ray at age 35, Tails at age 34, Knuckles at age 41, Amy at age 37, Tangle at age 40, Rouge at age 43, Blaze at age 40, Sally at age 41, Marine at age 33, Mina at age 42 and Tikal at age 40||25 regular live media and entertainment contest events (live media and entertainment contest events #126-150)||Two live bonus media and entertainment contest events (11th and 12th live bonus media and entertainment contest events)||{{start date and age|2027|4|14}}||{{start date and age|2027|6|9}}||{{start date and age|2027|6|12}}||{{start date and age|2027|6|13}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2028||Seventh Live Japan-United States Star Media and Entertainment Contest edition scheduled to feature Shadow at age 43, Silver at age 41, Mighty at age 43, Sonic at age 42, Ray at age 36, Tails at age 35, Knuckles at age 42, Amy at age 38, Tangle at age 41, Rouge at age 44, Blaze at age 41, Sally at age 42, Marine at age 34, Mina at age 43 and Tikal at age 41||25 regular live media and entertainment contest events (live media and entertainment contest events #151-175)||Two live bonus media and entertainment contest events (13th and 14th live bonus media and entertainment contest events)||{{start date and age|2028|4|12}}||{{start date and age|2028|6|7}}||{{start date and age|2028|6|10}}||{{start date and age|2028|6|11}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2029||Eighth Live Japan-United States Star Media and Entertainment Contest edition scheduled to feature Shadow at age 44, Silver at age 42, Mighty at age 44, Sonic at age 43, Ray at age 37, Tails at age 36, Knuckles at age 43, Amy at age 39, Tangle at age 42, Rouge at age 45, Blaze at age 42, Sally at age 43, Marine at age 35, Mina at age 44 and Tikal at age 42||25 regular live media and entertainment contest events (live media and entertainment contest events #176-200)||Two live bonus media and entertainment contest events (15th and 16th live bonus media and entertainment contest events)||{{start date and age|2029|4|11}}||{{start date and age|2029|6|6}}||{{start date and age|2029|6|9}}||{{start date and age|2029|6|10}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2030||Ninth Live Japan-United States Star Media and Entertainment Contest edition scheduled to feature Shadow at age 45, Silver at age 43, Mighty at age 45, Sonic at age 44, Ray at age 38, Tails at age 37, Knuckles at age 44, Amy at age 40, Tangle at age 43, Rouge at age 46, Blaze at age 43, Sally at age 44, Marine at age 36, Mina at age 45 and Tikal at age 43||25 regular live media and entertainment contest events (live media and entertainment contest events #201-225)||Two live bonus media and entertainment contest events (17th and 18th live bonus media and entertainment contest events)||{{start date and age|2030|4|17}}||{{start date and age|2030|6|12}}||{{start date and age|2030|6|15}}||{{start date and age|2030|6|16}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2031||Tenth Live Japan-United States Star Media and Entertainment Contest edition scheduled to feature Shadow at age 46, Silver at age 44, Mighty at age 46, Sonic at age 45, Ray at age 39, Tails at age 38, Knuckles at age 45, Amy at age 41, Tangle at age 44, Rouge at age 47, Blaze at age 44, Sally at age 45, Marine at age 37, Mina at age 46 and Tikal at age 44||25 regular live media and entertainment contest events (live media and entertainment contest events #226-250)||Two live bonus media and entertainment contest events (19th and 20th live bonus media and entertainment contest events)||{{start date and age|2031|4|16}}||{{start date and age|2031|6|11}}||{{start date and age|2031|6|14}}||{{start date and age|2031|6|15}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2032||11th Live Japan-United States Star Media and Entertainment Contest edition scheduled to feature Shadow at age 47, Silver at age 45, Mighty at age 47, Sonic at age 46, Ray at age 40, Tails at age 39, Knuckles at age 46, Amy at age 42, Tangle at age 45, Rouge at age 48, Blaze at age 45, Sally at age 46, Marine at age 38, Mina at age 47 and Tikal at age 45||25 regular live media and entertainment contest events (live media and entertainment contest events #251-275)||Two live bonus media and entertainment contest events (21st and 22nd live bonus media and entertainment contest events)||{{start date and age|2032|4|14}}||{{start date and age|2032|6|9}}||{{start date and age|2032|6|12}}||{{start date and age|2032|6|13}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2033||12th Live Japan-United States Star Media and Entertainment Contest edition scheduled to feature Shadow at age 48, Silver at age 46, Mighty at age 48, Sonic at age 47, Ray at age 41, Tails at age 40, Knuckles at age 47, Amy at age 43, Tangle at age 46, Rouge at age 49, Blaze at age 46, Sally at age 47, Marine at age 39, Mina at age 48 and Tikal at age 46||25 regular live media and entertainment contest events (live media and entertainment contest events #276-300)||Two live bonus media and entertainment contest events (23rd and 24th live bonus media and entertainment contest events)||{{start date and age|2033|4|13}}||{{start date and age|2033|6|8}}||{{start date and age|2033|6|11}}||{{start date and age|2033|6|12}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2034||13th Live Japan-United States Star Media and Entertainment Contest edition scheduled to feature Shadow at age 49, Silver at age 47, Mighty at age 49, Sonic at age 48, Ray at age 42, Tails at age 41, Knuckles at age 48, Amy at age 44, Tangle at age 47, Rouge at age 50, Blaze at age 47, Sally at age 48, Marine at age 40, Mina at age 49 and Tikal at age 47||25 regular live media and entertainment contest events (live media and entertainment contest events #301-325)||Two live bonus media and entertainment contest events (25th and 26th live bonus media and entertainment contest events)||{{start date and age|2034|4|12}}||{{start date and age|2034|6|7}}||{{start date and age|2034|6|10}}||{{start date and age|2034|6|11}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2035||14th Live Japan-United States Star Media and Entertainment Contest edition scheduled to feature Shadow at age 50, Silver at age 48, Mighty at age 50, Sonic at age 49, Ray at age 43, Tails at age 42, Knuckles at age 49, Amy at age 45, Tangle at age 48, Rouge at age 51, Blaze at age 48, Sally at age 49, Marine at age 41, Mina at age 50 and Tikal at age 48||25 regular live media and entertainment contest events (live media and entertainment contest events #326-350)||Two live bonus media and entertainment contest events (27th and 28th live bonus media and entertainment contest events)||{{start date and age|2035|4|11}}||{{start date and age|2035|6|6}}||{{start date and age|2035|6|9}}||{{start date and age|2035|6|10}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2036||15th Live Japan-United States Star Media and Entertainment Contest edition scheduled to feature Shadow at age 51, Silver at age 49, Mighty at age 51, Sonic at age 50, Ray at age 44, Tails at age 43, Knuckles at age 50, Amy at age 46, Tangle at age 49, Rouge at age 52, Blaze at age 49, Sally at age 50, Marine at age 42, Mina at age 51 and Tikal at age 49||25 regular live media and entertainment contest events (live media and entertainment contest events #351-375)||Two live bonus media and entertainment contest events (29th and 30th live bonus media and entertainment contest events)||{{start date and age|2036|4|16}}||{{start date and age|2036|6|11}}||{{start date and age|2036|6|14}}||{{start date and age|2036|6|15}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2037||16th Live Japan-United States Star Media and Entertainment Contest edition scheduled to feature Shadow at age 52, Silver at age 50, Mighty at age 52, Sonic at age 51, Ray at age 45, Tails at age 44, Knuckles at age 51, Amy at age 47, Tangle at age 50, Rouge at age 53, Blaze at age 50, Sally at age 51, Marine at age 43, Mina at age 52 and Tikal at age 50||25 regular live media and entertainment contest events (live media and entertainment contest events #376-400)||Two live bonus media and entertainment contest events (31st and 32nd live bonus media and entertainment contest events)||{{start date and age|2037|4|15}}||{{start date and age|2037|6|10}}||{{start date and age|2037|6|13}}||{{start date and age|2037|6|14}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2038||17th Live Japan-United States Star Media and Entertainment Contest edition scheduled to feature Shadow at age 53, Silver at age 51, Mighty at age 53, Sonic at age 52, Ray at age 46, Tails at age 45, Knuckles at age 52, Amy at age 48, Tangle at age 51, Rouge at age 54, Blaze at age 51, Sally at age 52, Marine at age 44, Mina at age 53 and Tikal at age 51||25 regular live media and entertainment contest events (live media and entertainment contest events #401-425)||Two live bonus media and entertainment contest events (33rd and 34th live bonus media and entertainment contest events)||{{start date and age|2038|4|14}}||{{start date and age|2038|6|9}}||{{start date and age|2038|6|12}}||{{start date and age|2038|6|13}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2039||18th Live Japan-United States Star Media and Entertainment Contest edition scheduled to feature Shadow at age 54, Silver at age 52, Mighty at age 54, Sonic at age 53, Ray at age 47, Tails at age 46, Knuckles at age 53, Amy at age 49, Tangle at age 52, Rouge at age 55, Blaze at age 52, Sally at age 53, Marine at age 45, Mina at age 54 and Tikal at age 52||25 regular live media and entertainment contest events (live media and entertainment contest events #426-450)||Two live bonus media and entertainment contest events (35th and 36th live bonus media and entertainment contest events)||{{start date and age|2039|4|13}}||{{start date and age|2039|6|8}}||{{start date and age|2039|6|11}}||{{start date and age|2039|6|12}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2040||19th Live Japan-United States Star Media and Entertainment Contest edition scheduled to feature Shadow at age 55, Silver at age 53, Mighty at age 55, Sonic at age 54, Ray at age 48, Tails at age 47, Knuckles at age 54, Amy at age 50, Tangle at age 53, Rouge at age 56, Blaze at age 53, Sally at age 54, Marine at age 46, Mina at age 55 and Tikal at age 53||25 regular live media and entertainment contest events (live media and entertainment contest events #451-475)||Two live bonus media and entertainment contest events (37th and 38th live bonus media and entertainment contest events)||{{start date and age|2040|4|11}}||{{start date and age|2040|6|6}}||{{start date and age|2040|6|9}}||{{start date and age|2040|6|10}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2041||20th Live Japan-United States Star Media and Entertainment Contest edition scheduled to feature Shadow at age 56, Silver at age 54, Mighty at age 56, Sonic at age 55, Ray at age 49, Tails at age 48, Knuckles at age 55, Amy at age 51, Tangle at age 54, Rouge at age 57, Blaze at age 54, Sally at age 55, Marine at age 47, Mina at age 56 and Tikal at age 54||25 regular live media and entertainment contest events (live media and entertainment contest events #476-500)||Two live bonus media and entertainment contest events (39th and 40th live bonus media and entertainment contest events)||{{start date and age|2041|4|17}}||{{start date and age|2041|6|12}}||{{start date and age|2041|6|15}}||{{start date and age|2041|6|16}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2042||21st Live Japan-United States Star Media and Entertainment Contest edition scheduled to feature Shadow at age 57, Silver at age 55, Mighty at age 57, Sonic at age 56, Ray at age 50, Tails at age 49, Knuckles at age 56, Amy at age 52, Tangle at age 55, Rouge at age 58, Blaze at age 55, Sally at age 56, Marine at age 48, Mina at age 57 and Tikal at age 55||25 regular live media and entertainment contest events (live media and entertainment contest events #501-525)||Two live bonus media and entertainment contest events (41st and 42nd live bonus media and entertainment contest events)||{{start date and age|2042|4|16}}||{{start date and age|2042|6|11}}||{{start date and age|2042|6|14}}||{{start date and age|2042|6|15}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2043||22nd Live Japan-United States Star Media and Entertainment Contest edition scheduled to feature Shadow at age 58, Silver at age 56, Mighty at age 58, Sonic at age 57, Ray at age 51, Tails at age 50, Knuckles at age 57, Amy at age 53, Tangle at age 56, Rouge at age 59, Blaze at age 56, Sally at age 57, Marine at age 49, Mina at age 58 and Tikal at age 56||25 regular live media and entertainment contest events (live media and entertainment contest events #526-550)||Two live bonus media and entertainment contest events (43rd and 44th live bonus media and entertainment contest events)||{{start date and age|2043|4|15}}||{{start date and age|2043|6|10}}||{{start date and age|2043|6|13}}||{{start date and age|2043|6|14}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2044||23rd Live Japan-United States Star Media and Entertainment Contest edition scheduled to feature Shadow at age 59, Silver at age 57, Mighty at age 59, Sonic at age 58, Ray at age 52, Tails at age 51, Knuckles at age 58, Amy at age 54, Tangle at age 57, Rouge at age 60, Blaze at age 57, Sally at age 58, Marine at age 50, Mina at age 59 and Tikal at age 57||25 regular live media and entertainment contest events (live media and entertainment contest events #551-575)||Two live bonus media and entertainment contest events (45th and 46th live bonus media and entertainment contest events)||{{start date and age|2044|4|13}}||{{start date and age|2044|6|8}}||{{start date and age|2044|6|11}}||{{start date and age|2044|6|12}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2045||24th Live Japan-United States Star Media and Entertainment Contest edition scheduled to feature Shadow at age 60, Silver at age 58, Mighty at age 60, Sonic at age 59, Ray at age 53, Tails at age 52, Knuckles at age 59, Amy at age 55, Tangle at age 58, Rouge at age 61, Blaze at age 58, Sally at age 59, Marine at age 51, Mina at age 60 and Tikal at age 58||25 regular live media and entertainment contest events (live media and entertainment contest events #576-600)||Two live bonus media and entertainment contest events (47th and 48th live bonus media and entertainment contest events)||{{start date and age|2045|4|12}}||{{start date and age|2045|6|7}}||{{start date and age|2045|6|10}}||{{start date and age|2045|6|11}}
|-
|Live Japan-United States Star Media and Entertainment Contest 2046||25th Live Japan-United States Star Media and Entertainment Contest edition scheduled to feature Shadow at age 61, Silver at age 59, Mighty at age 61, Sonic at age 60, Ray at age 54, Tails at age 53, Knuckles at age 60, Amy at age 56, Tangle at age 59, Rouge at age 62, Blaze at age 59, Sally at age 60, Marine at age 52, Mina at age 61 and Tikal at age 59||25 regular live media and entertainment contest events (live media and entertainment contest events #601-625)||Two live bonus media and entertainment contest events (49th and 50th live bonus media and entertainment contest events)||{{start date and age|2046|4|11}}||{{start date and age|2046|6|6}}||{{start date and age|2046|6|9}}||{{start date and age|2046|6|10}}
|}

==Outpost operation, criminal attack prevention and smoking or tobacco usage penalty or punishment tables==
===Outpost operation table I===
{|class="wikitable sortable"
!Star/personality!!Date of 100 outposts built and made operational for urban defense in the United States and Japan so far!!Date of 200 outposts built and made operational for urban defense in the United States and Japan so far!!Date of 500 outposts built and made operational for urban defense in the United States and Japan so far!!Date of 1,000 outposts built and made operational for urban defense in the United States and Japan so far!!Date of 2,500 outposts built and made operational for urban defense in the United States and Japan so far!!Date of 5,000 outposts built and made operational for urban defense in the United States and Japan so far!!Date of 10,000 outposts built and made operational for urban defense in the United States and Japan so far!!Date of 25,000 outposts built and made operational for urban defense in the United States and Japan so far!!Date of 50,000 outposts built and made operational for urban defense in the United States and Japan so far!!Date of 100,000 outposts scheduled to be built and made operational for urban defense in the United States and Japan so far!!Date of 200,000 outposts scheduled to be built and made operational for urban defense in the United States and Japan so far!!Date of 500,000 outposts scheduled to be built and made operational for urban defense in the United States and Japan so far!!Date of a million outposts scheduled to be built and made operational for urban defense in the United States and Japan so far
|-
|Shadow||rowspan="15"|{{start date and age|2022|4|13}}||rowspan="15"|{{start date and age|2022|4|14}}||rowspan="15"|{{start date and age|2022|4|17}}||rowspan="15"|{{start date and age|2022|4|22}}||rowspan="15"|{{start date and age|2022|5|7}}||rowspan="15"|{{start date and age|2022|6|1}}||rowspan="15"|{{start date and age|2022|7|21}}||rowspan="15"|{{start date and age|2022|12|18}}||rowspan="15"|{{start date and age|2023|8|25}}||rowspan="15"|{{start date and age|2025|1|6}}||rowspan="15"|{{start date and age|2027|10|3}}||rowspan="15"|{{start date and age|2035|12|20}}||rowspan="15"|{{start date and age|2049|8|28}}
|-
|Silver
|-
|Mighty
|-
|Sonic
|-
|Ray
|-
|Tails
|-
|Knuckles
|-
|Amy
|-
|Tangle
|-
|Rouge
|-
|Blaze
|-
|Sally
|-
|Marine
|-
|Mina
|-
|Tikal
|}

===Outpost operation table II===
{|class="wikitable sortable"
!Star/personality!!Age upon building 100 outposts and making them operational for urban defense in the United States and Japan so far!!Age upon building 200 outposts and making them operational for urban defense in the United States and Japan so far!!Age upon building 500 outposts and making them operational for urban defense in the United States and Japan so far!!Age upon building 1,000 outposts and making them operational for urban defense in the United States and Japan so far!!Age upon building 2,500 outposts and making them operational for urban defense in the United States and Japan so far!!Age upon building 5,000 outposts and making them operational for urban defense in the United States and Japan so far!!Age upon building 10,000 outposts and making them operational for urban defense in the United States and Japan so far!!Age upon building 25,000 outposts and making them operational for urban defense in the United States and Japan so far!!Age upon building 50,000 outposts and making them operational for urban defense in the United States and Japan so far!!Age upon being scheduled to build 100,000 outposts and make them operational for urban defense in the United States and Japan so far!!Age upon being scheduled to build 200,000 outposts and make them operational for urban defense in the United States and Japan so far!!Age upon being scheduled to build 500,000 outposts and make them operational for urban defense in the United States and Japan so far!!Age upon being scheduled to build a million outposts and make them operational for urban defense in the United States and Japan so far
|-
|Shadow||colspan="8"|37||38||39||42||50||64
|-
|Silver||colspan="8"|35||36||37||40||48||62
|-
|Mighty||colspan="8"|37||38||39||42||50||64
|-
|Sonic||colspan="8"|36||37||38||41||49||63
|-
|Ray||colspan="8"|30||31||32||35||43||57
|-
|Tails||colspan="8"|29||30||31||34||42||56
|-
|Knuckles||colspan="8"|36||37||38||41||49||63
|-
|Amy||colspan="8"|32||33||34||37||45||59
|-
|Tangle||colspan="8"|35||36||37||40||48||62
|-
|Rouge||colspan="8"|38||39||40||43||51||65
|-
|Blaze||colspan="8"|35||36||37||40||48||62
|-
|Sally||colspan="8"|36||37||38||41||49||63
|-
|Marine||colspan="8"|28||29||30||33||41||55
|-
|Mina||colspan="8"|37||38||39||42||50||64
|-
|Tikal||colspan="8"|35||36||37||40||48||62
|}

===Outpost operation table III===
{|class="wikitable sortable"
!Count of outposts built and made operational for urban defense in the United States and Japan every day!!Date of first outposts built and made operational for urban defense in the United States and Japan!!Outpost builder/operator #1!!Outpost builder/operator #2!!Outpost builder/operator #3!!Outpost builder/operator #4!!Outpost builder/operator #5!!Outpost builder/operator #6!!Outpost builder/operator #7!!Outpost builder/operator #8!!Outpost builder/operator #9!!Outpost builder/operator #10!!Outpost builder/operator #11!!Outpost builder/operator #12!!Outpost builder/operator #13!!Outpost builder/operator #14!!Outpost builder/operator #15
|-
|100 every day starting on April 13, 2022||{{start date and age|2022|4|13}}||Shadow (since April 13, 2022)||Silver (since April 13, 2022)||Mighty (since April 13, 2022)||Sonic (since April 13, 2022)||Ray (since April 13, 2022)||Tails (since April 13, 2022)||Knuckles (since April 13, 2022)||Amy (since April 13, 2022)||Tangle (since April 13, 2022)||Rouge (since April 13, 2022)||Blaze (since April 13, 2022)||Sally (since April 13, 2022)||Marine (since April 13, 2022)||Mina (since April 13, 2022)||Tikal (since April 13, 2022)
|}

