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2024 USAJMO Problems/Problem 4

Revision as of 12:31, 23 March 2024 by Erinb28lms (talk | contribs)

Let $n \ge 3$ be an integer. Rowan and Colin play a game on an $n \times n$ 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 of the grid. A grid coloring is $orderly$ if:

  • 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 column of the coloring, Rowan can then permute the rows to restore the original grid coloring;

In terms of $n$, how many orderly colorings are there?

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