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40x40 and 49x49 times of nxn - All-Russian MO 2000 Regional (R4) 10.4

Source:

September 26, 2024
combinatoricstilescombinatorial geometry

Problem Statement

For what smallest nn can a n×nn \times n square be cut into squares 40×4040 \times 40 and 49×4949 \times 49 so that squares of both types are present?
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