===Criminal attack prevention table I===
{|class="wikitable sortable"
!Star/personality!!Date of 100,000 criminal attacks prevented in the United States and Japan so far!!Date of 200,000 criminal attacks prevented in the United States and Japan so far!!Date of 500,000 criminal attacks prevented in the United States and Japan so far!!Date of a million criminal attacks prevented in the United States and Japan so far!!Date of two and a half million criminal attacks prevented in the United States and Japan so far!!Date of five million criminal attacks prevented in the United States and Japan so far!!Date of ten million criminal attacks prevented in the United States and Japan so far!!Date of 25 million criminal attacks prevented in the United States and Japan so far!!Date of 50 million criminal attacks prevented in the United States and Japan so far!!Date of 100 million criminal attacks scheduled to be prevented in the United States and Japan so far!!Date of 200 million criminal attacks scheduled to be prevented in the United States and Japan so far!!Date of 500 million criminal attacks scheduled to be prevented in the United States and Japan so far!!Date of a billion criminal attacks scheduled to be prevented in the United States and Japan so far
|-
|Shadow||rowspan="15"|{{start date and age|2022|4|13}}||rowspan="15"|{{start date and age|2022|4|14}}||rowspan="15"|{{start date and age|2022|4|17}}||rowspan="15"|{{start date and age|2022|4|22}}||rowspan="15"|{{start date and age|2022|5|7}}||rowspan="15"|{{start date and age|2022|6|1}}||rowspan="15"|{{start date and age|2022|7|21}}||rowspan="15"|{{start date and age|2022|12|18}}||rowspan="15"|{{start date and age|2023|8|25}}||rowspan="15"|{{start date and age|2025|1|6}}||rowspan="15"|{{start date and age|2027|10|3}}||rowspan="15"|{{start date and age|2035|12|20}}||rowspan="15"|{{start date and age|2049|8|28}}
|-
|Silver
|-
|Mighty
|-
|Sonic
|-
|Ray
|-
|Tails
|-
|Knuckles
|-
|Amy
|-
|Tangle
|-
|Rouge
|-
|Blaze
|-
|Sally
|-
|Marine
|-
|Mina
|-
|Tikal
|}

===Criminal attack prevention table II===
{|class="wikitable sortable"
!Star/personality!!Age upon preventing 100,000 criminal attacks in the United States and Japan so far!!Age upon preventing 200,000 criminal attacks in the United States and Japan so far!!Age upon preventing 500,000 criminal attacks in the United States and Japan so far!!Age upon preventing a million criminal attacks in the United States and Japan so far!!Age upon preventing two and a half million criminal attacks in the United States and Japan so far!!Age upon preventing five million criminal attacks in the United States and Japan so far!!Age upon preventing ten million criminal attacks in the United States and Japan so far!!Age upon preventing in the United States and Japan 25 million criminal attacks so far!!Age upon preventing 50 million criminal attacks in the United States and Japan so far!!Age upon being scheduled to prevent 100 million criminal attacks in the United States and Japan so far!!Age upon being scheduled to prevent 200 million criminal attacks in the United States and Japan so far!!Age upon being scheduled to prevent 500 million criminal attacks in the United States and Japan so far!!Age upon being scheduled to prevent a billion criminal attacks in the United States and Japan so far
|-
|Shadow||colspan="8"|37||38||39||42||50||64
|-
|Silver||colspan="8"|35||36||37||40||48||62
|-
|Mighty||colspan="8"|37||38||39||42||50||64
|-
|Sonic||colspan="8"|36||37||38||41||49||63
|-
|Ray||colspan="8"|30||31||32||35||43||57
|-
|Tails||colspan="8"|29||30||31||34||42||56
|-
|Knuckles||colspan="8"|36||37||38||41||49||63
|-
|Amy||colspan="8"|32||33||34||37||45||59
|-
|Tangle||colspan="8"|35||36||37||40||48||62
|-
|Rouge||colspan="8"|38||39||40||43||51||65
|-
|Blaze||colspan="8"|35||36||37||40||48||62
|-
|Sally||colspan="8"|36||37||38||41||49||63
|-
|Marine||colspan="8"|28||29||30||33||41||55
|-
|Mina||colspan="8"|37||38||39||42||50||64
|-
|Tikal||colspan="8"|35||36||37||40||48||62
|}

===Criminal attack prevention table III===
{|class="wikitable sortable"
!Count of criminal attacks prevented in the United States and Japan every day!!Date of first criminal attacks prevented in the United States and Japan!!Criminal attack prevention expert/master/professional #1!!Criminal attack prevention expert/master/professional #2!!Criminal attack prevention expert/master/professional #3!!Criminal attack prevention expert/master/professional #4!!Criminal attack prevention expert/master/professional #5!!Criminal attack prevention expert/master/professional #6!!Criminal attack prevention expert/master/professional #7!!Criminal attack prevention expert/master/professional #8!!Criminal attack prevention expert/master/professional #9!!Criminal attack prevention expert/master/professional #10!!Criminal attack prevention expert/master/professional #11!!Criminal attack prevention expert/master/professional #12!!Criminal attack prevention expert/master/professional #13!!Criminal attack prevention expert/master/professional #14!! Criminal attack prevention expert/master/professional #15
|-
|100 every day starting on April 13, 2022||{{start date and age|2022|4|13}}||Shadow (since April 13, 2022)||Silver (since April 13, 2022)||Mighty (since April 13, 2022)||Sonic (since April 13, 2022)||Ray (since April 13, 2022)||Tails (since April 13, 2022)||Knuckles (since April 13, 2022)||Amy (since April 13, 2022)||Tangle (since April 13, 2022)||Rouge (since April 13, 2022)||Blaze (since April 13, 2022)||Sally (since April 13, 2022)||Marine (since April 13, 2022)||Mina (since April 13, 2022)||Tikal (since April 13, 2022)
|}

===New outpost operation and criminal attack prevention table===
{|class="wikitable sortable
!Star/personality!!Outpost operation status!!Criminal attack prevention status!!Age upon starting to build outposts and make them operational for urban defense!!Age upon starting to prevent criminal attacks
|-
|Shadow||rowspan="15"|Building outposts and making them operational for urban defense indefinitely in the United States and Japan since April 13, 2022<br>Continuing to build outposts and make them operational for urban defense in the United States and Japan for many years in obedience to the announcement on June 8, 2022||rowspan="15"|Defending the United States and Japan against criminal attacks indefinitely since April 13, 2022<br>Continuing to defend the United States and Japan against criminal attacks for many years in obedience to the announcement on June 8, 2022||colspan="2"|37
|-
|Silver||colspan="2"|35
|-
|Mighty||colspan="2"|37
|-
|Sonic||colspan="2"|36
|-
|Ray||colspan="2"|30
|-
|Tails||colspan="2"|29
|-
|Knuckles||colspan="2"|36
|-
|Amy||colspan="2"|32
|-
|Tangle||colspan="2"|35
|-
|Rouge||colspan="2"|38
|-
|Blaze||colspan="2"|35
|-
|Sally||colspan="2"|36
|-
|Marine||colspan="2"|28
|-
|Mina||colspan="2"|37
|-
|Tikal||colspan="2"|35
|}

===Table focusing on smoking as the act punishable by up to 40 years in prison only in the United States and Japan===
{|class="wikitable sortable"
!Act!!Status!!Maximum penalty or punishment
|-
|Smoking||Completely illegal since April 13, 2022 (United States and Japan only)||40 years of imprisonment starting on April 13, 2022 (United States and Japan only)
|}

===Table focusing on tobacco usage as the act punishable by up to 40 years in prison only in the United States and Japan===
{|class="wikitable sortable"
!Act!!Status!!Maximum penalty or punishment
|-
|Tobacco usage||Completely illegal since April 13, 2022 (United States and Japan only)||40 years of imprisonment starting on April 13, 2022 (United States and Japan only)
|}

===Table focusing on the United States and Japan as anti-tobacco countries===
{|class="wikitable sortable"
!Country!!Anti-tobacco country
|-
|{{flagicon|USA}} United States||rowspan="2" {{Yes}} (since April 13, 2022)
|-
|{{flagicon|JPN}} Japan
|}

===Table focusing on the United States and Japan as tobacco-hating countries===
{|class="wikitable sortable"
!Country!!Tobacco-hating country
|-
|{{flagicon|USA}} United States||rowspan="2" {{Yes}} (since April 13, 2022)
|-
|{{flagicon|JPN}} Japan
|}

===Table focusing on the anti-tobacco law===
{|class="wikitable sortable"
!Law!!Date of imposition/enforcement!!Status
|-
|Anti-tobacco law||{{start date and age|2022|4|13}}||Effective or in effect since April 13, 2022 (United States and Japan only)
|}

===Table focusing on tobacco-hating stars===
{|class="wikitable sortable"
!Tobacco-hating star #1!!Tobacco-hating star #2!!Tobacco-hating star #3!!Tobacco-hating star #4!!Tobacco-hating star #5!!Tobacco-hating star #6!!Tobacco-hating star #7!!Tobacco-hating star #8!!Tobacco-hating star #9!!Tobacco-hating star #10!!Tobacco-hating star #11!!Tobacco-hating star #12!!Tobacco-hating star #13!!Tobacco-hating star #14!!Tobacco-hating star #15
|-
|Shadow (since April 13, 2022)||Silver (since April 13, 2022)||Mighty (since April 13, 2022)||Sonic (since April 13, 2022)||Ray (since April 13, 2022)||Tails (since April 13, 2022)||Knuckles (since April 13, 2022)||Amy (since April 13, 2022)||Tangle (since April 13, 2022)||Rouge (since April 13, 2022)||Blaze (since April 13, 2022)||Sally (since April 13, 2022)||Marine (since April 13, 2022)||Mina (since April 13, 2022)||Tikal (since April 13, 2022)
|}

