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Recreational mathematics or puzzles with serious mathematical content. Note that math contest problems are generally considered off-topic.
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Covering of a surface of a cube $n\times n \times n$ by pieces of paper $1\times 6$
Indeed, there is no solution for $n=5$, and also none for $n=7$. However, for $n=11$ there is a tiling of the requested form. I found it using a straightforward exact cover formulation and Knuth's ori …