MathDB
1% of an Infinite Grid is Blue

Source: Well-known

June 21, 2023
combinatoricsinfinite grid

Problem Statement

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.
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