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Cutting a nxn square in 1x1 and 2x2 pieces

Source: 2024 Polish Junior Math Olympiad Finals P2

May 5, 2024
combinatoricscombinatorics proposedsquare

Problem Statement

Determine the smallest integer n≥1n \ge 1 such that a n×nn \times n square can be cut into square pieces of size 1×11 \times 1 and 2×22 \times 2 with both types occuring the same number of times.
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