== Educational tables ==
=== Table focusing on classes and educational programs ===
{|class="wikitable sortable"
!Class/educational program type!!Description!!First day (featuring Japanese-American stars/personalities as teachers)!!Final day (featuring Japanese-American stars/personalities as teachers
|-
|Class of 2022||First class featuring Shadow at age 37, Silver at age 35, Mighty at age 37, Sonic at age 36, Ray at age 30, Tails at age 29, Knuckles at age 36, Amy at age 32, Tangle at age 35, Rouge at age 38, Blaze at age 35, Sally at age 36, Marine at age 28, Mina at age 37 and Tikal at age 35||{{start date and age|2022|4|13}}||{{start date and age|2022|6|28}}
|-
|Summer program 2022||First summer program featuring Shadow at age 37, Silver at age 35, Mighty at age 37, Sonic at age 36, Ray at age 30, Tails at age 29, Knuckles at age 36, Amy at age 32, Tangle at age 35, Rouge at age 38, Blaze at age 35, Sally at age 36, Marine at age 28, Mina at age 37 and Tikal at age 35||{{start date and age|2022|7|6}}||{{start date and age|2022|8|12}}
|-
|Class of 2023||Second class featuring Shadow at age 37 or 38, Silver at age 35 or 36, Mighty at age 37 or 38, Sonic at age 36 or 37, Ray at age 30 or 31, Tails at age 29 or 30, Knuckles at age 36 or 37, Amy at age 32 or 33, Tangle at age 35 or 36, Rouge at age 38 or 39, Blaze at age 35 or 36, Sally at age 36 or 37, Marine at age 28 or 29, Mina at age 37 or 38 and Tikal at age 35 or 36||{{start date and age|2022|9|8}}||{{start date and age|2023|6|28}}
|-
|Summer program 2023||Second summer program featuring Shadow at age 38, Silver at age 36, Mighty at age 38, Sonic at age 37, Ray at age 31, Tails at age 30, Knuckles at age 37, Amy at age 33, Tangle at age 36, Rouge at age 39, Blaze at age 36, Sally at age 37, Marine at age 29, Mina at age 38 and Tikal at age 36||{{start date and age|2023|7|6}}||{{start date and age|2023|8|14}}
|-
|Class of 2024||Third and current class featuring or scheduled to feature Shadow at age 38 or 39, Silver at age 36 or 37, Mighty at age 38 or 39, Sonic at age 37 or 38, Ray at age 31 or 32, Tails at age 30 or 31, Knuckles at age 37 or 38, Amy at age 33 or 34, Tangle at age 36 or 37, Rouge at age 39 or 40, Blaze at age 36 or 37, Sally at age 37 or 38, Marine at age 29 or 30, Mina at age 38 or 39 and Tikal at age 36 or 37||{{start date and age|2023|9|8}}||{{start date and age|2024|6|28}}
|-
|Summer program 2024||Third summer program scheduled to feature Shadow at age 39, Silver at age 37, Mighty at age 39, Sonic at age 38, Ray at age 32, Tails at age 31, Knuckles at age 38, Amy at age 34, Tangle at age 37, Rouge at age 40, Blaze at age 37, Sally at age 38, Marine at age 30, Mina at age 39 and Tikal at age 37||{{start date and age|2024|7|8}}||{{start date and age|2024|8|14}}
|-
|Class of 2025||Fourth class scheduled to feature Shadow at age 39 or 40, Silver at age 37 or 38, Mighty at age 39 or 40, Sonic at age 38 or 39, Ray at age 32 or 33, Tails at age 31 or 32, Knuckles at age 38 or 39, Amy at age 34 or 35, Tangle at age 37 or 38, Rouge at age 40 or 41, Blaze at age 37 or 38, Sally at age 38 or 39, Marine at age 30 or 31, Mina at age 39 or 40 and Tikal at age 37 or 38||{{start date and age|2024|9|9}}||{{start date and age|2025|6|27}}
|-
|Summer program 2025||Fourth summer program scheduled to feature Shadow at age 40, Silver at age 38, Mighty at age 40, Sonic at age 39, Ray at age 33, Tails at age 32, Knuckles at age 39, Amy at age 35, Tangle at age 38, Rouge at age 41, Blaze at age 38, Sally at age 39, Marine at age 31, Mina at age 40 and Tikal at age 38||{{start date and age|2025|7|7}}||{{start date and age|2025|8|14}}
|-
|Class of 2026||Fifth class scheduled to feature Shadow at age 40 or 41, Silver at age 38 or 39, Mighty at age 40 or 41, Sonic at age 39 or 40, Ray at age 33 or 34, Tails at age 32 or 33, Knuckles at age 39 or 40, Amy at age 35 or 36, Tangle at age 38 or 39, Rouge at age 41 or 42, Blaze at age 38 or 39, Sally at age 39 or 40, Marine at age 31 or 32, Mina at age 40 or 41 and Tikal at age 38 or 39||{{start date and age|2025|9|8}}||{{start date and age|2026|6|26}}
|-
|Summer program 2026||Fifth summer program scheduled to feature Shadow at age 41, Silver at age 39, Mighty at age 41, Sonic at age 40, Ray at age 34, Tails at age 33, Knuckles at age 40, Amy at age 36, Tangle at age 39, Rouge at age 42, Blaze at age 39, Sally at age 40, Marine at age 32, Mina at age 41 and Tikal at age 39||{{start date and age|2026|7|6}}||{{start date and age|2026|8|14}}
|-
|Class of 2027||Sixth class scheduled to feature Shadow at age 41 or 42, Silver at age 39 or 40, Mighty at age 41 or 42, Sonic at age 40 or 41, Ray at age 34 or 35, Tails at age 33 or 34, Knuckles at age 40 or 41, Amy at age 36 or 37, Tangle at age 39 or 40, Rouge at age 42 or 43, Blaze at age 39 or 40, Sally at age 40 or 41, Marine at age 32 or 33, Mina at age 41 or 42 and Tikal at age 39 or 40||{{start date and age|2026|9|8}}||{{start date and age|2027|6|28}}
|-
|Summer program 2027||Sixth summer program scheduled to feature Shadow at age 42, Silver at age 40, Mighty at age 42, Sonic at age 41, Ray at age 35, Tails at age 34, Knuckles at age 41, Amy at age 37, Tangle at age 40, Rouge at age 43, Blaze at age 40, Sally at age 41, Marine at age 33, Mina at age 42 and Tikal at age 40||{{start date and age|2027|7|6}}||{{start date and age|2027|8|13}}
|-
|Class of 2028||Seventh class scheduled to feature Shadow at age 42 or 43, Silver at age 40 or 41, Mighty at age 42 or 43, Sonic at age 41 or 42, Ray at age 35 or 36, Tails at age 34 or 35, Knuckles at age 41 or 42, Amy at age 37 or 38, Tangle at age 40 or 41, Rouge at age 43 or 44, Blaze at age 40 or 41, Sally at age 41 or 42, Marine at age 33 or 34, Mina at age 42 or 43 and Tikal at age 40 or 41||{{start date and age|2027|9|8}}||{{start date and age|2028|6|28}}
|-
|Summer program 2028||Seventh summer program scheduled to feature Shadow at age 43, Silver at age 41, Mighty at age 43, Sonic at age 42, Ray at age 36, Tails at age 35, Knuckles at age 42, Amy at age 38, Tangle at age 41, Rouge at age 44, Blaze at age 41, Sally at age 42, Marine at age 34, Mina at age 43 and Tikal at age 41||{{start date and age|2028|7|6}}||{{start date and age|2028|8|14}}
|-
|Class of 2029||Eighth class scheduled to feature Shadow at age 43 or 44, Silver at age 41 or 42, Mighty at age 43 or 44, Sonic at age 42 or 43, Ray at age 36 or 37, Tails at age 35 or 36, Knuckles at age 42 or 43, Amy at age 38 or 39, Tangle at age 41 or 42, Rouge at age 44 or 45, Blaze at age 41 or 42, Sally at age 42 or 43, Marine at age 34 or 35, Mina at age 43 or 44 and Tikal at age 41 or 42||{{start date and age|2028|9|8}}||{{start date and age|2029|6|28}}
|-
|Summer program 2029||Eighth summer program scheduled to feature Shadow at age 44, Silver at age 42, Mighty at age 44, Sonic at age 43, Ray at age 37, Tails at age 36, Knuckles at age 43, Amy at age 39, Tangle at age 42, Rouge at age 45, Blaze at age 42, Sally at age 43, Marine at age 35, Mina at age 44 and Tikal at age 42||{{start date and age|2029|7|6}}||{{start date and age|2029|8|14}}
|-
|Class of 2030||Ninth class scheduled to feature Shadow at age 44 or 45, Silver at age 42 or 43, Mighty at age 44 or 45, Sonic at age 43 or 44, Ray at age 37 or 38, Tails at age 36 or 37, Knuckles at age 43 or 44, Amy at age 39 or 40, Tangle at age 42 or 43, Rouge at age 45 or 46, Blaze at age 42 or 43, Sally at age 43 or 44, Marine at age 35 or 36, Mina at age 44 or 45 and Tikal at age 42 or 43||{{start date and age|2029|9|10}}||{{start date and age|2030|6|28}}
|-
|Summer program 2030||Ninth summer program scheduled to feature Shadow at age 45, Silver at age 43, Mighty at age 45, Sonic at age 44, Ray at age 38, Tails at age 37, Knuckles at age 44, Amy at age 40, Tangle at age 43, Rouge at age 46, Blaze at age 43, Sally at age 44, Marine at age 36, Mina at age 45 and Tikal at age 43||{{start date and age|2030|7|8}}||{{start date and age|2030|8|14}}
|-
|Class of 2031||Tenth class scheduled to feature Shadow at age 45 or 46, Silver at age 44 or 45, Mighty at age 45 or 46, Sonic at age 44 or 45, Ray at age 38 or 39, Tails at age 37 or 38, Knuckles at age 44 or 45, Amy at age 40 or 41, Tangle at age 43 or 44, Rouge at age 46 or 47, Blaze at age 43 or 44, Sally at age 44 or 45, Marine at age 36 or 37, Mina at age 45 or 46 and Tikal at age 43 or 44||{{start date and age|2030|9|9}}||{{start date and age|2031|6|27}}
|-
|Summer program 2031||Tenth summer program scheduled to feature Shadow at age 46, Silver at age 44, Mighty at age 46, Sonic at age 45, Ray at age 39, Tails at age 38, Knuckles at age 45, Amy at age 41, Tangle at age 44, Rouge at age 47, Blaze at age 44, Sally at age 45, Marine at age 37, Mina at age 46 and Tikal at age 44||{{start date and age|2031|7|7}}||{{start date and age|2031|8|14}}
|-
|Class of 2032||11th class scheduled to feature Shadow at age 46 or 47, Silver at age 44 or 45, Mighty at age 46 or 47, Sonic at age 45 or 46, Ray at age 39 or 40, Tails at age 38 or 39, Knuckles at age 45 or 46, Amy at age 41 or 42, Tangle at age 44 or 45, Rouge at age 47 or 48, Blaze at age 44 or 45, Sally at age 45 or 46, Marine at age 37 or 38, Mina at age 46 or 47 and Tikal at age 44 or 45||{{start date and age|2031|9|8}}||{{start date and age|2032|6|28}}
|-
|Summer program 2032||11th summer program scheduled to feature Shadow at age 47, Silver at age 45, Mighty at age 47, Sonic at age 46, Ray at age 40, Tails at age 39, Knuckles at age 46, Amy at age 42, Tangle at age 45, Rouge at age 48, Blaze at age 45, Sally at age 46, Marine at age 38, Mina at age 47 and Tikal at age 45||{{start date and age|2032|7|6}}||{{start date and age|2032|8|13}}
|-
|Class of 2033||12th class scheduled to feature Shadow at age 47 or 48, Silver at age 45 or 46, Mighty at age 47 or 48, Sonic at age 46 or 47, Ray at age 40 or 41, Tails at age 39 or 40, Knuckles at age 46 or 47, Amy at age 42 or 43, Tangle at age 45 or 46, Rouge at age 48 or 49, Blaze at age 45 or 46, Sally at age 46 or 47, Marine at age 38 or 39, Mina at age 47 or 48 and Tikal at age 45 or 46||{{start date and age|2032|9|8}}||{{start date and age|2033|6|28}}
|-
|Summer program 2033||12th summer program scheduled to feature Shadow at age 48, Silver at age 46, Mighty at age 48, Sonic at age 47, Ray at age 41, Tails at age 40, Knuckles at age 47, Amy at age 43, Tangle at age 46, Rouge at age 49, Blaze at age 46, Sally at age 47, Marine at age 39, Mina at age 48 and Tikal at age 46||{{start date and age|2033|7|6}}||{{start date and age|2033|8|12}}
|-
|Class of 2034||13th class scheduled to feature Shadow at age 48 or 49, Silver at age 46 or 47, Mighty at age 48 or 49, Sonic at age 47 or 48, Ray at age 41 or 42, Tails at age 40 or 41, Knuckles at age 47 or 48, Amy at age 43 or 44, Tangle at age 46 or 47, Rouge at age 49 or 50, Blaze at age 46 or 47, Sally at age 47 or 48, Marine at age 39 or 40, Mina at age 48 or 49 and Tikal at age 46 or 47||{{start date and age|2033|9|8}}||{{start date and age|2034|6|28}}
|-
|Summer program 2034||13th summer program scheduled to feature Shadow at age 49, Silver at age 47, Mighty at age 49, Sonic at age 48, Ray at age 42, Tails at age 41, Knuckles at age 48, Amy at age 44, Tangle at age 47, Rouge at age 50, Blaze at age 47, Sally at age 48, Marine at age 40, Mina at age 49 and Tikal at age 47||{{start date and age|2034|7|6}}||{{start date and age|2034|8|14}}
|-
|Class of 2035||14th class scheduled to feature Shadow at age 49 or 50, Silver at age 47 or 48, Mighty at age 49 or 50, Sonic at age 48 or 49, Ray at age 42 or 43, Tails at age 41 or 42, Knuckles at age 48 or 49, Amy at age 44 or 45, Tangle at age 47 or 48, Rouge at age 50 or 51, Blaze at age 47 or 48, Sally at age 48 or 49, Marine at age 40 or 41, Mina at age 49 or 50 and Tikal at age 47 or 48||{{start date and age|2034|9|8}}||{{start date and age|2035|6|28}}
|-
|Summer program 2035||14th summer program scheduled to feature Shadow at age 50, Silver at age 48, Mighty at age 50, Sonic at age 49, Ray at age 43, Tails at age 42, Knuckles at age 49, Amy at age 45, Tangle at age 48, Rouge at age 51, Blaze at age 48, Sally at age 49, Marine at age 41, Mina at age 50 and Tikal at age 48||{{start date and age|2035|7|6}}||{{start date and age|2035|8|14}}
|-
|Class of 2036||15th class scheduled to feature Shadow at age 50 or 51, Silver at age 48 or 49, Mighty at age 50 or 51, Sonic at age 49 or 50, Ray at age 43 or 44, Tails at age 42 or 43, Knuckles at age 49 or 50, Amy at age 45 or 46, Tangle at age 48 or 49, Rouge at age 51 or 52, Blaze at age 48 or 49, Sally at age 49 or 50, Marine at age 41 or 42, Mina at age 50 or 51 and Tikal at age 48 or 49||{{start date and age|2035|9|10}}||{{start date and age|2036|6|27}}
|-
|Summer program 2036||15th summer program scheduled to feature Shadow at age 51, Silver at age 49, Mighty at age 51, Sonic at age 50, Ray at age 44, Tails at age 43, Knuckles at age 50, Amy at age 46, Tangle at age 49, Rouge at age 52, Blaze at age 49, Sally at age 50, Marine at age 42, Mina at age 51 and Tikal at age 49||{{start date and age|2036|7|7}}||{{start date and age|2036|8|14}}
|-
|Class of 2037||16th class scheduled to feature Shadow at age 51 or 52, Silver at age 49 or 50, Mighty at age 51 or 52, Sonic at age 50 or 51, Ray at age 44 or 45, Tails at age 43 or 44, Knuckles at age 50 or 51, Amy at age 46 or 47, Tangle at age 49 or 50, Rouge at age 52 or 53, Blaze at age 49 or 50, Sally at age 50 or 51, Marine at age 42 or 43, Mina at age 51 or 52 and Tikal at age 49 or 50||{{start date and age|2036|9|8}}||{{start date and age|2037|6|26}}
|-
|Summer program 2037||16th summer program scheduled to feature Shadow at age 52, Silver at age 50, Mighty at age 52, Sonic at age 51, Ray at age 45, Tails at age 44, Knuckles at age 51, Amy at age 47, Tangle at age 50, Rouge at age 53, Blaze at age 50, Sally at age 51, Marine at age 43, Mina at age 52 and Tikal at age 50||{{start date and age|2037|7|6}}||{{start date and age|2037|8|14}}
|-
|Class of 2038||17th class scheduled to feature Shadow at age 52 or 53, Silver at age 50 or 51, Mighty at age 52 or 53, Sonic at age 51 or 52, Ray at age 45 or 46, Tails at age 44 or 45, Knuckles at age 51 or 52, Amy at age 47 or 48, Tangle at age 50 or 51, Rouge at age 53 or 54, Blaze at age 50 or 51, Sally at age 51 or 52, Marine at age 43 or 44, Mina at age 52 or 53 and Tikal at age 50 or 51||{{start date and age|2037|9|8}}||{{start date and age|2038|6|28}}
|-
|Summer program 2038||17th summer program scheduled to feature Shadow at age 53, Silver at age 51, Mighty at age 53, Sonic at age 52, Ray at age 46, Tails at age 45, Knuckles at age 52, Amy at age 48, Tangle at age 51, Rouge at age 54, Blaze at age 51, Sally at age 52, Marine at age 44, Mina at age 53 and Tikal at age 51||{{start date and age|2038|7|6}}||{{start date and age|2038|8|13}}
|-
|Class of 2039||18th class scheduled to feature Shadow at age 53 or 54, Silver at age 51 or 52, Mighty at age 53 or 54, Sonic at age 52 or 53, Ray at age 46 or 47, Tails at age 45 or 46, Knuckles at age 52 or 53, Amy at age 48 or 49, Tangle at age 51 or 52, Rouge at age 54 or 55, Blaze at age 51 or 52, Sally at age 52 or 53, Marine at age 44 or 45, Mina at age 53 or 54 and Tikal at age 51 or 52||{{start date and age|2038|9|8}}||{{start date and age|2039|6|28}}
|-
|Summer program 2039||18th summer program scheduled to feature Shadow at age 54, Silver at age 52, Mighty at age 54, Sonic at age 53, Ray at age 47, Tails at age 46, Knuckles at age 53, Amy at age 49, Tangle at age 52, Rouge at age 55, Blaze at age 52, Sally at age 53, Marine at age 45, Mina at age 54 and Tikal at age 52||{{start date and age|2039|7|6}}||{{start date and age|2039|8|12}}
|-
|Class of 2040||19th class scheduled to feature Shadow at age 54 or 55, Silver at age 52 or 53, Mighty at age 54 or 55, Sonic at age 53 or 54, Ray at age 47 or 48, Tails at age 46 or 47, Knuckles at age 53 or 54, Amy at age 49 or 50, Tangle at age 52 or 53, Rouge at age 55 or 56, Blaze at age 52 or 53, Sally at age 54 or 55, Marine at age 45 or 46, Mina at age 54 or 55 and Tikal at age 52 or 53||{{start date and age|2039|9|8}}||{{start date and age|2040|6|28}}
|-
|Summer program 2040||19th summer program scheduled to feature Shadow at age 55, Silver at age 53, Mighty at age 55, Sonic at age 54, Ray at age 48, Tails at age 47, Knuckles at age 54, Amy at age 50, Tangle at age 53, Rouge at age 56, Blaze at age 53, Sally at age 54, Marine at age 46, Mina at age 55 and Tikal at age 53||{{start date and age|2040|7|6}}||{{start date and age|2040|8|14}}
|-
|Class of 2041||20th class scheduled to feature Shadow at age 55 or 56, Silver at age 53 or 54, Mighty at age 55 or 56, Sonic at age 54 or 55, Ray at age 48 or 49, Tails at age 47 or 48, Knuckles at age 54 or 55, Amy at age 50 or 51, Tangle at age 53 or 54, Rouge at age 56 or 57, Blaze at age 53 or 54, Sally at age 54 or 55, Marine at age 46 or 47, Mina at age 55 or 56 and Tikal at age 53 or 54||{{start date and age|2040|9|10}}||{{start date and age|2041|6|28}}
|-
|Summer program 2041||20th summer program scheduled to feature Shadow at age 56, Silver at age 54, Mighty at age 56, Sonic at age 55, Ray at age 49, Tails at age 48, Knuckles at age 55, Amy at age 51, Tangle at age 54, Rouge at age 57, Blaze at age 54, Sally at age 55, Marine at age 47, Mina at age 56 and Tikal at age 54||{{start date and age|2041|7|8}}||{{start date and age|2041|8|14}}
|-
|Class of 2042||21st class scheduled to feature Shadow at age 56 or 57, Silver at age 54 or 55, Mighty at age 56 or 57, Sonic at age 55 or 56, Ray at age 49 or 50, Tails at age 48 or 49, Knuckles at age 55 or 56, Amy at age 51 or 52, Tangle at age 54 or 55, Rouge at age 57 or 58, Blaze at age 54 or 55, Sally at age 55 or 56, Marine at age 47 or 48, Mina at age 56 or 57 and Tikal at age 54 or 55||{{start date and age|2041|9|9}}||{{start date and age|2042|6|27}}
|-
|Summer program 2042||21st summer program scheduled to feature Shadow at age 57, Silver at age 55, Mighty at age 57, Sonic at age 56, Ray at age 50, Tails at age 49, Knuckles at age 56, Amy at age 52, Tangle at age 55, Rouge at age 58, Blaze at age 55, Sally at age 56, Marine at age 48, Mina at age 57 and Tikal at age 55||{{start date and age|2042|7|7}}||{{start date and age|2042|8|14}}
|-
|Class of 2043||22nd class scheduled to feature Shadow at age 57 or 58, Silver at age 55 or 56, Mighty at age 57 or 58, Sonic at age 56 or 57, Ray at age 50 or 51, Tails at age 49 or 50, Knuckles at age 56 or 57, Amy at age 52 or 53, Tangle at age 55 or 56, Rouge at age 58 or 59, Blaze at age 55 or 56, Sally at age 56 or 57, Marine at age 48 or 49, Mina at age 57 or 58 and Tikal at age 55 or 56||{{start date and age|2042|9|8}}||{{start date and age|2043|6|26}}
|-
|Summer program 2043||22nd summer program scheduled to feature Shadow at age 58, Silver at age 56, Mighty at age 58, Sonic at age 57, Ray at age 51, Tails at age 50, Knuckles at age 57, Amy at age 53, Tangle at age 56, Rouge at age 59, Blaze at age 56, Sally at age 57, Marine at age 49, Mina at age 58 and Tikal at age 56||{{start date and age|2043|7|6}}||{{start date and age|2043|8|14}}
|-
|Class of 2044||23rd class scheduled to feature Shadow at age 58 or 59, Silver at age 56 or 57, Mighty at age 58 or 59, Sonic at age 57 or 58, Ray at age 51 or 52, Tails at age 50 or 51, Knuckles at age 57 or 58, Amy at age 53 or 54, Tangle at age 56 or 57, Rouge at age 59 or 60, Blaze at age 56 or 57, Sally at age 57 or 58, Marine at age 49 or 50, Mina at age 58 or 59 and Tikal at age 56 or 57||{{start date and age|2043|9|8}}||{{start date and age|2044|6|28}}
|-
|Summer program 2044||23rd summer program scheduled to feature Shadow at age 59, Silver at age 57, Mighty at age 59, Sonic at age 58, Ray at age 52, Tails at age 51, Knuckles at age 58, Amy at age 54, Tangle at age 57, Rouge at age 60, Blaze at age 57, Sally at age 58, Marine at age 50, Mina at age 59 and Tikal at age 57||{{start date and age|2044|7|6}}||{{start date and age|2044|8|12}}
|-
|Class of 2045||24th class scheduled to feature Shadow at age 59 or 60, Silver at age 57 or 58, Mighty at age 59 or 60, Sonic at age 58 or 59, Ray at age 52 or 53, Tails at age 51 or 52, Knuckles at age 58 or 59, Amy at age 54 or 55, Tangle at age 57 or 58, Rouge at age 60 or 61, Blaze at age 57 or 58, Sally at age 58 or 59, Marine at age 50 or 51, Mina at age 59 or 60 and Tikal at age 57 or 58||{{start date and age|2044|9|8}}||{{start date and age|2045|6|28}}
|-
|Summer program 2045||24th summer program scheduled to feature Shadow at age 60, Silver at age 58, Mighty at age 60, Sonic at age 59, Ray at age 53, Tails at age 52, Knuckles at age 59, Amy at age 55, Tangle at age 58, Rouge at age 61, Blaze at age 58, Sally at age 59, Marine at age 51, Mina at age 60 and Tikal at age 58||{{start date and age|2045|7|6}}||{{start date and age|2045|8|14}}
|-
|Class of 2046||25th class scheduled to feature Shadow at age 60 or 61, Silver at age 58 or 59, Mighty at age 60 or 61, Sonic at age 59 or 60, Ray at age 53 or 54, Tails at age 52 or 53, Knuckles at age 59 or 60, Amy at age 55 or 56, Tangle at age 58 or 59, Rouge at age 61 or 62, Blaze at age 58 or 59, Sally at age 59 or 60, Marine at age 51 or 52, Mina at age 60 or 61 and Tikal at age 58 or 59||{{start date and age|2045|9|8}}||{{start date and age|2046|6|28}}
|-
|Summer program 2046||25th summer program scheduled to feature Shadow at age 61, Silver at age 59, Mighty at age 61, Sonic at age 60, Ray at age 54, Tails at age 53, Knuckles at age 60, Amy at age 56, Tangle at age 59, Rouge at age 62, Blaze at age 59, Sally at age 60, Marine at age 52, Mina at age 61 and Tikal at age 59||{{start date and age|2046|7|6}}||{{start date and age|2046|8|14}}
|}

=== Table focusing on educational careers of Japanese-American stars/personalities as teachers ===
{|class="wikitable sortable"
!Star/personality!!Date of start of educational career as a teacher!!Age upon becoming a teacher!!Educational status
|-
|Shadow||rowspan="15"|{{start date and age|2022|4|13}}||37||rowspan="15"|Working as teachers since April 13, 2022<br>Continuing to work as teachers for many years in obedience to the announcement on June 8, 2022
|-
|Silver||35
|-
|Mighty||37
|-
|Sonic||36
|-
|Ray||30
|-
|Tails||29
|-
|Knuckles||36
|-
|Amy||32
|-
|Tangle||35
|-
|Rouge||38
|-
|Blaze||35
|-
|Sally||36
|-
|Marine||28
|-
|Mina||37
|-
|Tikal||35
|}

=== Table focusing on live educational comebacks ===
{|class="wikitable sortable"
!Star/personality!!Date of first live educational comeback!!Date of second live educational comeback!!Date of third live educational comeback!!Date of fourth live educational comeback!!Date of fifth live educational comeback!!Date of sixth live educational comeback!!Date of seventh live educational comeback!!Date of eighth live educational comeback!!Date of ninth live educational comeback!!Date of tenth live educational comeback!!Date of 11th live educational comeback!!Date of 12th live educational comeback!!Date of 13th live educational comeback!!Date of 14th live educational comeback!!Date of 15th live educational comeback!!Date of 16th live educational comeback!!Date of 17th live educational comeback!!Date of 18th live educational comeback!!Date of 19th live educational comeback!!Date of 20th live educational comeback!!Date of 21st live educational comeback!!Date of 22nd live educational comeback!!Date of 23rd live educational comeback!!Date of 24th live educational comeback!!Date of 25th live educational comeback!!Date of 26th live educational comeback!!Date of 27th live educational comeback!!Date of 28th live educational comeback!!Date of 29th live educational comeback!!Date of 30th live educational comeback!!Date of 31st live educational comeback!!Date of 32nd live educational comeback!!Date of 33rd live educational comeback!!Date of 34th live educational comeback!!Date of 35th live educational comeback!!Date of 36th live educational comeback!!Date of 37th live educational comeback!!Date of 38th live educational comeback!!Date of 39th live educational comeback!!Date of 40th live educational comeback!!Date of 41st live educational comeback!!Date of 42nd live educational comeback!!Date of 43rd live educational comeback!!Date of 44th live educational comeback!!Date of 45th live educational comeback!!Date of 46th live educational comeback!!Date of 47th live educational comeback!!Date of 48th live educational comeback!!Date of 49th live educational comeback!!Date of 50th live educational comeback
|-
|Shadow||rowspan="15"|{{start date and age|2022|7|6}}||rowspan="15"|{{start date and age|2022|9|8}}||rowspan="15"|{{start date and age|2023|7|6}}||rowspan="15"|{{start date and age|2023|9|8}}||rowspan="15"|{{start date and age|2024|7|8}}||rowspan="15"|{{start date and age|2024|9|9}}||rowspan="15"|{{start date and age|2025|7|7}}||rowspan="15"|{{start date and age|2025|9|8}}||rowspan="15"|{{start date and age|2026|7|6}}||rowspan="15"|{{start date and age|2026|9|8}}||rowspan="15"|{{start date and age|2027|7|6}}||rowspan="15"|{{start date and age|2027|9|8}}||rowspan="15"|{{start date and age|2028|7|6}}||rowspan="15"|{{start date and age|2028|9|8}}||rowspan="15"|{{start date and age|2029|7|6}}||rowspan="15"|{{start date and age|2029|9|10}}||rowspan="15"|{{start date and age|2030|7|8}}||rowspan="15"|{{start date and age|2030|9|9}}||rowspan="15"|{{start date and age|2031|7|7}}||rowspan="15"|{{start date and age|2031|9|8}}||rowspan="15"|{{start date and age|2032|7|6}}||rowspan="15"|{{start date and age|2032|9|8}}||rowspan="15"|{{start date and age|2033|7|6}}||rowspan="15"|{{start date and age|2033|9|8}}||rowspan="15"|{{start date and age|2034|7|6}}||rowspan="15"|{{start date and age|2034|9|8}}||rowspan="15"|{{start date and age|2035|7|6}}||rowspan="15"|{{start date and age|2035|9|10}}||rowspan="15"|{{start date and age|2036|7|7}}||rowspan="15"|{{start date and age|2036|9|8}}||rowspan="15"|{{start date and age|2037|7|6}}||rowspan="15"|{{start date and age|2037|9|8}}||rowspan="15"|{{start date and age|2038|7|6}}||rowspan="15"|{{start date and age|2038|9|8}}||rowspan="15"|{{start date and age|2039|7|6}}||rowspan="15"|{{start date and age|2039|9|8}}||rowspan="15"|{{start date and age|2040|7|6}}||rowspan="15"|{{start date and age|2040|9|10}}||rowspan="15"|{{start date and age|2041|7|8}}||rowspan="15"|{{start date and age|2041|9|9}}||rowspan="15"|{{start date and age|2042|7|7}}||rowspan="15"|{{start date and age|2042|9|8}}||rowspan="15"|{{start date and age|2043|7|6}}||rowspan="15"|{{start date and age|2043|9|8}}||rowspan="15"|{{start date and age|2044|7|6}}||rowspan="15"|{{start date and age|2044|9|8}}||rowspan="15"|{{start date and age|2045|7|6}}||rowspan="15"|{{start date and age|2045|9|8}}||rowspan="15"|{{start date and age|2046|7|6}}||rowspan="15"|{{start date and age|2046|9|10}}
|-
|Silver
|-
|Mighty
|-
|Sonic
|-
|Ray
|-
|Tails
|-
|Knuckles
|-
|Amy
|-
|Tangle
|-
|Rouge
|-
|Blaze
|-
|Sally
|-
|Marine
|-
|Mina
|-
|Tikal
|}

