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mxn rectangles in a 3x7 colored blue or yellow grid

Source: 1984 Swedish Mathematical Competition p2

March 28, 2021
Coloringcombinatorial geometrycombinatorics

Problem Statement

The squares in a 3×73\times 7 grid are colored either blue or yellow. Consider all m×nm\times n rectangles in this grid, where m∈{2,3}m \in \{2,3\}, n∈{2,...,7}n \in \{2,...,7\}. Prove that at least one of these rectangles has all four corner squares the same color.
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