I am a geneticist and unfortunately have not worked much with advanced calc since undergrad. In genetics, as you likely know, a male is denoted as XY and a female as XX. I plan to leave a riddle for my husband and his colleagues at his workplace in order for them to solve. The solution will be an unexpected announcement of the baby's sex.
I am looking for 2 high-level calculus equations - one of which solves to X and the other to Y (and/or two proofs, one of which is true and equals X, and another which is false and equals Y). If anyone would be willing to provide some ideas for this endeavor, the help would be greatly appreciated. Any variations on XX,XY,b(boy),g(girl), etc. would also work. It's a lab full of PhDs, theoretical physicists, and engineers -- so I would imagine the harder the better ;) Bonus points if you can stump them.
Some fields covered by the lab are optics, microwave photonics, radio-over-fiber, quantum computing, etc. Keep in mind they are good, but they are not mathematicians (there may be 1 or 2, but who knows if they'll be around).
Thanks ahead of time!