MathDB
Parity of edges

Source: Iran MO Third Round C2

September 8, 2022
combinatoricsrectangleParity

Problem Statement

m×nm\times n grid is tiled by mosaics 2×22\times2 and 1×31\times3 (horizontal and vertical). Prove that the number of ways to choose a 1×21\times2 rectangle (horizontal and vertical) such that one of its cells is tiled by 2×22\times2 mosaic and the other cell is tiled by 1×31\times3 mosaic [horizontal and vertical] is an even number.
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