Ask HN: are there (addicting, video) games which improve mathematical thinking?

There are a lot of really addicting video games on the market today and so I wonder: are there video games which encourage, or provide feedback for, a deductive style of thinking (or the same sort of thought patterns a mathematician uses)?

If you were to expose this game to kids, I think it would be of tremendous value (assuming it was just as entertaining as other modern games).