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covering a 6×6 square board with eighteen 2×1 rectangles

Source: Mexican Mathematical Olympiad 1996 OMM P3

July 28, 2018
geometryrectanglecombinatorics

Problem Statement

Prove that it is not possible to cover a 6×66\times 6 square board with eighteen 2×12\times 1 rectangles, in such a way that each of the lines going along the interior gridlines cuts at least one of the rectangles. Show also that it is possible to cover a 6×56\times 5 rectangle with fifteen 2×12\times 1 rectangles so that the above condition is fulfilled.
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