math puzzle Show more

These were popular last time so I will try and post puzzles more regularly. Please spoiler-cw your solutions.

Let \(S\) be the [Smith-Volterra-Cantor set][0] repeated on the whole real line. (That is, the union of all integer translations of the Smith-Volterra-Cantor set.) Prove that for any 2 points on the real line, there exists some translation of \(S\) containing both points.

[0]: https://en.wikipedia.org/wiki/Smith%E2%80%93Volterra%E2%80%93Cantor_set

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