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Let
be an integer. Rowan and Colin play a game on an
grid of squares, where each square is colored either red or blue. Rowan is allowed to permute the rows of the grid and Colin is allowed to permute the columns. A grid coloring is orderly if:
, how many orderly colorings are there?
Proposed by Alec Sun


- no matter how Rowan permutes the rows of the coloring, Colin can then permute the columns to restore the original grid coloring; and
- no matter how Colin permutes the columns of the coloring, Rowan can then permute the rows to restore the original grid coloring.

Proposed by Alec Sun
This post has been edited 3 times. Last edited by GrantStar, Mar 21, 2024, 7:37 PM