=== Other table focusing on live educational comebacks ===
{|class="wikitable sortable"
!Star/personality!!Age upon first live educational comeback!!Age upon second live educational comeback!!Age upon third live educational comeback!!Age upon fourth live educational comeback!!Age upon fifth live educational comeback!!Age upon sixth live educational comeback!!Age upon seventh live educational comeback!!Age upon eighth live educational comeback!!Age upon ninth live educational comeback!!Age upon tenth live educational comeback!!Age upon 11th live educational comeback!!Age upon 12th live educational comeback!!Age upon 13th live educational comeback!!Age upon 14th live educational comeback!!Age upon 15th live educational comeback!!Age upon 16th live educational comeback!!Age upon 17th live educational comeback!!Age upon 18th live educational comeback!!Age upon 19th live educational comeback!!Age upon 20th live educational comeback!!Age upon 21st live educational comeback!!Age upon 22nd live educational comeback!!Age upon 23rd live educational comeback!!Age upon 24th live educational comeback!!Age upon 25th live educational comeback!!Age upon 26th live educational comeback!!Age upon 27th live educational comeback!!Age upon 28th live educational comeback!!Age upon 29th live educational comeback!!Age upon 30th live educational comeback!!Age upon 31st live educational comeback!!Age upon 32nd live educational comeback!!Age upon 33rd live educational comeback!!Age upon 34th live educational comeback!!Age upon 35th live educational comeback!!Age upon 36th live educational comeback!!Age upon 37th live educational comeback!!Age upon 38th live educational comeback!!Age upon 39th live educational comeback!!Age upon 40th live educational comeback!!Age upon 41st live educational comeback!!Age upon 42nd live educational comeback!!Age upon 43rd live educational comeback!!Age upon 44th live educational comeback!!Age upon 45th live educational comeback!!Age upon 46th live educational comeback!!Age upon 47th live educational comeback!!Age upon 48th live educational comeback!!Age upon 49th live educational comeback!!Age upon 50th live educational comeback
|-
|Shadow||colspan="2"|37||colspan="2"|38||colspan="2"|39||colspan="2"|40||colspan="2"|41||colspan="2"|42||colspan="2"|43||colspan="2"|44||colspan="2"|45||colspan="2"|46||colspan="2"|47||colspan="2"|48||colspan="2"|49||colspan="2"|50||colspan="2"|51||colspan="2"|52||colspan="2"|53||colspan="2"|54||colspan="2"|55||colspan="2"|56||colspan="2"|57||colspan="2"|58||colspan="2"|59||colspan="2"|60||colspan="2"|61
|-
|Silver||colspan="2"|35||colspan="2"|36||colspan="2"|37||colspan="2"|38||colspan="2"|39||colspan="2"|40||colspan="2"|41||colspan="2"|42||colspan="2"|43||colspan="2"|44||colspan="2"|45||colspan="2"|46||colspan="2"|47||colspan="2"|48||colspan="2"|49||colspan="2"|50||colspan="2"|51||colspan="2"|52||colspan="2"|53||colspan="2"|54||colspan="2"|55||colspan="2"|56||colspan="2"|57||colspan="2"|58||colspan="2"|59
|-
|Mighty||colspan="2"|37||colspan="2"|38||colspan="2"|39||colspan="2"|40||colspan="2"|41||colspan="2"|42||colspan="2"|43||colspan="2"|44||colspan="2"|45||colspan="2"|46||colspan="2"|47||colspan="2"|48||colspan="2"|49||colspan="2"|50||colspan="2"|51||colspan="2"|52||colspan="2"|53||colspan="2"|54||colspan="2"|55||colspan="2"|56||colspan="2"|57||colspan="2"|58||colspan="2"|59||colspan="2"|60||colspan="2"|61
|-
|Sonic||colspan="2"|36||colspan="2"|37||colspan="2"|38||colspan="2"|39||colspan="2"|40||colspan="2"|41||colspan="2"|42||colspan="2"|43||colspan="2"|44||colspan="2"|45||colspan="2"|46||colspan="2"|47||colspan="2"|48||colspan="2"|49||colspan="2"|50||colspan="2"|51||colspan="2"|52||colspan="2"|53||colspan="2"|54||colspan="2"|55||colspan="2"|56||colspan="2"|57||colspan="2"|58||colspan="2"|59||colspan="2"|60
|-
|Ray||colspan="2"|30||colspan="2"|31||colspan="2"|32||colspan="2"|33||colspan="2"|34||colspan="2"|35||colspan="2"|36||colspan="2"|37||colspan="2"|38||colspan="2"|39||colspan="2"|40||colspan="2"|41||colspan="2"|42||colspan="2"|43||colspan="2"|44||colspan="2"|45||colspan="2"|46||colspan="2"|47||colspan="2"|48||colspan="2"|49||colspan="2"|50||colspan="2"|51||colspan="2"|52||colspan="2"|53||colspan="2"|54
|-
|Tails||colspan="2"|29||colspan="2"|30||colspan="2"|31||colspan="2"|32||colspan="2"|33||colspan="2"|34||colspan="2"|35||colspan="2"|36||colspan="2"|37||colspan="2"|38||colspan="2"|39||colspan="2"|40||colspan="2"|41||colspan="2"|42||colspan="2"|43||colspan="2"|44||colspan="2"|45||colspan="2"|46||colspan="2"|47||colspan="2"|48||colspan="2"|49||colspan="2"|50||colspan="2"|51||colspan="2"|52||colspan="2"|53
|-
|Knuckles||colspan="2"|36||colspan="2"|37||colspan="2"|38||colspan="2"|39||colspan="2"|40||colspan="2"|41||colspan="2"|42||colspan="2"|43||colspan="2"|44||colspan="2"|45||colspan="2"|46||colspan="2"|47||colspan="2"|48||colspan="2"|49||colspan="2"|50||colspan="2"|51||colspan="2"|52||colspan="2"|53||colspan="2"|54||colspan="2"|55||colspan="2"|56||colspan="2"|57||colspan="2"|58||colspan="2"|59||colspan="2"|60
|-
|Amy||colspan="2"|32||colspan="2"|33||colspan="2"|34||colspan="2"|35||colspan="2"|36||colspan="2"|37||colspan="2"|38||colspan="2"|39||colspan="2"|40||colspan="2"|41||colspan="2"|42||colspan="2"|43||colspan="2"|44||colspan="2"|45||colspan="2"|46||colspan="2"|47||colspan="2"|48||colspan="2"|49||colspan="2"|50||colspan="2"|51||colspan="2"|52||colspan="2"|53||colspan="2"|54||colspan="2"|55||colspan="2"|56
|-
|Tangle||colspan="2"|35||colspan="2"|36||colspan="2"|37||colspan="2"|38||colspan="2"|39||colspan="2"|40||colspan="2"|41||colspan="2"|42||colspan="2"|43||colspan="2"|44||colspan="2"|45||colspan="2"|46||colspan="2"|47||colspan="2"|48||colspan="2"|49||colspan="2"|50||colspan="2"|51||colspan="2"|52||colspan="2"|53||colspan="2"|54||colspan="2"|55||colspan="2"|56||colspan="2"|57||colspan="2"|58||colspan="2"|59
|-
|Rouge||colspan="2"|38||colspan="2"|39||colspan="2"|40||colspan="2"|41||colspan="2"|42||colspan="2"|43||colspan="2"|44||colspan="2"|45||colspan="2"|46||colspan="2"|47||colspan="2"|48||colspan="2"|49||colspan="2"|50||colspan="2"|51||colspan="2"|52||colspan="2"|53||colspan="2"|54||colspan="2"|55||colspan="2"|56||colspan="2"|57||colspan="2"|58||colspan="2"|59||colspan="2"|60||colspan="2"|61||colspan="2"|62
|-
|Blaze||colspan="2"|35||colspan="2"|36||colspan="2"|37||colspan="2"|38||colspan="2"|39||colspan="2"|40||colspan="2"|41||colspan="2"|42||colspan="2"|43||colspan="2"|44||colspan="2"|45||colspan="2"|46||colspan="2"|47||colspan="2"|48||colspan="2"|49||colspan="2"|50||colspan="2"|51||colspan="2"|52||colspan="2"|53||colspan="2"|54||colspan="2"|55||colspan="2"|56||colspan="2"|57||colspan="2"|58||colspan="2"|59
|-
|Sally||colspan="2"|36||colspan="2"|37||colspan="2"|38||colspan="2"|39||colspan="2"|40||colspan="2"|41||colspan="2"|42||colspan="2"|43||colspan="2"|44||colspan="2"|45||colspan="2"|46||colspan="2"|47||colspan="2"|48||colspan="2"|49||colspan="2"|50||colspan="2"|51||colspan="2"|52||colspan="2"|53||colspan="2"|54||colspan="2"|55||colspan="2"|56||colspan="2"|57||colspan="2"|58||colspan="2"|59||colspan="2"|60
|-
|Marine||colspan="2"|28||colspan="2"|29||colspan="2"|30||colspan="2"|31||colspan="2"|32||colspan="2"|33||colspan="2"|34||colspan="2"|35||colspan="2"|36||colspan="2"|37||colspan="2"|38||colspan="2"|39||colspan="2"|40||colspan="2"|41||colspan="2"|42||colspan="2"|43||colspan="2"|44||colspan="2"|45||colspan="2"|46||colspan="2"|47||colspan="2"|48||colspan="2"|49||colspan="2"|50||colspan="2"|51||colspan="2"|52
|-
|Mina||colspan="2"|37||colspan="2"|38||colspan="2"|39||colspan="2"|40||colspan="2"|41||colspan="2"|42||colspan="2"|43||colspan="2"|44||colspan="2"|45||colspan="2"|46||colspan="2"|47||colspan="2"|48||colspan="2"|49||colspan="2"|50||colspan="2"|51||colspan="2"|52||colspan="2"|53||colspan="2"|54||colspan="2"|55||colspan="2"|56||colspan="2"|57||colspan="2"|58||colspan="2"|59||colspan="2"|60||colspan="2"|61
|-
|Tikal||colspan="2"|35||colspan="2"|36||colspan="2"|37||colspan="2"|38||colspan="2"|39||colspan="2"|40||colspan="2"|41||colspan="2"|42||colspan="2"|43||colspan="2"|44||colspan="2"|45||colspan="2"|46||colspan="2"|47||colspan="2"|48||colspan="2"|49||colspan="2"|50||colspan="2"|51||colspan="2"|52||colspan="2"|53||colspan="2"|54||colspan="2"|55||colspan="2"|56||colspan="2"|57||colspan="2"|58||colspan="2"|59
|}

== Quadratic equations solved by factorization ==

4''x''² – 16''x'' + 15 = 0

(2''x'' – 3)(2''x'' – 5) = 0

''x'' = {{sfrac|3|2}} and ''x'' = {{sfrac|5|2}}

Quadratic equation solved by factorization in late June or early summer 2022 by Shadow (37 by age at that time)

15''x''² – 16''x'' + 4 = 0

(5''x'' – 2)(3''x'' – 2) = 0

''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|2|3}}

Quadratic equation solved by factorization in late June or early summer 2022 by Silver (35 by age at that time)

6''x''² – 19''x'' + 15 = 0

(2''x'' – 3)(3''x'' – 5) = 0

''x'' = {{sfrac|3|2}} and ''x'' = {{sfrac|5|3}}

Quadratic equation solved by factorization in late June or early summer 2022 by Mighty (37 by age at that time)

15''x''² – 19''x'' + 6 = 0

(5''x'' – 3)(3''x'' – 2) = 0

''x'' = {{sfrac|3|5}} and ''x'' = {{sfrac|2|3}}

Quadratic equation solved by factorization in late June or early summer 2022 by Sonic (36 by age at that time)

6''x''² – 25''x'' + 25 = 0

(3''x'' – 5)(2''x'' – 5) = 0

''x'' = {{sfrac|5|3}} and ''x'' = {{sfrac|5|2}}

Quadratic equation solved by factorization in late June or early summer 2022 by Ray (30 by age at that time)

25''x''² – 25''x'' + 6 = 0

(5''x'' – 2)(5''x'' – 3) = 0

''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|3|5}}

Quadratic equation solved by factorization in late June or early summer 2022 by Tails (29 by age at that time)

6''x''² – 19''x'' + 10 = 0

(3''x'' – 2)(2''x'' – 5) = 0

''x'' = {{sfrac|2|3}} and ''x'' = {{sfrac|5|2}}

Quadratic equation solved by factorization in late June or early summer 2022 by Mina (37 by age at that time)

10''x''² – 19''x'' + 6 = 0

(5''x'' – 2)(2''x'' – 3) = 0

''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|3|2}}

Quadratic equation solved by factorization in late June or early summer 2022 by Tikal (35 by age at that time)

9''x''² – 21''x'' + 10 = 0

(3''x'' – 2)(3''x'' – 5) = 0

''x'' = {{sfrac|2|3}} and ''x'' = {{sfrac|5|3}}

Quadratic equation solved by factorization in late June or early summer 2022 by Rouge (38 by age at that time)

10''x''² – 21''x'' + 9 = 0

(5''x'' – 3)(2''x'' – 3) = 0

''x'' = {{sfrac|3|5}} and ''x'' = {{sfrac|3|2}}

Quadratic equation solved by factorization in late June or early summer 2022 by Blaze (35 by age at that time)

10''x''² – 31''x'' + 15 = 0

(5''x'' – 3)(2''x'' – 5) = 0

''x'' = {{sfrac|3|5}} and ''x'' = {{sfrac|5|2}}

Quadratic equation solved by factorization in late June or early summer 2022 by Sally (36 by age at that time)

15''x''² – 31''x'' + 10 = 0

(5''x'' – 2)(3''x'' – 5) = 0

''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|5|3}}

Quadratic equation solved by factorization in late June or early summer 2022 by Marine (28 by age at that time)

6''x''² – 13''x'' + 6 = 0

(3''x'' – 2)(2''x'' – 3) = 0

''x'' = {{sfrac|2|3}} and ''x'' = {{sfrac|3|2}}

Quadratic equation solved by factorization in late June or early summer 2022 by Amy (32 by age at that time)

10''x''² – 29''x'' + 10 = 0

(5''x'' – 2)(2''x'' – 5) = 0

''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|5|2}}

Quadratic equation solved by factorization in late June or early summer 2022 by Tangle (35 by age at that time)

15''x''² – 34''x'' + 15 = 0

(5''x'' – 3)(3''x'' – 5) = 0

''x'' = {{sfrac|3|5}} and ''x'' = {{sfrac|5|3}}

Quadratic equation solved by factorization in late June or early summer 2022 by Knuckles (36 by age at that time)

== Quadratic equations solved by square completion ==

4''x''² – 16''x'' + 15 = 0

4''x''² – 16''x'' + 16 = 1

(2''x'' – 4)² = 1

2''x'' – 4 = ±1

2''x'' = 4 ± 1

''x'' = {{sfrac|4 ± 1|2}}

''x'' = {{sfrac|5|2}} and ''x'' = {{sfrac|3|2}}

Quadratic equation solved by square completion in late June or early summer 2022 by Shadow (37 by age at that time)

15''x''² – 16''x'' + 4 = 0

225''x''² – 240''x'' + 60 = 0

225''x''² – 240''x'' + 64 = 4

(15''x'' – 8)² = 4

15''x'' – 8 = ±2

15''x'' = 8 ± 2

''x'' = {{sfrac|8 ± 2|15}}

''x'' = {{sfrac|2|3}} and ''x'' = {{sfrac|2|5}}

Quadratic equation solved by square completion in late June or early summer 2022 by Silver (35 by age at that time)

6''x''² – 19''x'' + 15 = 0

144''x''² – 456''x'' + 360 = 0

144''x''² – 456''x'' + 361 = 1

(12''x'' – 19)² = 1

12''x'' – 19 = ±1

12''x'' = 19 ± 1

''x'' = {{sfrac|19 ± 1|12}}

''x'' = {{sfrac|5|3}} and ''x'' = {{sfrac|3|2}}

Quadratic equation solved by square completion in late June or early summer 2022 by Mighty (37 by age at that time)

15''x''² – 19''x'' + 6 = 0

900''x''² – 1,140''x'' + 360 = 0

900''x''² – 1,140''x'' + 361 = 1

(30''x'' – 19)² = 1

30''x'' – 19 = ±1

30''x'' = 19 ± 1

''x'' = {{sfrac|19 ± 1|30}}

''x'' = {{sfrac|2|3}} and ''x'' = {{sfrac|3|5}}

Quadratic equation solved by square completion in late June or early summer 2022 by Sonic (36 by age at that time)

6''x''² – 25''x'' + 25 = 0

144''x''² – 600''x'' + 600 = 0

144''x''² – 600''x'' + 625 = 25

(12''x'' – 25)² = 25

12''x'' – 25 = ±5

12''x'' = 25 ± 5

''x'' = {{sfrac|25 ± 5|12}}

''x'' = {{sfrac|5|2}} and ''x'' = {{sfrac|5|3}}

Quadratic equation solved by square completion in late June or early summer 2022 by Ray (30 by age at that time)

25''x''² – 25''x'' + 6 = 0

100''x''² – 100''x'' + 24 = 0

100''x''² – 100''x'' + 25 = 1

(10''x'' – 5)² = 1

10''x'' – 5 = ±1

10''x'' = 5 ± 1

''x'' = {{sfrac|5 ± 1|10}}

''x'' = {{sfrac|3|5}} and ''x'' = {{sfrac|2|5}}

Quadratic equation solved by square completion in late June or early summer 2022 by Tails (29 by age at that time)

6''x''² – 19''x'' + 10 = 0

144''x''² – 456''x'' + 240 = 0

144''x''² – 456''x'' + 361 = 121

(12''x'' – 19)² = 121

12''x'' – 19 = ±11

12''x'' = 19 ± 11

''x'' = {{sfrac|19 ± 11|12}}

''x'' = {{sfrac|5|2}} and ''x'' = {{sfrac|2|3}}

Quadratic equation solved by square completion in late June or early summer 2022 by Mina (37 by age at that time)

10''x''² – 19''x'' + 6 = 0

400''x''² – 760''x'' + 240 = 0

400''x''² – 760''x'' + 361 = 121

(20''x'' – 19)² = 121

20''x'' – 19 = ±11

20''x'' = 19 ± 11

''x'' = {{sfrac|19 ± 11|20}}

''x'' = {{sfrac|3|2}} and ''x'' = {{sfrac|2|5}}

Quadratic equation solved by square completion in late June or early summer 2022 by Tikal (35 by age at that time)

9''x''² – 21''x'' + 10 = 0

36''x''² – 84''x'' + 40 = 0

36''x''² – 84''x'' + 49 = 9

(6''x'' – 7)² = 9

6''x'' – 7 = ±3

6''x'' = 7 ± 3

''x'' = {{sfrac|7 ± 3|6}}

''x'' = {{sfrac|5|3}} and ''x'' = {{sfrac|2|3}}

Quadratic equation solved by square completion in late June or early summer 2022 by Rouge (38 by age at that time)

10''x''² – 21''x'' + 9 = 0

400''x''² – 840''x'' + 360 = 0

400''x''² – 840''x'' + 441 = 81

(20''x'' – 21)² = 81

20''x'' – 21 = ±9

20''x'' = 21 ± 9

''x'' = {{sfrac|21 ± 9|20}}

''x'' = {{sfrac|3|2}} and ''x'' = {{sfrac|3|5}}

Quadratic equation solved by square completion in late June or early summer 2022 by Blaze (35 by age at that time)

10''x''² – 31''x'' + 15 = 0

400''x''² – 1,240''x'' + 600 = 0

400''x''² – 1,240''x'' + 961 = 361

(20''x'' – 31)² = 361

20''x'' – 31 = ±19

20''x'' = 31 ± 19

''x'' = {{sfrac|31 ± 19|20}}

''x'' = {{sfrac|5|2}} and ''x'' = {{sfrac|3|5}}

Quadratic equation solved by square completion in late June or early summer 2022 by Sally (36 by age at that time)

15''x''² – 31''x'' + 10 = 0

900''x''² – 1,860''x'' + 600 = 0

900''x''² – 1,860''x'' + 961 = 361

(30''x'' – 31)² = 361

30''x'' – 31 = ±19

30''x'' = 31 ± 19

''x'' = {{sfrac|31 ± 19|30}}

''x'' = {{sfrac|5|3}} and ''x'' = {{sfrac|2|5}}

Quadratic equation solved by square completion in late June or early summer 2022 by Marine (28 by age at that time)

