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Omni-MATH / Let n≥3 be an integer. Rowan and Colin play a game on an n×n grid of squares, where each square is colored either red or blue. Rowan is allowed to permute the rows of the grid and …

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problem

Let n≥3n \geq 3 be an integer. Rowan and Colin play a game on an n×nn \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 [i]orderly[/i] if: [list] [*]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. [/list] In terms of nn, how many orderly colorings are there?
Plain-text mathematical notation (without MathML)
Let n≥3 be an integer. Rowan and Colin play a game on an n×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 [i]orderly[/i] if: [list] [*]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. [/list] In terms of n, how many orderly colorings are there?
Original LaTeX notation
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 [i]orderly[/i] if: [list] [*]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. [/list] In terms of $n$, how many orderly colorings are there?

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Source and history

task_id
1e5f4dca-c1bd-5f62-8cdb-2d122ae52d10
task_key
test--1e5f4dca-c1bd-5f62-8cdb-2d122ae52d10
task_revision_id
1
config / split
/ test

Official source

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