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removing rectangles from mxn - All-Russian MO 2001 Regional (R4) 8.4

Source:

September 25, 2024
rectangletilescombinatorics

Problem Statement

An angle of size n×mn \times m, where m,n≥2m, n \ge 2, is called a figure, resulting from a rectangle of size n×mn \times m cells by removing the rectangle size (n−1)×(m−1)(n - 1) \times (m - 1) cells. Two players take turns making moves consisting in painting in a corner an arbitrary non-zero number of cells forming a rectangle or square.
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