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covering a given 100×100 square with sides on the division lines

Source: All Russian MO 1994 ARO IX P8

July 29, 2018
combinatoricscombinatorial geometrygrid

Problem Statement

A plane is divided into unit squares by two collections of parallel lines. For any n×nn\times n square with sides on the division lines, we define its frame as the set of those unit squares which internally touch the boundary of the n×nn\times n square. Prove that there exists only one way of covering a given 100×100100\times 100 square whose sides are on the division lines with frames of 5050 squares (not necessarily contained in the 100×100100\times 100 square).
(A. Perlin)
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