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cut a 6x6 square into tiles 1x2 (2023 Novosibirsk Oral Geo Oly 7.1)

Source:

September 4, 2023
geometrytilescombinatorial geometry

Problem Statement

Let's call a corner the figure that is obtained by removing one cell from a 2×22 \times 2 square. Cut the 6×66 \times 6 square into corners so that no two of them form a 2×32 \times 3 or 3×23 \times 2 rectangle together.