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Packet 8: Bonus 1

Morwen Thistlethwaite created an algorithm that can reduce this group into four subgroups to aid in solving it. For 10 points each:
[10e] Name this mathematical group that may be more familiar as a rotating toy with six faces colored white, red, blue, orange, green, and yellow.
ANSWER: Rubik's Cube [accept Rubik’s Cube group]
[10h] Because a composition of cube moves is not commutative, meaning that the order does matter, the Rubik's Cube [emphasize] is not one of these groups.
ANSWER: Abelian (“AYE-bee–lian”)groups [reject “Non-Abelian”]
[10m] Because Rubik's cube face centers are fixed, they are part of a group named for this operation, which also names a calculus rule with the mnemonic "Low d high minus high d low, over low squared."
ANSWER: quotient [accept quotient group or quotient rule]
<Science - Math, Vikram Narasimhan> | VAULT II Packet 08

HeardPPBE %M %H %
4418.8686%57%46%

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Conversion

TeamOpponentPart 1Part 2Part 3TotalParts
Georgia ACalifornia100010E
New YorkTexas B010010H
North CarolinaGeorgia B100010E
Texas AGeorgia C100010E
WashingtonKentucky100010E

Summary

TournamentEditionMatchHeardPPBE %M %H %
VAULT II at Georgia Tech2026-01-24✓620.0083%67%50%
Triangle Cup2026-03-13✓310.00100%0%0%
VAULT II at Eden Prairie HS2026-03-13✓320.00100%67%33%
VAULT II at McGill2026-03-13✓410.0025%75%0%
VAULT II at UCSB2026-03-13✓524.00100%80%60%
VAULT II Northern UK2026-04-24✓320.00100%67%33%
VAULT II Southern UK2026-04-24✓425.00100%75%75%
VAULT II at Harvard2026-04-30✓330.00100%100%100%
VAULT II at MINT2026-06-19✓510.0080%0%20%
VAULT II Stanford Online2026-07-17✓820.0088%50%63%