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Recreational mathematics or puzzles with serious mathematical content. Note that math contest problems are generally considered off-topic.

9 votes

Undecidable puzzles

This answer is not entirely serious, but it does not fit as a comment. Numberwang is undecidable. Numberwang, of course, is a fictional popular game show featured as a running gag in the real sketch …
Yoav Kallus's user avatar
  • 5,971
10 votes

A function that is defined everywhere but has unknown values

Your (1) could be substituted for pedagogical ease of presentation with the Conway's Game of Life "halting problem" (note that they are equivalent). That is, the function which for any starting config …
Yoav Kallus's user avatar
  • 5,971
48 votes
Accepted

"The Two Sheriffs" puzzle

Here's a solution for the case of seven suspects that uses the Fano plane. Let the seven points of the Fano plane represent the seven suspects. Alice and Bob both reveal the name of the suspect comple …
Yoav Kallus's user avatar
  • 5,971