As a general suggestion about puzzles... there are two kinds. (a) There are those with a slick canned pre-made answer. Those can be fun, and serve an educational purpose. But they do not result in new mathematics and new discoveries. (b) There are open-ended problems, which nevertheless somebody who is well short of being Albert Einstein, can nevertheless make progress on, thanks to, e.g. computer searches they program. For these, the readers of the puzzle column might well be able to make new discoveries and find new records, and outdo professional mathematicians. I would recommend a mix of both kinds of puzzle. Martin Gardner understood this. http://rangevoting.org/PuzzlePage.html is a collection of democracy-related math puzzles mainly by me. Puzzle #66 is of type (b). Puzzle #0 is of type (a). Puzzle #2 is intermediate type.