In one such interview, I was asked for a way to implement Rock Paper Scissors in OOP without using a conditional. I came up with a neat way to do it with modulo operations and array lookups, but that wasn't The Right Way. So I came up with a way to do it with exceptions, but it wasn't The Right Way. Finally I came up with the solution the interviewer had in mind, which used Java's method overloading (my background is not Java).
I'm not sure if I "passed" the interview, but it certainly didn't make me want to.