When they say 'oral exams', are the applicants expected to shoot out an answer without actually looking at the problem or writing a solution? And if that's the case, how much time would they get to solve these problems mentally? I can't imagine being able to solve any of these without a pen and paper. I would assume that unless you already know the answer, there isn't a way for an 'unwanted' applicant to be able to do so either.
No - an oral exam in this context is more like a programming interview. You get a board and chalk, and you solve the problem on the board in front of the teacher, explaining what you're doing along the way. This is opposed to a "normal" exam where you have your pen and paper and a pre-set amount of time to struggle with the problem on your own.
