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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 \ge 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 of the grid. A grid coloring is orderlyorderly 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 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 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?
Original LaTeX notation
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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Source and history

task_id
05f30f73-249f-55fe-bdff-77bbec2305b1
task_key
test--05f30f73-249f-55fe-bdff-77bbec2305b1
task_revision_id
1
config / split
/ test

Official source

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