6''x''² – 13''x'' + 6 = 0

144''x''² – 312''x'' + 144 = 0

144''x''² – 312''x'' + 169 = 25

(12''x'' – 13)² = 25

12''x'' – 13 = ±5

12''x'' = 13 ± 5

''x'' = {{sfrac|13 ± 5|12}}

''x'' = {{sfrac|3|2}} and ''x'' = {{sfrac|2|3}}

Quadratic equation solved by square completion in late June or early summer 2022 by Amy (32 by age at that time)

10''x''² – 29''x'' + 10 = 0

400''x''² – 1,160''x'' + 400 = 0

400''x''² – 1,160''x'' + 841 = 441

(20''x'' – 29)² = 441

20''x'' – 29 = ±21

20''x'' = 29 ± 21

''x'' = {{sfrac|29 ± 21|20}}

''x'' = {{sfrac|5|2}} and ''x'' = {{sfrac|2|5}}

Quadratic equation solved by square completion in late June or early summer 2022 by Tangle (35 by age at that time)

15''x''² – 34''x'' + 15 = 0

225''x''² – 510''x'' + 225 = 0

225''x''² – 510''x'' + 289 = 64

(15''x'' – 17)² = 64

15''x'' – 17 = ±8

15''x'' = 17 ± 8

''x'' = {{sfrac|17 ± 8|15}}

''x'' = {{sfrac|5|3}} and ''x'' = {{sfrac|3|5}}

Quadratic equation solved by square completion in late June or early summer 2022 by Knuckles (36 by age at that time)

== Quadratic equations solved by the formula ==

4''x''² – 16''x'' + 15 = 0

''a'' = 4, ''b'' = –16 and ''c'' = 15

''b''² – 4''ac'' = 16

''x'' = {{sfrac|16 ± {{sqrt|16}}|8}}

''x'' = {{sfrac|16 ± 4|8}}

''x'' = {{sfrac|4 ± 1|2}}

''x'' = {{sfrac|5|2}} and ''x'' = {{sfrac|3|2}}

Quadratic equation solved by the formula in late June or early summer 2022 by Shadow (37 by age at that time)

15''x''² – 16''x'' + 4 = 0

''a'' = 15, ''b'' = –16 and ''c'' = 4

''b''² – 4''ac'' = 16

''x'' = {{sfrac|16 ± {{sqrt|16}}|30}}

''x'' = {{sfrac|16 ± 4|30}}

''x'' = {{sfrac|8 ± 2|15}}

''x'' = {{sfrac|2|3}} and ''x'' = {{sfrac|2|5}}

Quadratic equation solved by the formula in late June or early summer 2022 by Silver (35 by age at that time)

6''x''² – 19''x'' + 15 = 0

''a'' = 6, ''b'' = –19 and ''c'' = 15

''b''² – 4''ac'' = 1

''x'' = {{sfrac|19 ± {{sqrt|1}}|12}}

''x'' = {{sfrac|19 ± 1|12}}

''x'' = {{sfrac|5|3}} and ''x'' = {{sfrac|3|2}}

Quadratic equation solved by the formula in late June or early summer 2022 by Mighty (37 by age at that time)

15''x''² – 19''x'' + 6 = 0

''a'' = 15, ''b'' = –19 and ''c'' = 6

''b''² – 4''ac'' = 1

''x'' = {{sfrac|19 ± {{sqrt|1}}|30}}

''x'' = {{sfrac|19 ± 1|30}}

''x'' = {{sfrac|2|3}} and ''x'' = {{sfrac|3|5}}

Quadratic equation solved by the formula in late June or early summer 2022 by Sonic (36 by age at that time)

6''x''² – 25''x'' + 25 = 0

''a'' = 6, ''b'' = –25 and ''c'' = 25

''b''² – 4''ac'' = 25

''x'' = {{sfrac|25 ± {{sqrt|25}}|12}}

''x'' = {{sfrac|25 ± 5|12}}

''x'' = {{sfrac|5|2}} and ''x'' = {{sfrac|5|3}}

Quadratic equation solved by the formula in late June or early summer 2022 by Ray (30 by age at that time)

25''x''² – 25''x'' + 6 = 0

''a'' = 25, ''b'' = –25 and ''c'' = 6

''b''² – 4''ac'' = 25

''x'' = {{sfrac|25 ± {{sqrt|25}}|50}}

''x'' = {{sfrac|25 ± 5|50}}

''x'' = {{sfrac|5 ± 1|10}}

''x'' = {{sfrac|3|5}} and ''x'' = {{sfrac|2|5}}

Quadratic equation solved by the formula in late June or early summer 2022 by Tails (29 by age at that time)

6''x''² – 19''x'' + 10 = 0

''a'' = 6, ''b'' = –19 and ''c'' = 10

''b''² – 4''ac'' = 121

''x'' = {{sfrac|19 ± {{sqrt|121}}|12}}

''x'' = {{sfrac|19 ± 11|12}}

''x'' = {{sfrac|5|2}} and ''x'' = {{sfrac|2|3}}

Quadratic equation solved by the formula in late June or early summer 2022 by Mina (37 by age at that time)

10''x''² – 19''x'' + 6 = 0

''a'' = 10, ''b'' = –19 and ''c'' = 6

''b''² – 4''ac'' = 121

''x'' = {{sfrac|19 ± {{sqrt|121}}|20}}

''x'' = {{sfrac|19 ± 11|20}}

''x'' = {{sfrac|3|2}} and ''x'' = {{sfrac|2|5}}

Quadratic equation solved by the formula in late June or early summer 2022 by Tikal (35 by age at that time)

9''x''² – 21''x'' + 10 = 0

''a'' = 9, ''b'' = –21 and ''c'' = 10

''b''² – 4''ac'' = 81

''x'' = {{sfrac|21 ± {{sqrt|81}}|18}}

''x'' = {{sfrac|21 ± 9|18}}

''x'' = {{sfrac|7 ± 3|6}}

''x'' = {{sfrac|5|3}} and ''x'' = {{sfrac|2|3}}

Quadratic equation solved by the formula in late June or early summer 2022 by Rouge (38 by age at that time)

10''x''² – 21''x'' + 9 = 0

''a'' = 10, ''b'' = –21 and ''c'' = 9

''b''² – 4''ac'' = 81

''x'' = {{sfrac|21 ± {{sqrt|81}}|20}}

''x'' = {{sfrac|21 ± 9|20}}

''x'' = {{sfrac|3|2}} and ''x'' = {{sfrac|3|5}}

Quadratic equation solved by the formula in late June or early summer 2022 by Blaze (35 by age at that time)

10''x''² – 31''x'' + 15 = 0

''a'' = 10, ''b'' = –31 and ''c'' = 15

''b''² – 4''ac'' = 361

''x'' = {{sfrac|31 ± {{sqrt|361}}|20}}

''x'' = {{sfrac|31 ± 19|20}}

''x'' = {{sfrac|5|2}} and ''x'' = {{sfrac|3|5}}

Quadratic equation solved by the formula in late June or early summer 2022 by Sally (36 by age at that time)

15''x''² – 31''x'' + 10 = 0

''a'' = 15, ''b'' = –31 and ''c'' = 10

''b''² – 4''ac'' = 361

''x'' = {{sfrac|31 ± {{sqrt|361}}|30}}

''x'' = {{sfrac|31 ± 19|30}}

''x'' = {{sfrac|5|3}} and ''x'' = {{sfrac|2|5}}

Quadratic equation solved by the formula in late June or early summer 2022 by Marine (28 by age at that time)

6''x''² – 13''x'' + 6 = 0

''a'' = 6, ''b'' = –13 and ''c'' = 6

''b''² – 4''ac'' = 25

''x'' = {{sfrac|13 ± {{sqrt|25}}|12}}

''x'' = {{sfrac|13 ± 5|12}}

''x'' = {{sfrac|3|2}} and ''x'' = {{sfrac|2|3}}

Quadratic equation solved by the formula in late June or early summer 2022 by Amy (32 by age at that time)

10''x''² – 29''x'' + 10 = 0

''a'' = 10, ''b'' = –29 and ''c'' = 10

''b''² – 4''ac'' = 441

''x'' = {{sfrac|29 ± {{sqrt|441}}|20}}

''x'' = {{sfrac|29 ± 21|20}}

''x'' = {{sfrac|5|2}} and ''x'' = {{sfrac|2|5}}

Quadratic equation solved by the formula in late June or early summer 2022 by Tangle (35 by age at that time)

15''x''² – 34''x'' + 15 = 0

''a'' = 15, ''b'' = –34 and ''c'' = 15

''b''² – 4''ac'' = 256

''x'' = {{sfrac|34 ± {{sqrt|256}}|30}}

''x'' = {{sfrac|34 ± 16|30}}

''x'' = {{sfrac|17 ± 8|15}}

''x'' = {{sfrac|5|3}} and ''x'' = {{sfrac|3|5}}

Quadratic equation solved by the formula in late June or early summer 2022 by Knuckles (36 by age at that time)

== Quadratic expressions converted to other forms ==

4''x''² – 16''x'' + 15 = (2''x'' – 4)² – 1

4''x''² – 16''x'' + 15 = (2''x'' – 3)(2''x'' – 5)

(2''x'' – 4)² – 1 = (2''x'' – 3)(2''x'' – 5)

Quadratic expression converted to other forms in late June or early summer 2022 by Shadow (37 by age at that time)

15''x''² – 16''x'' + 4 = {{sfrac|(15''x'' – 8)² – 4|15}}

15''x''² – 16''x'' + 4 = (5''x'' – 2)(3''x'' – 2)

{{sfrac|(15''x'' – 8)² – 4|15}} = (5''x'' – 2)(3''x'' – 2)

Quadratic expression converted to other forms in late June or early summer 2022 by Silver (35 by age at that time)

6''x''² – 19''x'' + 15 = {{sfrac|(12''x'' – 19)² – 1|24}}

6''x''² – 19''x'' + 15 = (2''x'' – 3)(3''x'' – 5)

{{sfrac|(12''x'' – 19)² – 1|24}} = (2''x'' – 3)(3''x'' – 5)

Quadratic expression converted to other forms in late June or early summer 2022 by Mighty (37 by age at that time)

15''x''² – 19''x'' + 6 = {{sfrac|(30''x'' – 19)² – 1|60}}

15''x''² – 19''x'' + 6 = (5''x'' – 3)(3''x'' – 2)

{{sfrac|(30''x'' – 19)² – 1|60}} = (5''x'' – 3)(3''x'' – 2)

Quadratic expression converted to other forms in late June or early summer 2022 by Sonic (36 by age at that time)

6''x''² – 25''x'' + 25 = {{sfrac|(12''x'' – 25)² – 25|24}}

6''x''² – 25''x'' + 25 = (3''x'' – 5)(2''x'' – 5)

{{sfrac|(12''x'' – 25)² – 25|24}} = (3''x'' – 5)(2''x'' – 5)

Quadratic expression converted to other forms in late June or early summer 2022 by Ray (30 by age at that time)

25''x''² – 25''x'' + 6 = {{sfrac|(10''x'' – 5)² – 1|4}}

25''x''² – 25''x'' + 6 = (5''x'' – 2)(5''x'' – 3)

{{sfrac|(10''x'' – 5)² – 1|4}} = (5''x'' – 2)(5''x'' – 3)

Quadratic expression converted to other forms in late June or early summer 2022 by Tails (29 by age at that time)

6''x''² – 19''x'' + 10 = {{sfrac|(12''x'' – 19)² – 121|24}}

6''x''² – 19''x'' + 10 = (3''x'' – 2)(2''x'' – 5)

{{sfrac|(12''x'' – 19)² – 121|24}} = (3''x'' – 2)(2''x'' – 5)

Quadratic expression converted to other forms in late June or early summer 2022 by Mina (37 by age at that time)

10''x''² – 19''x'' + 6 = {{sfrac|(20''x'' – 19)² – 121|40}}

10''x''² – 19''x'' + 6 = (5''x'' – 2)(2''x'' – 3)

{{sfrac|(20''x'' – 19)² – 121|40}} = (5''x'' – 2)(2''x'' – 3)

Quadratic expression converted to other forms in late June or early summer 2022 by Tikal (35 by age at that time)

9''x''² – 21''x'' + 10 = {{sfrac|(6''x'' – 7)² – 9|4}}

9''x''² – 21''x'' + 10 = (3''x'' – 2)(3''x'' – 5)

{{sfrac|(6''x'' – 7)² – 9|4}} = (3''x'' – 2)(3''x'' – 5)

Quadratic expression converted to other forms in late June or early summer 2022 by Rouge (38 by age at that time)

10''x''² – 21''x'' + 9 = {{sfrac|(20''x'' – 21)² – 81|40}}

10''x''² – 21''x'' + 9 = (5''x'' – 3)(2''x'' – 3)

{{sfrac|(20''x'' – 21)² – 81|40}} = (5''x'' – 3)(2''x'' – 3)

Quadratic expression converted to other forms in late June or early summer 2022 by Blaze (35 by age at that time)

10''x''² – 31''x'' + 15 = {{sfrac|(20''x'' – 31)² – 361|40}}

10''x''² – 31''x'' + 15 = (5''x'' – 3)(2''x'' – 5)

{{sfrac|(20''x'' – 31)² – 361|40}} = (5''x'' – 3)(2''x'' – 5)

Quadratic expression converted to other forms in late June or early summer 2022 by Sally (36 by age at that time)

15''x''² – 31''x'' + 10 = {{sfrac|(30''x'' – 31)² – 361|60}}

15''x''² – 31''x'' + 10 = (5''x'' – 2)(3''x'' – 5)

{{sfrac|(30''x'' – 31)² – 361|60}} = (5''x'' – 2)(3''x'' – 5)

Quadratic expression converted to other forms in late June or early summer 2022 by Marine (28 by age at that time)

6''x''² – 13''x'' + 6 = {{sfrac|(12''x'' – 13)² – 25|24}}

6''x''² – 13''x'' + 6 = (3''x'' – 2)(2''x'' – 3)

{{sfrac|(12''x'' – 13)² – 25|24}} = (3''x'' – 2)(2''x'' – 3)

Quadratic expression converted to other forms in late June or early summer 2022 by Amy (32 by age at that time)

10''x''² – 29''x'' + 10 = {{sfrac|(20''x'' – 29)² – 441|40}}

10''x''² – 29''x'' + 10 = (5''x'' – 2)(2''x'' – 5)

{{sfrac|(20''x'' – 29)² – 441|40}} = (5''x'' – 2)(2''x'' – 5)

Quadratic expression converted to other forms in late June or early summer 2022 by Tangle (35 by age at that time)

15''x''² – 34''x'' + 15 = {{sfrac|(15''x'' – 17)² – 64|15}}

15''x''² – 34''x'' + 15 = (5''x'' – 3)(3''x'' – 5)

{{sfrac|(15''x'' – 17)² – 64|15}} = (5''x'' – 3)(3''x'' – 5)

Quadratic expression converted to other forms in late June or early summer 2022 by Knuckles (36 by age at that time)

== Quadratic expression ranges ==

4''x''² – 16''x'' + 15 >= –1

Quadratic expression range defined in late June or early summer 2022 by Shadow (37 by age at that time)

15''x''² – 16''x'' + 4 >= –{{sfrac|4|15}}

Quadratic expression range defined in late June or early summer 2022 by Silver (35 by age at that time)

6''x''² – 19''x'' + 15 >= –{{sfrac|1|24}}

Quadratic expression range defined in late June or early summer 2022 by Mighty (37 by age at that time)

15''x''² – 19''x'' + 6 >= –{{sfrac|1|60}}

Quadratic expression range defined in late June or early summer 2022 by Sonic (36 by age at that time)

6''x''² – 25''x'' + 25 >= –{{sfrac|25|24}}

Quadratic expression range defined in late June or early summer 2022 by Ray (30 by age at that time)

25''x''² – 25''x'' + 6 >= –{{sfrac|1|4}}

Quadratic expression range defined in late June or early summer 2022 by Tails (29 by age at that time)

6''x''² – 19''x'' + 10 >= –{{sfrac|121|24}}

Quadratic expression range defined in late June or early summer 2022 by Mina (37 by age at that time)

10''x''² – 19''x'' + 6 >= –{{sfrac|121|40}}

Quadratic expression range defined in late June or early summer 2022 by Tikal (35 by age at that time)

9''x''² – 21''x'' + 10 >= –{{sfrac|9|4}}

Quadratic expression range defined in late June or early summer 2022 by Rouge (38 by age at that time)

10''x''² – 21''x'' + 9 >= –{{sfrac|81|40}}

Quadratic expression range defined in late June or early summer 2022 by Blaze (35 by age at that time)

10''x''² – 31''x'' + 15 >= –{{sfrac|361|40}}

Quadratic expression range defined in late June or early summer 2022 by Sally (36 by age at that time)

15''x''² – 31''x'' + 10 >= –{{sfrac|361|60}}

Quadratic expression range defined in late June or early summer 2022 by Marine (28 by age at that time)

6''x''² – 13''x'' + 6 >= –{{sfrac|25|24}}

Quadratic expression range defined in late June or early summer 2022 by Amy (32 by age at that time)

10''x''² – 29''x'' + 10 >= –{{sfrac|441|40}}

Quadratic expression range defined in late June or early summer 2022 by Tangle (35 by age at that time)

15''x''² – 34''x'' + 15 >= –{{sfrac|64|15}}

Quadratic expression range defined in late June or early summer 2022 by Knuckles (36 by age at that time)

== Quadratic function switches ==

4''x''² – 16''x'' + 15 = ''y''

4''x''² – 16''x'' + 16 = ''y'' + 1

(2''x'' – 4)² = ''y'' + 1

2''x'' – 4 = ±{{sqrt|''y'' + 1}}

2''x'' = 4 ± {{sqrt|''y'' + 1}}

''x'' = {{sfrac|4 ± {{sqrt|''y'' + 1}}|2}}

Quadratic function switch performed in late June or early summer 2022 by Shadow (37 by age at that time)

15''x''² – 16''x'' + 4 = ''y''

225''x''² – 240''x'' + 60 = 15''y''

225''x''² – 240''x'' + 64 = 15''y'' + 4

(15''x'' – 8)² = 15''y'' + 4

15''x'' – 8 = ±{{sqrt|15''y'' + 4}}

15''x'' = 8 ± {{sqrt|15''y'' + 4}}

''x'' = {{sfrac|8 ± {{sqrt|15''y'' + 4}}|15}}

Quadratic function switch performed in late June or early summer 2022 by Silver (35 by age at that time)

6''x''² – 19''x'' + 15 = ''y''

144''x''² – 456''x'' + 360 = 24''y''

144''x''² – 456''x'' + 361 = 24''y'' + 1

(12''x'' – 19)² = 24''y'' + 1

12''x'' – 19 = ±{{sqrt|24''y'' + 1}}

12''x'' = 19 ± {{sqrt|24''y'' + 1}}

''x'' = {{sfrac|19 ± {{sqrt|24''y'' + 1}}|12}}

Quadratic function switch performed in late June or early summer 2022 by Mighty (37 by age at that time)

15''x''² – 19''x'' + 6 = ''y''

900''x''² – 1,140''x'' + 360 = 60''y''

900''x''² – 1,140''x'' + 361 = 60''y'' + 1

(30''x'' – 19)² = 60''y'' + 1

30''x'' – 19 = ±{{sqrt|60''y'' + 1}}

30''x'' = 19 ± {{sqrt|60''y'' + 1}}

''x'' = {{sfrac|19 ± {{sqrt|60''y'' + 1}}|30}}

Quadratic function switch performed in late June or early summer 2022 by Sonic (36 by age at that time)

6''x''² – 25''x'' + 25 = ''y''

144''x''² – 600''x'' + 600 = 24''y''

144''x''² – 600''x'' + 625 = 24''y'' + 25

(12''x'' – 25)² = 24''y'' + 25

12''x'' – 25 = ±{{sqrt|24''y'' + 25}}

12''x'' = 25 ± {{sqrt|24''y'' + 25}}

''x'' = {{sfrac|25 ± {{sqrt|24''y'' + 25}}|12}}

Quadratic function switch performed in late June or early summer 2022 by Ray (30 by age at that time)

25''x''² – 25''x'' + 6 = ''y''

100''x''² – 100''x'' + 24 = 4''y''

100''x''² – 100''x'' + 25 = 4''y'' + 1

(10''x'' – 5)² = 4''y'' + 1

10''x'' – 5 = ±{{sqrt|4''y'' + 1}}

10''x'' = 5 ± {{sqrt|4''y'' + 1}}

''x'' = {{sfrac|5 ± {{sqrt|4''y'' + 1}}|10}}

Quadratic function switch performed in late June or early summer 2022 by Tails (29 by age at that time)

