permutation - 2025 PACE NSC

Question

The number of fixed points under this operation co-determines a corresponding rencontres ("ruhn-CON-truh") number. This operation is described in the subscript of the Levi-Civita ("LEV-ee chih-VEE-tuh") symbol. (0[1])This operation's (20[1]0[1])order (0[1])equals the least common multiple of the lengths of its cycles. This operation has a sign of one if it is equivalent to an even number of transpositions. (20[5]0[1])This operation is an automorphism because it involves (*) bijecting (0[1])a set onto itself. (10[2])One in every e ways of performing this operation yields a (10[1])derangement. (10[2])Symmetric groups consist of n-factorial (10[1])ways (10[1])to perform (10[1])this operation (10[2]0[1])on (0[1])n (10[1])objects. (10[2])For 10 points, (10[1])name this operation that yields an ordered (10[1])rearrangement (0[1])of a set, (10[1])contrasted with (10[1])combination. (10[4]0[1])■END■ (10[8]0[1])

ANSWER: permutation [prompt on bijection or automorphism until read]

= Average correct buzz position

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Buzzes

Player	Team	Opponent	Buzz Position	Value
Samy El-Zahabi	Chattahoochee B	Homewood-Flossmoor	23	0
Kevin Qiu	Wayzata	Lambert A	25	0
Brodie Henry	West Point	Winston Churchill A	25	20
Camden Williams	Audrain County AT	Thomas Jefferson A	26	0
Daniel Sheffield	Belmont	Lexington	54	20
Tony Han	Kane County AT	White Pigeon	54	20
Omkar Marathe	Fremd	Montgomery Blair A	54	20
Tristan Andre	North Quincy	Solon	54	0
Kaiden Lee	Northview	Northmont	54	20
Eshaan Sombhatta	Thomas Jefferson C	Irvington	54	20
Ameya Bhalerao	Downingtown STEM	Parkway West	63	0
Brandon Torres	Carl Sandburg	Quince Orchard	67	10
Andrew Zhao	Richard Montgomery	Alabama Cyber Tech	67	10
Karthik Jayaram	Walker	Seven Lakes	78	10
Max Chen	Strake Jesuit A	Adlai E. Stevenson A	79	10
Maggie Sun	Hunter A	Uni of Illinois Laboratory	79	10
Beckett Pursey	Edina	Centennial A	84	10
Aaron Liu	Okemos	Fairfield County AT	85	10
Tarun Devi	Chattahoochee A	Northside College Prep	87	10
Amber Dong	Adlai E. Stevenson B	Strake Jesuit B	89	10
Arjun Vijaykumar	Saratoga	Barrington	89	10
Nico Bobis	Glenbrook South	Thomas Jefferson B	89	0
Daniel Guo	Uni School of Nashville A	Lambert B	90	0
Camille Pimentel	Hunter B	Russell	91	10
Sreyas Sabbani	Innovation Academy B	Great Valley	92	10
Hrishi Bhooma	Thomas Jefferson D	Yukon A	92	10
Anjali Prasad	Carmel B	Uni School of Nashville B	95	10
Saathvik Koneru	Detroit Catholic Central B	Detroit Catholic Central C	102	10
Charan Pratapeneni	Classen SAS	Carmel A	103	0
Shaun Iyer	Innovation Academy A	Eastchester	106	10
Evan Xue	Johns Creek	Park Tudor	108	10
Ben Yancey	Detroit Catholic Central A	Grosse Pointe South	109	10
Sophia Swain	Herron	Lincoln-Way East A	109	10
Stephen Langdon	Lincoln-Way East B	Yukon B	109	0
Sasha Tripathi	Parkway West	Downingtown STEM	109	10
Rochan Saireddy	Lambert B	Uni School of Nashville A	109	10
Anthony Pho	Carmel A	Classen SAS	110	10
Aarushi Kanigicherla	Thomas Jefferson B	Glenbrook South	110	10
Everett Van Til	Homewood-Flossmoor	Chattahoochee B	110	10
Roman Salda	Yukon B	Lincoln-Way East B	110	0
Wyatt Johnson	Solon	North Quincy	110	10
Teddy Berente	Saint Joseph	Coronado	110	10
Aaryan Sumesh	Thomas Jefferson A	Audrain County AT	110	10
Crystal He	Thomas Jefferson E	Virginia	110	10
Sanjay Shanmuga Perumal	Lambert A	Wayzata	110	10

Summary

Tournament	Edition	Exact Match?	TUH	Conv. %	Power %	Neg %	Average Buzz
2025 PACE NSC	06/07/2025	Y	36	97%	17%	0%	88.60