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3x1 papers cover n x n x n cube

Source: Switzerland - 2008 Swiss MO Final Round p4

December 26, 2022
combinatoricscombinatorial geometry

Problem Statement

Consider three sides of an n×n×nn \times n \times n cube that meet at one of the corners of the cube. For which nn is it possible to use this completely and without overlapping to cover strips of paper of size 3×13 \times 1? The paper strips can also do this glued over the edges between these cube faces.
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