Question 4
Let $n\ge3$. Rowan may permute rows and Colin may permute columns of an $n\times n$ grid colored red or blue. A coloring is orderly if every row permutation can be undone by a column permutation, and every column permutation can be undone by a row permutation, restoring the original coloring in each case. How many orderly colorings are there?
Proposed by Alec Sun. Source: Evan Chen’s third-party compilation; https://aops.com/community/p30227193. One editorial point; manual grading.
Proposed by Alec Sun. Source: Evan Chen’s third-party compilation; https://aops.com/community/p30227193. One editorial point; manual grading.