It might be fun and surprising to come up with seemingly unsolveable problems in math, but it isn't actually that hard. Especially if you come from the angle of computer science. Math does not have common tools I'm aware of to deal with many of those problems.
Bitwise AND is not a linear function, which is a first obstacle.
For bitwise and you have to be solving it in a Galois field (And consider what AND does) which is actually easier than the general solution but points you more accurately at the cryptographic origin of the question.
Bitwise AND is not a linear function, which is a first obstacle.