In #224 I noticed that all sudoku variants are just different constraints on the same underlying system and they can all be solved with linear programming.

Watching a talk about puzzle game design has gotten me wondering if many puzzle games are exploring some known area of mathematics with a lot of window dressing.

Probably something like group theory or graph theory most of the time.

Are those the only fields which translate well to puzzle games?

Rather than the standard process of exploration and prototyping, I wonder if one could steal puzzle concepts directly from mathematics.

A topic which mathematicians spent lifetimes examining must have a lot of surprise to offer the layman.

I think it wouldn't be hard to teach advanced concepts to players that they wouldn't be interested in learning otherwise, and fun too if they were allowed to enjoy discovery rather than being given theorems up front.

Also it would be a funny twist at the end to reveal explicitly to the player how each puzzle maps onto mathematical notation.