MathDB

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Part of 2023 Myanmar IMO Training

Problems(1)

1% of an Infinite Grid is Blue

Source: Well-known

6/21/2023
Some cells of an infinite chessboard (infinite in all directions) are coloured blue so that at least one of the 100100 cells in any 10×1010 \times 10 rectangular grid is blue. Prove that, for any positive integer nn, it is possible to select nn rows and nn columns so that all of the n2n^2 cells in their intersections are blue.
combinatoricsinfinite grid