6''x''² – 19''x'' + 10 = ''y''

144''x''² – 456''x'' + 240 = 24''y''

144''x''² – 456''x'' + 361 = 24''y'' + 121

(12''x'' – 19)² = 24''y'' + 121

12''x'' – 19 = ±{{sqrt|24''y'' + 121}}

12''x'' = 19 ± {{sqrt|24''y'' + 121}}

''x'' = {{sfrac|19 ± {{sqrt|24''y'' + 121}}|12}}

Quadratic function switch performed in late June or early summer 2022 by Mina (37 by age at that time)

10''x''² – 19''x'' + 6 = ''y''

400''x''² – 760''x'' + 240 = 40''y''

400''x''² – 760''x'' + 361 = 40''y'' + 121

(20''x'' – 19)² = 40''y'' + 121

20''x'' – 19 = ±{{sqrt|40''y'' + 121}}

20''x'' = 19 ± {{sqrt|40''y'' + 121}}

''x'' = {{sfrac|19 ± {{sqrt|40''y'' + 121}}|20}}

Quadratic function switch performed in late June or early summer 2022 by Tikal (35 by age at that time)

9''x''² – 21''x'' + 10 = ''y''

36''x''² – 84''x'' + 40 = 4''y''

36''x''² – 84''x'' + 49 = 4''y'' + 9

(6''x'' – 7)² = 4''y'' + 9

6''x'' – 7 = ±{{sqrt|4''y'' + 9}}

6''x'' = 7 ± {{sqrt|4''y'' + 9}}

''x'' = {{sfrac|7 ± {{sqrt|4''y'' + 9}}|6}}

Quadratic function switch performed in late June or early summer 2022 by Rouge (38 by age at that time)

10''x''² – 21''x'' + 9 = ''y''

400''x''² – 840''x'' + 360 = 40''y''

400''x''² – 840''x'' + 441 = 40''y'' + 81

(20''x'' – 21)² = 40''y'' + 81

20''x'' – 21 = ±{{sqrt|40''y'' + 81}}

20''x'' = 21 ± {{sqrt|40''y'' + 81}}

''x'' = {{sfrac|21 ± {{sqrt|40''y'' + 81}}|20}}

Quadratic function switch performed in late June or early summer 2022 by Blaze (35 by age at that time)

10''x''² – 31''x'' + 15 = ''y''

400''x''² – 1,240''x'' + 600 = 40''y''

400''x''² – 1,240''x'' + 961 = 40''y'' + 361

(20''x'' – 31)² = 40''y'' + 361

20''x'' – 31 = ±{{sqrt|40''y'' + 361}}

20''x'' = 31 ± {{sqrt|40''y'' + 361}}

''x'' = {{sfrac|31 ± {{sqrt|40''y'' + 361}}|20}}

Quadratic function switch performed in late June or early summer 2022 by Sally (36 by age at that time)

15''x''² – 31''x'' + 10 = ''y''

900''x''² – 1,860''x'' + 600 = 60''y''

900''x''² – 1,860''x'' + 961 = 60''y'' + 361

(30''x'' – 31)² = 60''y'' + 361

30''x'' – 31 = ±{{sqrt|60''y'' + 361}}

30''x'' = 31 ± {{sqrt|60''y'' + 361}}

''x'' = {{sfrac|31 ± {{sqrt|60''y'' + 361}}|30}}

Quadratic function switch performed in late June or early summer 2022 by Marine (28 by age at that time)

6''x''² – 13''x'' + 6 = ''y''

144''x''² – 312''x'' + 144 = 24''y''

144''x''² – 312''x'' + 169 = 24''y'' + 25

(12''x'' – 13)² = 24''y'' + 25

12''x'' – 13 = ±{{sqrt|24''y'' + 25}}

12''x'' = 13 ± {{sqrt|24''y'' + 25}}

''x'' = {{sfrac|13 ± {{sqrt|24''y'' + 25}}|12}}

Quadratic function switch performed in late June or early summer 2022 by Amy (32 by age at that time)

10''x''² – 29''x'' + 10 = ''y''

400''x''² – 1,160''x'' + 400 = 40''y''

400''x''² – 1,160''x'' + 841 = 40''y'' + 441

(20''x'' – 29)² = 40''y'' + 441

20''x'' – 29 = ±{{sqrt|40''y'' + 441}}

20''x'' = 29 ± {{sqrt|40''y'' + 441}}

''x'' = {{sfrac|29 ± {{sqrt|40''y'' + 441}}|20}}

Quadratic function switch performed in late June or early summer 2022 by Tangle (35 by age at that time)

15''x''² – 34''x'' + 15 = ''y''

225''x''² – 510''x'' + 225 = 15''y''

225''x''² – 510''x'' + 289 = 15''y'' + 64

(15''x'' – 17)² = 15''y'' + 64

15''x'' – 17 = ±{{sqrt|15''y'' + 64}}

15''x'' = 17 ± {{sqrt|15''y'' + 64}}

''x'' = {{sfrac|17 ± {{sqrt|15''y'' + 64}}|15}}

Quadratic function switch performed in late June or early summer 2022 by Knuckles (36 by age at that time)

== Equation systems solved ==

''x'' + ''y'' = 4

4''xy'' = 15

''y'' = 4 – ''x''

4''x''(4 – ''x'') = 15

4''x''² – 16''x'' + 15 = 0

(2''x'' – 3)(2''x'' – 5) = 0

''x'' = {{sfrac|3|2}} and ''x'' = {{sfrac|5|2}}

''y'' = {{sfrac|5|2}} and ''y'' = {{sfrac|3|2}}

({{sfrac|3|2}}, {{sfrac|5|2}}) and ({{sfrac|5|2}}, {{sfrac|3|2}})

Equation system solved in late June or early summer 2022 by Shadow (37 by age at that time)

15''x'' + 15''y'' = 16

15''xy'' = 4

15''y'' = 16 – 15''x''

''y'' = {{sfrac|16 – 15''x''|15}}

15''x''({{sfrac|16 – 15''x''|15}}) = 4

15''x''² – 16''x'' + 4 = 0

(5''x'' – 2)(3''x'' – 2) = 0

''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|2|3}}

''y'' = {{sfrac|2|3}} and ''y'' = {{sfrac|2|5}}

({{sfrac|2|5}}, {{sfrac|2|3}}) and ({{sfrac|2|3}}, {{sfrac|2|5}})

Equation system solved in late June or early summer 2022 by Silver (35 by age at that time)

6''x'' + 6''y'' = 19

2''xy'' = 5

6''y'' = 19 – 6''x''

''y'' = {{sfrac|19 – 6''x''|6}}

2''x''({{sfrac|19 – 6''x''|6}}) = 5

6''x''² – 19''x'' + 15 = 0

(2''x'' – 3)(3''x'' – 5) = 0

''x'' = {{sfrac|3|2}} and ''x'' = {{sfrac|5|3}}

''y'' = {{sfrac|5|3}} and ''y'' = {{sfrac|3|2}}

({{sfrac|3|2}}, {{sfrac|5|3}}) and ({{sfrac|5|3}}, {{sfrac|3|2}})

Equation system solved in late June or early summer 2022 by Mighty (37 by age at that time)

15''x'' + 15''y'' = 19

5''xy'' = 2

15''y'' = 19 – 15''x''

''y'' = {{sfrac|19 – 15''x''|15}}

5''x''({{sfrac|19 – 15''x''|15}}) = 2

15''x''² – 19''x'' + 6 = 0

(5''x'' – 3)(3''x'' – 2) = 0

''x'' = {{sfrac|3|5}} and ''x'' = {{sfrac|2|3}}

''y'' = {{sfrac|2|3}} and ''y'' = {{sfrac|3|5}}

({{sfrac|3|5}}, {{sfrac|2|3}}) and ({{sfrac|2|3}}, {{sfrac|3|5}})

Equation system solved in late June or early summer 2022 by Sonic (36 by age at that time)

6''x'' + 6''y'' = 25

6''xy'' = 25

6''y'' = 25 – 6''x''

''y'' = {{sfrac|25 – 6''x''|6}}

6''x''({{sfrac|25 – 6''x''|6}}) = 25

6''x''² – 25''x'' + 25 = 0

(3''x'' – 5)(2''x'' – 5) = 0

''x'' = {{sfrac|5|3}} and ''x'' = {{sfrac|5|2}}

''y'' = {{sfrac|5|2}} and ''y'' = {{sfrac|5|3}}

({{sfrac|5|3}}, {{sfrac|5|2}}) and ({{sfrac|5|2}}, {{sfrac|5|3}})

Equation system solved in late June or early summer 2022 by Ray (30 by age at that time)

''x'' + ''y'' = 1

25''xy'' = 6

''y'' = 1 – ''x''

25''x''(1 – ''x'') = 6

25''x''² – 25''x'' + 6 = 0

(5''x'' – 2)(5''x'' – 3) = 0

''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|3|5}}

''y'' = {{sfrac|3|5}} and ''y'' = {{sfrac|2|5}}

({{sfrac|2|5}}, {{sfrac|3|5}}) and ({{sfrac|3|5}}, {{sfrac|2|5}})

Equation system solved in late June or early summer 2022 by Tails (29 by age at that time)

6''x'' + 6''y'' = 19

3''xy'' = 5

6''y'' = 19 – 6''x''

''y'' = {{sfrac|19 – 6''x''|6}}

3''x''({{sfrac|19 – 6''x''|6}}) = 5

6''x''² – 19''x'' + 10 = 0

(3''x'' – 2)(2''x'' – 5) = 0

''x'' = {{sfrac|2|3}} and ''x'' = {{sfrac|5|2}}

''y'' = {{sfrac|5|2}} and ''y'' = {{sfrac|2|3}}

({{sfrac|2|3}}, {{sfrac|5|2}}) and ({{sfrac|5|2}}, {{sfrac|2|3}})

Equation system solved in late June or early summer 2022 by Mina (37 by age at that time)

10''x'' + 10''y'' = 19

5''xy'' = 3

10''y'' = 19 – 10''x''

''y'' = {{sfrac|19 – 10''x''|10}}

5''x''({{sfrac|19 – 10''x''|10}}) = 3

10''x''² – 19''x'' + 6 = 0

(5''x'' – 2)(2''x'' – 3) = 0

''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|3|2}}

''y'' = {{sfrac|3|2}} and ''y'' = {{sfrac|2|5}}

({{sfrac|2|5}}, {{sfrac|3|2}}) and ({{sfrac|3|2}}, {{sfrac|2|5}})

Equation system solved in late June or early summer 2022 by Tikal (35 by age at that time)

3''x'' + 3''y'' = 7

9''xy'' = 10

3''y'' = 7 – 3''x''

''y'' = {{sfrac|7 – 3''x''|3}}

9''x''({{sfrac|7 – 3''x''|3}}) = 10

9''x''² – 21''x'' + 10 = 0

(3''x'' – 2)(3''x'' – 5) = 0

''x'' = {{sfrac|2|3}} and ''x'' = {{sfrac|5|3}}

''y'' = {{sfrac|5|3}} and ''y'' = {{sfrac|2|3}}

({{sfrac|2|3}}, {{sfrac|5|3}}) and ({{sfrac|5|3}}, {{sfrac|2|3}})

Equation system solved in late June or early summer 2022 by Rouge (38 by age at that time)

10''x'' + 10''y'' = 21

10''xy'' = 9

10''y'' = 21 – 10''x''

''y'' = {{sfrac|21 – 10''x''|10}}

10''x''({{sfrac|21 – 10''x''|10}}) = 9

10''x''² – 21''x'' + 9 = 0

(5''x'' – 3)(2''x'' – 3) = 0

''x'' = {{sfrac|3|5}} and ''x'' = {{sfrac|3|2}}

''y'' = {{sfrac|3|2}} and ''y'' = {{sfrac|3|5}}

({{sfrac|3|5}}, {{sfrac|3|2}}) and ({{sfrac|3|2}}, {{sfrac|3|5}})

Equation system solved in late June or early summer 2022 by Blaze (35 by age at that time)

10''x'' + 10''y'' = 31

2''xy'' = 3

10''y'' = 31 – 10''x''

''y'' = {{sfrac|31 – 10''x''|10}}

2''x''({{sfrac|31 – 10''x''|10}}) = 3

10''x''² – 31''x'' + 15 = 0

(5''x'' – 3)(2''x'' – 5) = 0

''x'' = {{sfrac|3|5}} and ''x'' = {{sfrac|5|2}}

''y'' = {{sfrac|5|2}} and ''y'' = {{sfrac|3|5}}

({{sfrac|3|5}}, {{sfrac|5|2}}) and ({{sfrac|5|2}}, {{sfrac|3|5}})

Equation system solved in late June or early summer 2022 by Sally (36 by age at that time)

15''x'' + 15''y'' = 31

3''xy'' = 2

15''y'' = 31 – 15''x''

''y'' = {{sfrac|31 – 15''x''|15}}

3''x''({{sfrac|31 – 15''x''|15}}) = 2

15''x''² – 31''x'' + 10 = 0

(5''x'' – 2)(3''x'' – 5) = 0

''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|5|3}}

''y'' = {{sfrac|5|3}} and ''y'' = {{sfrac|2|5}}

({{sfrac|2|5}}, {{sfrac|5|3}}) and ({{sfrac|5|3}}, {{sfrac|2|5}})

Equation system solved in late June or early summer 2022 by Marine (28 by age at that time)

6''x'' + 6''y'' = 13

''xy'' = 1

6''y'' = 13 – 6''x''

''y'' = {{sfrac|13 – 6''x''|6}}

''x''({{sfrac|13 – 6''x''|6}}) = 1

6''x''² – 13''x'' + 6 = 0

(3''x'' – 2)(2''x'' – 3) = 0

''x'' = {{sfrac|2|3}} and ''x'' = {{sfrac|3|2}}

''y'' = {{sfrac|3|2}} and ''y'' = {{sfrac|2|3}}

({{sfrac|2|3}}, {{sfrac|3|2}}) and ({{sfrac|3|2}}, {{sfrac|2|3}})

Equation system solved in late June or early summer 2022 by Amy (32 by age at that time)

10''x'' + 10''y'' = 29

''xy'' = 1

10''y'' = 29 – 10''x''

''y'' = {{sfrac|29 – 10''x''|10}}

''x''({{sfrac|29 – 10''x''|10}}) = 1

10''x''² – 29''x'' + 10 = 0

(5''x'' – 2)(2''x'' – 5) = 0

''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|5|2}}

''y'' = {{sfrac|5|2}} and ''y'' = {{sfrac|2|5}}

({{sfrac|2|5}}, {{sfrac|5|2}}) and ({{sfrac|5|2}}, {{sfrac|2|5}})

Equation system solved in late June or early summer 2022 by Tangle (35 by age at that time)

15''x'' + 15''y'' = 34

''xy'' = 1

15''y'' = 34 – 15''x''

''y'' = {{sfrac|34 – 15''x''|15}}

''x''({{sfrac|34 – 15''x''|15}}) = 1

15''x''² – 34''x'' + 15 = 0

(5''x'' – 3)(3''x'' – 5) = 0

''x'' = {{sfrac|3|5}} and ''x'' = {{sfrac|5|3}}

''y'' = {{sfrac|5|3}} and ''y'' = {{sfrac|3|5}}

({{sfrac|3|5}}, {{sfrac|5|3}}) and ({{sfrac|5|3}}, {{sfrac|3|5}})

Equation system solved in late June or early summer 2022 by Knuckles (36 by age at that time)

== Tangents to parabolae at intersection points relative to the horizontal axis ==

4''x'' + ''y'' = 6 at ({{sfrac|3|2}}, 0)

''y'' = 4''x'' – 10 at ({{sfrac|5|2}}, 0)

Tangents to ''y'' = 4''x''² – 16''x'' + 15, the parabola drawn in late June or early summer 2022 by Shadow (37 by age at that time), at intersection points relative to the ''x''-axis

20''x'' + 5''y'' = 8 at ({{sfrac|2|5}}, 0)

3''y'' = 12''x'' – 8 at ({{sfrac|2|3}}, 0)

Tangents to ''y'' = 15''x''² – 16''x'' + 4, the parabola drawn in late June or early summer 2022 by Silver (35 by age at that time), at intersection points relative to the ''x''-axis

2''x'' + 2''y'' = 3 at ({{sfrac|3|2}}, 0)

3''y'' = 3''x'' – 5 at ({{sfrac|5|3}}, 0)

Tangents to ''y'' = 6''x''² – 19''x'' + 15, the parabola drawn in late June or early summer 2022 by Mighty (37 by age at that time), at intersection points relative to the ''x''-axis

5''x'' + 5''y'' = 3 at ({{sfrac|3|5}}, 0)

3''y'' = 3''x'' – 2 at ({{sfrac|2|3}}, 0)

Tangents to ''y'' = 15''x''² – 19''x'' + 6, the parabola drawn in late June or early summer 2022 by Sonic (36 by age at that time), at intersection points relative to the ''x''-axis

15''x'' + 3''y'' = 25 at ({{sfrac|5|3}}, 0)

2''y'' = 10''x'' – 25 at ({{sfrac|5|2}}, 0)

Tangents to ''y'' = 6''x''² – 25''x'' + 25, the parabola drawn in late June or early summer 2022 by Ray (30 by age at that time), at intersection points relative to the ''x''-axis

5''x'' + ''y'' = 2 at ({{sfrac|2|5}}, 0)

''y'' = 5''x'' – 3 at ({{sfrac|3|5}}, 0)

Tangents to ''y'' = 25''x''² – 25''x'' + 6, the parabola drawn in late June or early summer 2022 by Tails (29 by age at that time), at intersection points relative to the ''x''-axis

33''x'' + 3''y'' = 22 at ({{sfrac|2|3}}, 0)

2''y'' = 22''x'' – 55 at ({{sfrac|5|2}}, 0)

Tangents to ''y'' = 6''x''² – 19''x'' + 10, the parabola drawn in late June or early summer 2022 by Mina (37 by age at that time), at intersection points relative to the ''x''-axis

55''x'' + 5''y'' = 22 at ({{sfrac|2|5}}, 0)

2''y'' = 22''x'' – 33 at ({{sfrac|3|2}}, 0)

Tangents to ''y'' = 10''x''² – 19''x'' + 6, the parabola drawn in late June or early summer 2022 by Tikal (35 by age at that time), at intersection points relative to the ''x''-axis

9''x'' + ''y'' = 6 at ({{sfrac|2|3}}, 0)

''y'' = 9''x'' – 15 at ({{sfrac|5|3}}, 0)

Tangents to ''y'' = 9''x''² – 21''x'' + 10, the parabola drawn in late June or early summer 2022 by Rouge (38 by age at that time), at intersection points relative to the ''x''-axis

45''x'' + 5''y'' = 27 at ({{sfrac|3|5}}, 0)

2''y'' = 18''x'' – 27 at ({{sfrac|3|2}}, 0)

Tangents to ''y'' = 10''x''² – 21''x'' + 9, the parabola drawn in late June or early summer 2022 by Blaze (35 by age at that time), at intersection points relative to the ''x''-axis

95''x'' + 5''y'' = 57 at ({{sfrac|3|5}}, 0)

2''y'' = 38''x'' – 95 at ({{sfrac|5|2}}, 0)

Tangents to ''y'' = 10''x''² – 31''x'' + 15, the parabola drawn in late June or early summer 2022 by Sally (36 by age at that time), at intersection points relative to the ''x''-axis

95''x'' + 5''y'' = 38 at ({{sfrac|2|5}}, 0)

3''y'' = 57''x'' – 95 at ({{sfrac|5|3}}, 0)

Tangents to ''y'' = 15''x''² – 31''x'' + 10, the parabola drawn in late June or early summer 2022 by Marine (28 by age at that time), at intersection points relative to the ''x''-axis

15''x'' + 3''y'' = 10 at ({{sfrac|2|3}}, 0)

2''y'' = 10''x'' – 15 at ({{sfrac|3|2}}, 0)

Tangents to ''y'' = 6''x''² – 13''x'' + 6, the parabola drawn in late June or early summer 2022 by Amy (32 by age at that time), at intersection points relative to the ''x''-axis

105''x'' + 5''y'' = 42 at ({{sfrac|2|5}}, 0)

2''y'' = 42''x'' – 105 at ({{sfrac|5|2}}, 0)

Tangents to ''y'' = 10''x''² – 29''x'' + 10, the parabola drawn in late June or early summer 2022 by Tangle (35 by age at that time), at intersection points relative to the ''x''-axis

80''x'' + 5''y'' = 48 at ({{sfrac|3|5}}, 0)

3''y'' = 48''x'' – 80 at ({{sfrac|5|3}}, 0)

Tangents to ''y'' = 15''x''² – 34''x'' + 15, the parabola drawn in late June or early summer 2022 by Knuckles (36 by age at that time), at intersection points relative to the ''x''-axis

== Sayings focusing on quadratic equations ==

In late June or early summer 2022:

* Shadow (37 by age at that time) said “4''x''² – 16''x'' + 15 = 0 becomes (2''x'' – 4)² = 1. My theory shows that (2''x'' – 4)² is on the left side and that one is on the right side. ''x'' = {{sfrac|3|2}} and ''x'' = {{sfrac|5|2}} are solutions to my quadratic equation.”

