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one of side lengths is divisible by 6 if rectangle is tiled with 6x1 rectangles

Source: 1996 Swedish Mathematical Competition p6

April 2, 2021
combinatorial geometrycombinatoricstilesTilinggeometryrectangle

Problem Statement

A rectangle is tiled with rectangles of size 6×16\times 1. Prove that one of its side lengths is divisible by 66.