Difference between revisions of "2024 USAJMO Problems/Problem 4"
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| + | == Problem == | ||
Let <math>n \ge 3</math> be an integer. Rowan and Colin play a game on an <math>n \times n</math> 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 <math>orderly</math> if: | Let <math>n \ge 3</math> be an integer. Rowan and Colin play a game on an <math>n \times n</math> 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 <math>orderly</math> if: | ||
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In terms of <math>n</math>, how many orderly colorings are there? | In terms of <math>n</math>, how many orderly colorings are there? | ||
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| + | == Solution 1 == | ||
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| + | ==See Also== | ||
| + | {{USAJMO newbox|year=2024|num-b=2|num-a=4}} | ||
| + | {{MAA Notice}} | ||
Revision as of 12:36, 23 March 2024
Contents
Problem
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 of the grid. A grid coloring is 
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 
, how many orderly colorings are there?
Solution 1
See Also
| 2024 USAJMO (Problems • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAJMO Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
