Do integers n greater than 2 exist such that all the squares of sides 1, 2, 3, ..., n can be partitioned into two or more sets (none a singleton) each of whose squares can be used to tile a rectangle?
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asked May 23, 2019 at 13:55
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$\begingroup$ A few questions: 1) Are we allowed to use multiple copies of a square when tiling a respective rectangle? 2) As formulated now, there is a trivial partition into $n$ singleton sets, with each square tiling a rectangle = itself. Should there be additional restrictions, like none of the tiled rectangles can be a square, or the partition should be non-trivial? $\endgroup$– Mikhail TikhomirovCommented May 24, 2019 at 23:24
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$\begingroup$ @MikhailTikhomirov I have clarified the second issue. The answer to the first is no, no multiple copies of each square. $\endgroup$– Bernardo Recamán SantosCommented May 26, 2019 at 13:00
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