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] 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.