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total number of tiling triangles is even

Source: TOT 511 1996 Autumn J A4 Tournament Of Towns

August 16, 2024
combinatoricstilesTilingcombinatorial geometry

Problem Statement

(a) A square is cut into right triangles with legs of lengths 33 and 44. Prove that the total number of the triangles is even.
(b) A rectangle is cut into right triangles with legs of lengths 11 and 22. Prove that the total number of the triangles is even.
(A Shapovalov)
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