Personally, I am only interested in puzzles which are "well-defined" - that is puzzles which have a clear goal and a clear set of possible options, with the assurance that there is a demonstrably correct answer. This is as opposed to riddles or enigmatic puzzles, where finding the answer generally requires more open ended thought or searching for patterns or trying to apply various interpretations to the question itself.
I think that this is a meaningful category of puzzle, and one that I would certainly like to have an explicit tag for it. The closest we have is mathematics, but this is not quite the same. For one, it includes puzzles that have riddle elements in addition to references to or usages of mathematics. Also, I've certainly seen puzzles that have a well defined nature, but are not tagged under mathematics (as they may not as directly relate to mathematics, or may relate to specific subfields - this often applies to strategy or geometry). Especially since these sort of puzzles are relatively infrequent on the site, it would be nice if they were gathered into a better form.
Should we create a new tag to encompass such puzzles?