* Silver (35 by age at that time) said “15''x''² – 16''x'' + 4 = 0 becomes (15''x'' – 8)² = 4. My theory shows that (15''x'' – 8)² is on the left side and that four is on the right side. ''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|2|3}} are solutions to my quadratic equation.”

* Mighty (37 by age at that time) said “6''x''² – 19''x'' + 15 = 0 becomes (12''x'' – 19)² = 1. My theory shows that (12''x'' – 19)² is on the left side and that one is on the right side. ''x'' = {{sfrac|3|2}} and ''x'' = {{sfrac|5|3}} are solutions to my quadratic equation.”

* Sonic (36 by age at that time) said “15''x''² – 19''x'' + 6 = 0 becomes (30''x'' – 19)² = 1. My theory shows that (30''x'' – 19)² is on the left side and that one is on the right side. ''x'' = {{sfrac|3|5}} and ''x'' = {{sfrac|2|3}} are solutions to my quadratic equation.”

* Ray (30 by age at that time) said “6''x''² – 25''x'' + 25 = 0 becomes (12''x'' – 25)² = 25. My theory shows that (12''x'' – 25)² is on the left side and that 25 is on the right side. ''x'' = {{sfrac|5|3}} and ''x'' = {{sfrac|5|2}} are solutions to my quadratic equation.”

* Tails (29 by age at that time) said “25''x''² – 25''x'' + 6 = 0 becomes (10''x'' – 5)² = 1. My theory shows that (10''x'' – 5)² is on the left side and that one is on the right side. ''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|3|5}} are solutions to my quadratic equation.”

* Mina (37 by age at that time) said “6''x''² – 19''x'' + 10 = 0 becomes (12''x'' – 19)² = 121. My theory shows that (12''x'' – 19)² is on the left side and that 121 is on the right side. ''x'' = {{sfrac|2|3}} and ''x'' = {{sfrac|5|2}} are solutions to my quadratic equation.”

* Tikal (35 by age at that time) said “10''x''² – 19''x'' + 6 = 0 becomes (20''x'' – 19)² = 121. My theory shows that (20''x'' – 19)² is on the left side and that 121 is on the right side. ''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|3|2}} are solutions to my quadratic equation.”

* Rouge (38 by age at that time) said “9''x''² – 21''x'' + 10 = 0 becomes (6''x'' – 7)² = 9. My theory shows that (6''x'' – 7)² is on the left side and that nine is on the right side. ''x'' = {{sfrac|2|3}} and ''x'' = {{sfrac|5|3}} are solutions to my quadratic equation.”

* Blaze (35 by age at that time) said “10''x''² – 21''x'' + 9 = 0 becomes (20''x'' – 21)² = 81. My theory shows that (20''x'' – 21)² is on the left side and that 81 is on the right side. ''x'' = {{sfrac|3|5}} and ''x'' = {{sfrac|3|2}} are solutions to my quadratic equation.”

* Sally (36 by age at that time) said “10''x''² – 31''x'' + 15 = 0 becomes (20''x'' – 31)² = 361. My theory shows that (20''x'' – 31)² is on the left side and that 361 is on the right side. ''x'' = {{sfrac|3|5}} and ''x'' = {{sfrac|5|2}} are solutions to my quadratic equation.”

* Marine (28 by age at that time) said “15''x''² – 31''x'' + 10 = 0 becomes (30''x'' – 31)² = 361. My theory shows that (30''x'' – 31)² is on the left side and that 361 is on the right side. ''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|5|3}} are solutions to my quadratic equation.”

* Amy (32 by age at that time) said “6''x''² – 13''x'' + 6 = 0 becomes (12''x'' – 13)² = 25. My theory shows that (12''x'' – 13)² is on the left side and that 25 is on the right side. ''x'' = {{sfrac|2|3}} and ''x'' = {{sfrac|3|2}} are solutions to my quadratic equation.”

* Tangle (35 by age at that time) said “10''x''² – 29''x'' + 10 = 0 becomes (20''x'' – 29)² = 441. My theory shows that (20''x'' – 29)² is on the left side and that 441 is on the right side. ''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|5|2}} are solutions to my quadratic equation.”

* Knuckles (36 by age at that time) said “15''x''² – 34''x'' + 15 = 0 becomes (15''x'' – 17)² = 64. My theory shows that (15''x'' – 17)² is on the left side and that 64 is on the right side. ''x'' = {{sfrac|3|5}} and ''x'' = {{sfrac|5|3}} are solutions to my quadratic equation.”

== Sayings focusing on quadratic expressions ==

In late June or early summer 2022:

* Shadow (37 by age at that time) said “(4''x''² – 16''x'' + 15) is written in vertex form as {(2''x'' – 4)² – 1} and in factorized form as (2''x'' – 3)(2''x'' – 5). It decreases for ''x'' < 2, i.e. before ''x'' = 2, has a minimum stationary value, written as negative one, at ''x'' = 2, increases for ''x'' > 2, i.e. after ''x'' = 2, and is negative for {{sfrac|3|2}} < ''x'' < {{sfrac|5|2}}, i.e. after ''x'' = {{sfrac|3|2}} but before ''x'' = {{sfrac|5|2}}, zero at ''x'' = {{sfrac|3|2}} and ''x'' = {{sfrac|5|2}} and positive for ''x'' < {{sfrac|3|2}}, i.e. before ''x'' = {{sfrac|3|2}}, and ''x'' > {{sfrac|5|2}}, i.e. after ''x'' = {{sfrac|5|2}}.”

* Silver (35 by age at that time) said “(15''x''² – 16''x'' + 4) is written in vertex form as {{sfrac|(15''x'' – 8)² – 4|15}} and in factorized form as (5''x'' – 2)(3''x'' – 2). It decreases for ''x'' < {{sfrac|8|15}}, i.e. before ''x'' = {{sfrac|8|15}}, has a minimum stationary value, written as –{{sfrac|4|15}}, at ''x'' = {{sfrac|8|15}}, increases for ''x'' > {{sfrac|8|15}}, i.e. after ''x'' = {{sfrac|8|15}}, and is negative for {{sfrac|2|5}} < ''x'' < {{sfrac|2|3}}, i.e. after ''x'' = {{sfrac|2|5}} but before ''x'' = {{sfrac|2|3}}, zero at ''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|2|3}} and positive for ''x'' < {{sfrac|2|5}}, i.e. before ''x'' = {{sfrac|2|5}}, and ''x'' > {{sfrac|2|3}}, i.e. after ''x'' = {{sfrac|2|3}}.”

* Mighty (37 by age at that time) said “(6''x''² – 19''x'' + 15) is written in vertex form as {{sfrac|(12''x'' – 19)² – 1|24}} and in factorized form as (2''x'' – 3)(3''x'' – 5). It decreases for ''x'' < {{sfrac|19|12}}, i.e. before ''x'' = {{sfrac|19|12}}, has a minimum stationary value, written as –{{sfrac|1|24}}, at ''x'' = {{sfrac|19|12}}, increases for ''x'' > {{sfrac|19|12}}, i.e. after ''x'' = {{sfrac|19|12}}, and is negative for {{sfrac|3|2}} < ''x'' < {{sfrac|5|3}}, i.e. after ''x'' = {{sfrac|3|2}} but before ''x'' = {{sfrac|5|3}}, zero at ''x'' = {{sfrac|3|2}} and ''x'' = {{sfrac|5|3}} and positive for ''x'' < {{sfrac|3|2}}, i.e. before ''x'' = {{sfrac|3|2}}, and ''x'' > {{sfrac|5|3}}, i.e. after ''x'' = {{sfrac|5|3}}.”

* Sonic (36 by age at that time) said “(15''x''² – 19''x'' + 6) is written in vertex form as {{sfrac|(30''x'' – 19)² – 1|60}} and in factorized form as (5''x'' – 3)(3''x'' – 2). It decreases for ''x'' < {{sfrac|19|30}}, i.e. before ''x'' = {{sfrac|19|30}}, has a minimum stationary value, written as –{{sfrac|1|60}}, at ''x'' = {{sfrac|19|30}}, increases for ''x'' > {{sfrac|19|30}}, i.e. after ''x'' = {{sfrac|19|30}}, and is negative for {{sfrac|3|5}} < ''x'' < {{sfrac|2|3}}, i.e. after ''x'' = {{sfrac|3|5}} but before ''x'' = {{sfrac|2|3}}, zero at ''x'' = {{sfrac|3|5}} and ''x'' = {{sfrac|2|3}} and positive for ''x'' < {{sfrac|3|5}}, i.e. before ''x'' = {{sfrac|3|5}}, and ''x'' > {{sfrac|2|3}}, i.e. after ''x'' = {{sfrac|2|3}}.”

* Ray (30 by age at that time) said “(6''x''² – 25''x'' + 25) is written in vertex form as {{sfrac|(12''x'' – 25)² – 25|24}} and in factorized form as (3''x'' – 5)(2''x'' – 5). It decreases for ''x'' < {{sfrac|25|12}}, i.e. before ''x'' = {{sfrac|25|12}}, has a minimum stationary value, written as –{{sfrac|25|24}}, at ''x'' = {{sfrac|25|12}}, increases for ''x'' > {{sfrac|25|12}}, i.e. after ''x'' = {{sfrac|25|12}}, and is negative for {{sfrac|5|3}} < ''x'' < {{sfrac|5|2}}, i.e. after ''x'' = {{sfrac|5|3}} but before ''x'' = {{sfrac|5|2}}, zero at ''x'' = {{sfrac|5|3}} and ''x'' = {{sfrac|5|2}} and positive for ''x'' < {{sfrac|5|3}}, i.e. before ''x'' = {{sfrac|5|3}}, and ''x'' > {{sfrac|5|2}}, i.e. after ''x'' = {{sfrac|5|2}}.”

* Tails (29 by age at that time) said “(25''x''² – 25''x'' + 6) is written in vertex form as {{sfrac|(10''x'' – 5)² – 1|4}} and in factorized form as (5''x'' – 2)(5''x'' – 3). It decreases for ''x'' < {{sfrac|1|2}}, i.e. before ''x'' = {{sfrac|1|2}}, has a minimum stationary value, written as –{{sfrac|1|4}}, at ''x'' = {{sfrac|1|2}}, increases for ''x'' > {{sfrac|1|2}}, i.e. after ''x'' = {{sfrac|1|2}}, and is negative for {{sfrac|2|5}} < ''x'' < {{sfrac|3|5}}, i.e. after ''x'' = {{sfrac|2|5}} but before ''x'' = {{sfrac|3|5}}, zero at ''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|3|5}} and positive for ''x'' < {{sfrac|2|5}}, i.e. before ''x'' = {{sfrac|2|5}}, and ''x'' > {{sfrac|3|5}}, i.e. after ''x'' = {{sfrac|3|5}}.”

* Mina (37 by age at that time) said “(6''x''² – 19''x'' + 10) is written in vertex form as {{sfrac|(12''x'' – 19)² – 121|24}} and in factorized form as (3''x'' – 2)(2''x'' – 5). It decreases for ''x'' < {{sfrac|19|12}}, i.e. before ''x'' = {{sfrac|19|12}}, has a minimum stationary value, written as –{{sfrac|121|24}}, at ''x'' = {{sfrac|19|12}}, increases for ''x'' > {{sfrac|19|12}}, i.e. after ''x'' = {{sfrac|19|12}}, and is negative for {{sfrac|2|3}} < ''x'' < {{sfrac|5|2}}, i.e. after ''x'' = {{sfrac|2|3}} but before ''x'' = {{sfrac|5|2}}, zero at ''x'' = {{sfrac|2|3}} and ''x'' = {{sfrac|5|2}} and positive for ''x'' < {{sfrac|2|3}}, i.e. before ''x'' = {{sfrac|2|3}}, and ''x'' > {{sfrac|5|2}}, i.e. after ''x'' = {{sfrac|5|2}}.”

* Tikal (35 by age at that time) said “(10''x''² – 19''x'' + 6) is written in vertex form as {{sfrac|(20''x'' – 19)² – 121|40}} and in factorized form as (5''x'' – 2)(2''x'' – 3). It decreases for ''x'' < {{sfrac|19|20}}, i.e. before ''x'' = {{sfrac|19|20}}, has a minimum stationary value, written as –{{sfrac|121|40}}, at ''x'' = {{sfrac|19|20}}, increases for ''x'' > {{sfrac|19|20}}, i.e. after ''x'' = {{sfrac|19|20}}, and is negative for {{sfrac|2|5}} < ''x'' < {{sfrac|3|2}}, i.e. after ''x'' = {{sfrac|2|5}} but before ''x'' = {{sfrac|3|2}}, zero at ''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|3|2}} and positive for ''x'' < {{sfrac|2|5}}, i.e. before ''x'' = {{sfrac|2|5}}, and ''x'' > {{sfrac|3|2}}, i.e. after ''x'' = {{sfrac|3|2}}.”

* Rouge (38 by age at that time) said “(9''x''² – 21''x'' + 10) is written in vertex form as {{sfrac|(6''x'' – 7)² – 9|4}} and in factorized form as (3''x'' – 2)(3''x'' – 5). It decreases for ''x'' < {{sfrac|7|6}}, i.e. before ''x'' = {{sfrac|7|6}}, has a minimum stationary value, written as –{{sfrac|9|4}}, at ''x'' = {{sfrac|7|6}}, increases for ''x'' > {{sfrac|7|6}}, i.e. after ''x'' = {{sfrac|7|6}}, and is negative for {{sfrac|2|3}} < ''x'' < {{sfrac|5|3}}, i.e. after ''x'' = {{sfrac|2|3}} but before ''x'' = {{sfrac|5|3}}, zero at ''x'' = {{sfrac|2|3}} and ''x'' = {{sfrac|5|3}} and positive for ''x'' < {{sfrac|2|3}}, i.e. before ''x'' = {{sfrac|2|3}}, and ''x'' > {{sfrac|5|3}}, i.e. after ''x'' = {{sfrac|5|3}}.”

* Blaze (35 by age at that time) said “(10''x''² – 21''x'' + 9) is written in vertex form as {{sfrac|(20''x'' – 21)² – 81|40}} and in factorized form as (5''x'' – 3)(2''x'' – 3). It decreases for ''x'' < {{sfrac|21|20}}, i.e. before ''x'' = {{sfrac|21|20}}, has a minimum stationary value, written as –{{sfrac|81|40}}, at ''x'' = {{sfrac|21|20}}, increases for ''x'' > {{sfrac|21|20}}, i.e. after ''x'' = {{sfrac|21|20}}, and is negative for {{sfrac|3|5}} < ''x'' < {{sfrac|3|2}}, i.e. after ''x'' = {{sfrac|3|5}} but before ''x'' = {{sfrac|3|2}}, zero at ''x'' = {{sfrac|3|5}} and ''x'' = {{sfrac|3|2}} and positive for ''x'' < {{sfrac|3|5}}, i.e. before ''x'' = {{sfrac|3|5}}, and ''x'' > {{sfrac|3|2}}, i.e. after ''x'' = {{sfrac|3|2}}.”

* Sally (36 by age at that time) said “(10''x''² – 31''x'' + 15) is written in vertex form as {{sfrac|(20''x'' – 31)² – 361|40}} and in factorized form as (5''x'' – 3)(2''x'' – 5). It decreases for ''x'' < {{sfrac|31|20}}, i.e. before ''x'' = {{sfrac|31|20}}, has a minimum stationary value, written as –{{sfrac|361|40}}, at ''x'' = {{sfrac|31|20}}, increases for ''x'' > {{sfrac|31|20}}, i.e. after ''x'' = {{sfrac|31|20}}, and is negative for {{sfrac|3|5}} < ''x'' < {{sfrac|5|2}}, i.e. after ''x'' = {{sfrac|3|5}} but before ''x'' = {{sfrac|5|2}}, zero at ''x'' = {{sfrac|3|5}} and ''x'' = {{sfrac|5|2}} and positive for ''x'' < {{sfrac|3|5}}, i.e. before ''x'' = {{sfrac|3|5}}, and ''x'' > {{sfrac|5|2}}, i.e. after ''x'' = {{sfrac|5|2}}.”

* Marine (28 by age at that time) said “(15''x''² – 31''x'' + 10) is written in vertex form as {{sfrac|(30''x'' – 31)² – 361|60}} and in factorized form as (5''x'' – 2)(3''x'' – 5). It decreases for ''x'' < {{sfrac|31|30}}, i.e. before ''x'' = {{sfrac|31|30}}, has a minimum stationary value, written as –{{sfrac|361|60}}, at ''x'' = {{sfrac|31|30}}, increases for ''x'' > {{sfrac|31|30}}, i.e. after ''x'' = {{sfrac|31|30}}, and is negative for {{sfrac|2|5}} < ''x'' < {{sfrac|5|3}}, i.e. after ''x'' = {{sfrac|2|5}} but before ''x'' = {{sfrac|5|3}}, zero at ''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|5|3}} and positive for ''x'' < {{sfrac|2|5}}, i.e. before ''x'' = {{sfrac|2|5}}, and ''x'' > {{sfrac|5|3}}, i.e. after ''x'' = {{sfrac|5|3}}.”

* Amy (32 by age at that time) said “(6''x''² – 13''x'' + 6) is written in vertex form as {{sfrac|(12''x'' – 13)² – 25|24}} and in factorized form as (3''x'' – 2)(2''x'' – 3). It decreases for ''x'' < {{sfrac|13|12}}, i.e. before ''x'' = {{sfrac|13|12}}, has a minimum stationary value, written as –{{sfrac|25|24}}, at ''x'' = {{sfrac|13|12}}, increases for ''x'' > {{sfrac|13|12}}, i.e. after ''x'' = {{sfrac|13|12}}, and is negative for {{sfrac|2|3}} < ''x'' < {{sfrac|3|2}}, i.e. after ''x'' = {{sfrac|2|3}} but before ''x'' = {{sfrac|3|2}}, zero at ''x'' = {{sfrac|2|3}} and ''x'' = {{sfrac|3|2}} and positive for ''x'' < {{sfrac|2|3}}, i.e. before ''x'' = {{sfrac|2|3}}, and ''x'' > {{sfrac|3|2}}, i.e. after ''x'' = {{sfrac|3|2}}.”

* Tangle (35 by age at that time) said “(10''x''² – 29''x'' + 10) is written in vertex form as {{sfrac|(20''x'' – 29)² – 441|40}} and in factorized form as (5''x'' – 2)(2''x'' – 5). It decreases for ''x'' < {{sfrac|29|20}}, i.e. before ''x'' = {{sfrac|29|20}}, has a minimum stationary value, written as –{{sfrac|441|40}}, at ''x'' = {{sfrac|29|20}}, increases for ''x'' > {{sfrac|29|20}}, i.e. after ''x'' = {{sfrac|29|20}}, and is negative for {{sfrac|2|5}} < ''x'' < {{sfrac|5|2}}, i.e. after ''x'' = {{sfrac|2|5}} but before ''x'' = {{sfrac|5|2}}, zero at ''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|5|2}} and positive for ''x'' < {{sfrac|2|5}}, i.e. before ''x'' = {{sfrac|2|5}}, and ''x'' > {{sfrac|5|2}}, i.e. after ''x'' = {{sfrac|5|2}}.”

* Knuckles (36 by age at that time) said “(15''x''² – 34''x'' + 15) is written in vertex form as {{sfrac|(15''x'' – 17)² – 64|15}} and in factorized form as (5''x'' – 3)(3''x'' – 5). It decreases for ''x'' < {{sfrac|17|15}}, i.e. before ''x'' = {{sfrac|17|15}}, has a minimum stationary value, written as –{{sfrac|64|15}}, at ''x'' = {{sfrac|17|15}}, increases for ''x'' > {{sfrac|17|15}}, i.e. after ''x'' = {{sfrac|17|15}}, and is negative for {{sfrac|3|5}} < ''x'' < {{sfrac|5|3}}, i.e. after ''x'' = {{sfrac|3|5}} but before ''x'' = {{sfrac|5|3}}, zero at ''x'' = {{sfrac|3|5}} and ''x'' = {{sfrac|5|3}} and positive for ''x'' < {{sfrac|3|5}}, i.e. before ''x'' = {{sfrac|3|5}}, and ''x'' > {{sfrac|5|3}}, i.e. after ''x'' = {{sfrac|5|3}}.”

