MathDB

Let

n \geq 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. 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 columns 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?
Proposed by Alec Sun

Problem Statement