So.... Have you figured out Cheryl's birthday yet?
It's funny how so few people regard this puzzle as real math (as opposed to calculating a derivative or something.) In my mind, THIS is real math; taking a complicated situation, digging out and exposing the logical skeletal structure underlying it, studying that structure and abusing it to say something conclusive about the situation. Problem solving, in a nutshell, is mathematics. Or perhaps real math is learning how to synthesize and generalize the logical structure so that it can be used again in other puzzles, or situations.
Either way.... This is real math.