== Sayings focusing on quadratic function switches ==

In late June or early summer 2022:

* Shadow (37 by age at that time) said “4''x''² – 16''x'' + 15 = ''y'' becomes (2''x'' – 4)² = ''y'' + 1. My theory shows that (2''x'' – 4)² is on the left side and that (''y'' + 1) is on the right side. ''x'' = {{sfrac|4 ± {{sqrt|''y'' + 1}}|2}} is my switch.”

* Silver (35 by age at that time) said “15''x''² – 16''x'' + 4 = ''y'' becomes (15''x'' – 8)² = 15''y'' + 4. My theory shows that (15''x'' – 8)² is on the left side and that (15''y'' + 4) is on the right side. ''x'' = {{sfrac|8 ± {{sqrt|15''y'' + 4}}|15}} is my switch.”

* Mighty (37 by age at that time) said “6''x''² – 19''x'' + 15 = ''y'' becomes (12''x'' – 19)² = 24''y'' + 1. My theory shows that (12''x'' – 19)² is on the left side and that (24''y'' + 1) is on the right side. ''x'' = {{sfrac|19 ± {{sqrt|24''y'' + 1}}|12}} is my switch.”

* Sonic (36 by age at that time) said “15''x''² – 19''x'' + 6 = ''y'' becomes (30''x'' – 19)² = 60''y'' + 1. My theory shows that (30''x'' – 19)² is on the left side and that (60''y'' + 1) is on the right side. ''x'' = {{sfrac|19 ± {{sqrt|60''y'' + 1}}|30}} is my switch.”

* Ray (30 by age at that time) said “6''x''² – 25''x'' + 25 = ''y'' becomes (12''x'' – 25)² = 24''y'' + 25. My theory shows that (12''x'' – 25)² is on the left side and that (24''y'' + 25) is on the right side. ''x'' = {{sfrac|25 ± {{sqrt|24''y'' + 25}}|12}} is my switch.”

* Tails (29 by age at that time) said “25''x''² – 25''x'' + 6 = ''y'' becomes (10''x'' – 5)² = 4''y'' + 1. My theory shows that (10''x'' – 5)² is on the left side and that (4''y'' + 1) is on the right side. ''x'' = {{sfrac|5 ± {{sqrt|4''y'' + 1}}|10}} is my switch.”

* Mina (37 by age at that time) said “6''x''² – 19''x'' + 10 = ''y'' becomes (12''x'' – 19)² = 24''y'' + 121. My theory shows that (12''x'' – 19)² is on the left side and that (24''y'' + 121) is on the right side. ''x'' = {{sfrac|19 ± {{sqrt|24''y'' + 121}}|12}} is my switch.”

* Tikal (35 by age at that time) said “10''x''² – 19''x'' + 6 = ''y'' becomes (20''x'' – 19)² = 40''y'' + 121. My theory shows that (20''x'' – 19)² is on the left side and that (40''y'' + 121) is on the right side. ''x'' = {{sfrac|19 ± {{sqrt|40''y'' + 121}}|20}} is my switch.”

* Rouge (38 by age at that time) said “9''x''² – 21''x'' + 10 = ''y'' becomes (6''x'' – 7)² = 4''y'' + 9. My theory shows that (6''x'' – 7)² is on the left side and that (4''y'' + 9) is on the right side. ''x'' = {{sfrac|7 ± {{sqrt|4''y'' + 9}}|6}} is my switch.”

* Blaze (35 by age at that time) said “10''x''² – 21''x'' + 9 = ''y'' becomes (20''x'' – 21)² = 40''y'' + 81. My theory shows that (20''x'' – 21)² is on the left side and that (40''y'' + 81) is on the right side. ''x'' = {{sfrac|21 ± {{sqrt|40''y'' + 81}}|20}} is my switch.”

* Sally (36 by age at that time) said “10''x''² – 31''x'' + 15 = ''y'' becomes (20''x'' – 31)² = 40''y'' + 361. My theory shows that (20''x'' – 31)² is on the left side and that (40''y'' + 361) is on the right side. ''x'' = {{sfrac|31 ± {{sqrt|40''y'' + 361}}|20}} is my switch.”

* Marine (28 by age at that time) said “15''x''² – 31''x'' + 10 = ''y'' becomes (30''x'' – 31)² = 60''y'' + 361. My theory shows that (30''x'' – 31)² is on the left side and that (60''y'' + 361) is on the right side. ''x'' = {{sfrac|31 ± {{sqrt|60''y'' + 361}}|30}} is my switch.”

* Amy (32 by age at that time) said “6''x''² – 13''x'' + 6 = ''y'' becomes (12''x'' – 13)² = 24''y'' + 25. My theory shows that (12''x'' – 13)² is on the left side and that (24''y'' + 25) is on the right side. ''x'' = {{sfrac|13 ± {{sqrt|24''y'' + 25}}|12}} is my switch.”

* Tangle (35 by age at that time) said “10''x''² – 29''x'' + 10 = ''y'' becomes (20''x'' – 29)² = 40''y'' + 441. My theory shows that (20''x'' – 29)² is on the left side and that (40''y'' + 441) is on the right side. ''x'' = {{sfrac|29 ± {{sqrt|40''y'' + 441}}|20}} is my switch.”

* Knuckles (36 by age at that time) said “15''x''² – 34''x'' + 15 = ''y'' becomes (15''x'' – 17)² = 15''y'' + 64. My theory shows that (15''x'' – 17)² is on the left side and that (40''y'' + 361) is on the right side. ''x'' = {{sfrac|17 ± {{sqrt|15''y'' + 64}}|15}} is my switch.”

== Sayings focusing on quadratic function switches ==

In late June or early summer 2022:

* Shadow (37 by age at that time) said “4''x'' + ''y'' = 6 is the tangent to ''y'' = 4''x''² – 16''x'' + 15 at ({{sfrac|3|2}}, 0). ''y'' = 4''x'' – 10 is the tangent to my parabola at ({{sfrac|5|2}}, 0).”

* Silver (35 by age at that time) said “20''x'' + 5''y'' = 8 is the tangent to ''y'' = 15''x''² – 16''x'' + 4 at ({{sfrac|2|5}}, 0). 3''y'' = 12''x'' – 8 is the tangent to my parabola at ({{sfrac|2|3}}, 0).”

* Mighty (37 by age at that time) said “2''x'' + 2''y'' = 3 is the tangent to ''y'' = 6''x''² – 19''x'' + 15 at ({{sfrac|3|2}}, 0). 3''y'' = 3''x'' – 5 is the tangent to my parabola at ({{sfrac|5|3}}, 0).”

* Sonic (36 by age at that time) said “5''x'' + 5''y'' = 3 is the tangent to ''y'' = 15''x''² – 19''x'' + 6 at ({{sfrac|3|5}}, 0). 3''y'' = 3''x'' – 2 is the tangent to my parabola at ({{sfrac|2|3}}, 0).”

* Ray (30 by age at that time) said “15''x'' + 3''y'' = 25 is the tangent to ''y'' = 6''x''² – 25''x'' + 25 at ({{sfrac|5|3}}, 0). 2''y'' = 10''x'' – 25 is the tangent to my parabola at ({{sfrac|5|2}}, 0).”

* Tails (29 by age at that time) said “5''x'' + ''y'' = 2 is the tangent to ''y'' = 25''x''² – 25''x'' + 6 at ({{sfrac|2|5}}, 0). ''y'' = 5''x'' – 3 is the tangent to my parabola at ({{sfrac|3|5}}, 0).”

* Mina (37 by age at that time) said “33''x'' + 3''y'' = 22 is the tangent to ''y'' = 6''x''² – 19''x'' + 10 at ({{sfrac|2|3}}, 0). 2''y'' = 22''x'' – 55 is the tangent to my parabola at ({{sfrac|5|2}}, 0).”

* Tikal (35 by age at that time) said “55''x'' + 5''y'' = 22 is the tangent to ''y'' = 10''x''² – 19''x'' + 6 at ({{sfrac|2|5}}, 0). 2''y'' = 22''x'' – 33 is the tangent to my parabola at ({{sfrac|3|2}}, 0).”

* Rouge (38 by age at that time) said “9''x'' + ''y'' = 6 is the tangent to ''y'' = 9''x''² – 21''x'' + 10 at ({{sfrac|2|3}}, 0). ''y'' = 9''x'' – 15 is the tangent to my parabola at ({{sfrac|5|3}}, 0).”

* Blaze (35 by age at that time) said “45''x'' + 5''y'' = 27 is the tangent to ''y'' = 10''x''² – 21''x'' + 9 at ({{sfrac|3|5}}, 0). 2''y'' = 18''x'' – 27 is the tangent to my parabola at ({{sfrac|3|2}}, 0).”

* Sally (36 by age at that time) said “95''x'' + 5''y'' = 57 is the tangent to ''y'' = 10''x''² – 31''x'' + 15 at ({{sfrac|3|5}}, 0). 2''y'' = 38''x'' – 95 is the tangent to my parabola at ({{sfrac|5|2}}, 0).”

* Marine (28 by age at that time) said “95''x'' + 5''y'' = 38 is the tangent to ''y'' = 15''x''² – 31''x'' + 10 at ({{sfrac|2|5}}, 0). 3''y'' = 57''x'' – 95 is the tangent to my parabola at ({{sfrac|5|3}}, 0).”

* Amy (32 by age at that time) said “15''x'' + 3''y'' = 10 is the tangent to ''y'' = 6''x''² – 13''x'' + 6 at ({{sfrac|2|3}}, 0). 2''y'' = 10''x'' – 15 is the tangent to my parabola at ({{sfrac|3|2}}, 0).”

* Tangle (35 by age at that time) said “105''x'' + 5''y'' = 42 is the tangent to ''y'' = 10''x''² – 29''x'' + 10 at ({{sfrac|2|5}}, 0). 2''y'' = 42''x'' – 105 is the tangent to my parabola at ({{sfrac|5|2}}, 0).”

* Knuckles (36 by age at that time) said “80''x'' + 5''y'' = 48 is the tangent to ''y'' = 15''x''² – 34''x'' + 15 at ({{sfrac|3|5}}, 0). 3''y'' = 48''x'' – 80 is the tangent to my parabola at ({{sfrac|5|3}}, 0).”

== Sayings focusing on horizontal intercepts ==

In late June or early summer 2022:

* Shadow (37 by age at that time) said “''y'' = 4''x''² – 16''x'' + 15 has two ''x''-intercepts, i.e. it crosses or cuts the ''x''-axis twice, once at ''x'' = {{sfrac|3|2}} and again at ''x'' = {{sfrac|5|2}}.”

* Silver (35 by age at that time) said “''y'' = 15''x''² – 16''x'' + 4 has two ''x''-intercepts, i.e. it crosses or cuts the ''x''-axis twice, once at ''x'' = {{sfrac|2|5}} and again at ''x'' = {{sfrac|2|3}}.”

* Mighty (37 by age at that time) said “''y'' = 6''x''² – 19''x'' + 15 has two ''x''-intercepts, i.e. it crosses or cuts the ''x''-axis twice, once at ''x'' = {{sfrac|3|2}} and again at ''x'' = {{sfrac|5|3}}.”

* Sonic (36 by age at that time) said “''y'' = 15''x''² – 19''x'' + 6 has two ''x''-intercepts, i.e. it crosses or cuts the ''x''-axis twice, once at ''x'' = {{sfrac|3|5}} and again at ''x'' = {{sfrac|2|3}}.”

* Ray (30 by age at that time) said “''y'' = 6''x''² – 25''x'' + 25 has two ''x''-intercepts, i.e. it crosses or cuts the ''x''-axis twice, once at ''x'' = {{sfrac|3|2}} and again at ''x'' = {{sfrac|5|2}}.”

* Tails (29 by age at that time) said “''y'' = 25''x''² – 25''x'' + 6 has two ''x''-intercepts, i.e. it crosses or cuts the ''x''-axis twice, once at ''x'' = {{sfrac|2|5}} and again at ''x'' = {{sfrac|3|5}}.”

* Mina (37 by age at that time) said “''y'' = 6''x''² – 19''x'' + 10 has two ''x''-intercepts, i.e. it crosses or cuts the ''x''-axis twice, once at ''x'' = {{sfrac|2|3}} and again at ''x'' = {{sfrac|5|2}}.”

* Tikal (35 by age at that time) said “''y'' = 10''x''² – 19''x'' + 6 has two ''x''-intercepts, i.e. it crosses or cuts the ''x''-axis twice, once at ''x'' = {{sfrac|2|5}} and again at ''x'' = {{sfrac|3|2}}.”

* Rouge (38 by age at that time) said “''y'' = 9''x''² – 21''x'' + 10 has two ''x''-intercepts, i.e. it crosses or cuts the ''x''-axis twice, once at ''x'' = {{sfrac|2|3}} and again at ''x'' = {{sfrac|5|3}}.”

* Blaze (35 by age at that time) said “''y'' = 10''x''² – 21''x'' + 9 has two ''x''-intercepts, i.e. it crosses or cuts the ''x''-axis twice, once at ''x'' = {{sfrac|3|5}} and again at ''x'' = {{sfrac|3|2}}.”

* Sally (36 by age at that time) said “''y'' = 10''x''² – 31''x'' + 15 has two ''x''-intercepts, i.e. it crosses or cuts the ''x''-axis twice, once at ''x'' = {{sfrac|3|5}} and again at ''x'' = {{sfrac|5|2}}.”

* Marine (28 by age at that time) said “''y'' = 15''x''² – 31''x'' + 10 has two ''x''-intercepts, i.e. it crosses or cuts the ''x''-axis twice, once at ''x'' = {{sfrac|2|5}} and again at ''x'' = {{sfrac|5|3}}.”

* Amy (32 by age at that time) said “''y'' = 6''x''² – 13''x'' + 6 has two ''x''-intercepts, i.e. it crosses or cuts the ''x''-axis twice, once at ''x'' = {{sfrac|2|3}} and again at ''x'' = {{sfrac|3|2}}.”

* Tangle (35 by age at that time) said “''y'' = 10''x''² – 29''x'' + 10 has two ''x''-intercepts, i.e. it crosses or cuts the ''x''-axis twice, once at ''x'' = {{sfrac|2|5}} and again at ''x'' = {{sfrac|5|2}}.”

* Knuckles (36 by age at that time) said “''y'' = 15''x''² – 34''x'' + 15 has two ''x''-intercepts, i.e. it crosses or cuts the ''x''-axis twice, once at ''x'' = {{sfrac|3|5}} and again at ''x'' = {{sfrac|5|3}}.”

=== Sayings focusing on axes of symmetry ===

In late June or early summer 2022:

* Shadow (37 by age at that time) said “''x'' = 2 is the axis of symmetry, which is in the middle and halfway between ''x'' = {{sfrac|3|2}} and ''x'' = {{sfrac|5|2}}, the ''x''-intercepts of ''y'' = 4''x''² – 16''x'' + 15.”

* Silver (35 by age at that time) said “''x'' = {{sfrac|8|15}} is the axis of symmetry, which is in the middle and halfway between ''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|2|3}}, the ''x''-intercepts of ''y'' = 15''x''² – 16''x'' + 4.”

* Mighty (37 by age at that time) said “''x'' = {{sfrac|19|12}} is the axis of symmetry, which is in the middle and halfway between ''x'' = {{sfrac|3|2}} and ''x'' = {{sfrac|5|3}}, the ''x''-intercepts of ''y'' = 6''x''² – 19''x'' + 15.”

* Sonic (36 by age at that time) said “''x'' = {{sfrac|19|30}} is the axis of symmetry, which is in the middle and halfway between ''x'' = {{sfrac|3|5}} and ''x'' = {{sfrac|2|3}}, the ''x''-intercepts of ''y'' = 15''x''² – 19''x'' + 6.”

* Ray (30 by age at that time) said “''x'' = {{sfrac|25|12}} is the axis of symmetry, which is in the middle and halfway between ''x'' = {{sfrac|5|3}} and ''x'' = {{sfrac|5|2}}, the ''x''-intercepts of ''y'' = 6''x''² – 25''x'' + 25.”

* Tails (29 by age at that time) said “''x'' = {{sfrac|1|2}} is the axis of symmetry, which is in the middle and halfway between ''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|3|5}}, the ''x''-intercepts of ''y'' = 25''x''² – 25''x'' + 6.”

* Mina (37 by age at that time) said “''x'' = {{sfrac|19|12}} is the axis of symmetry, which is in the middle and halfway between ''x'' = {{sfrac|2|3}} and ''x'' = {{sfrac|5|2}}, the ''x''-intercepts of ''y'' = 6''x''² – 19''x'' + 10.”

* Tikal (35 by age at that time) said “''x'' = {{sfrac|19|20}} is the axis of symmetry, which is in the middle and halfway between ''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|3|2}}, the ''x''-intercepts of ''y'' = 10''x''² – 19''x'' + 6.”

* Rouge (38 by age at that time) said “''x'' = {{sfrac|7|6}} is the axis of symmetry, which is in the middle and halfway between ''x'' = {{sfrac|2|3}} and ''x'' = {{sfrac|5|3}}, the ''x''-intercepts of ''y'' = 9''x''² – 21''x'' + 10.”

* Blaze (35 by age at that time) said “''x'' = {{sfrac|21|20}} is the axis of symmetry, which is in the middle and halfway between ''x'' = {{sfrac|3|5}} and ''x'' = {{sfrac|3|2}}, the ''x''-intercepts of ''y'' = 10''x''² – 21''x'' + 9.”

* Sally (36 by age at that time) said “''x'' = {{sfrac|31|20}} is the axis of symmetry, which is in the middle and halfway between ''x'' = {{sfrac|3|5}} and ''x'' = {{sfrac|5|2}}, the ''x''-intercepts of ''y'' = 10''x''² – 31''x'' + 15.”

* Marine (28 by age at that time) said “''x'' = {{sfrac|31|30}} is the axis of symmetry, which is in the middle and halfway between ''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|5|3}}, the ''x''-intercepts of ''y'' = 15''x''² – 31''x'' + 10.”

* Amy (32 by age at that time) said “''x'' = {{sfrac|13|12}} is the axis of symmetry, which is in the middle and halfway between ''x'' = {{sfrac|2|3}} and ''x'' = {{sfrac|3|2}}, the ''x''-intercepts of ''y'' = 6''x''² – 13''x'' + 6.”

* Tangle (35 by age at that time) said “''x'' = {{sfrac|29|20}} is the axis of symmetry, which is in the middle and halfway between ''x'' = {{sfrac|2|5}} and ''x'' = {{sfrac|5|2}}, the ''x''-intercepts of ''y'' = 10''x''² – 29''x'' + 10.”

* Knuckles (36 by age at that time) said “''x'' = {{sfrac|17|15}} is the axis of symmetry, which is in the middle and halfway between ''x'' = {{sfrac|3|5}} and ''x'' = {{sfrac|5|3}}, the ''x''-intercepts of ''y'' = 15''x''² – 34''x'' + 15.”

== Motion of American and Japanese cars ==

American and Japanese cars containing Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal as their famous drivers in multiple live events held in multiple American and Japanese cities or urban areas in May/June 2022 were at the starting point when they were at rest. As they accelerated, they stopped being at the starting point. These cars accelerated to 62 mph in 2.4 seconds and were nearly two miles away upon attaining 311 mph as their top speed in 36 seconds. Their acceleration decreased in first 36 seconds. Their velocity increased at a decreasing rate.

== American and Japanese cars launched directly on the racetrack close to Apple Park on May 25, 2022 ==

On May 25, 2022, American and Japanese cars containing Shadow, Silver, Mighty, Sonic, Ray, Tails, Knuckles, Amy, Tangle, Rouge, Blaze, Sally, Marine, Mina and Tikal as their famous drivers were launched directly on the racetrack close to Apple Park. When they were at rest, they were at the starting point. These cars stopped being at the starting point as they accelerated after being launched directly on the racetrack close to Apple Park. They attained 31 mph in 0.9 second, 62 mph in 2.4 seconds, 93 mph in 4.5 seconds, 124 mph on 7.2 seconds, 155 mph in 10.5 seconds, 186 mph in 14.4 seconds, 217 mph in 18.9 seconds, 249 mph in 24 seconds, 280 mph in 29.7 seconds and 311 mph in 36 seconds as their top speed. These cars were nearly two miles away after 36 seconds. As their acceleration decreased, their velocity increased at a decreasing rate.