In general, no, because:
a) You are not their student and you don't want to be treated like their student.
b) You won't be at your best doing this at a job interview unless you are phenomenally good under pressure (in which case, it might be to your benefit to demonstrate this)
c) Any problem you can solve in the amount of time someone will give you for an interview is a pretty trivial problem and can only work against you if you can't solve it.
d) You spend years building credentials. Stand on years of credentials instead of minutes of dog and pony show.
e) It's just not crafty interviewing. Crafty interviewing means you need to be at least a little manipulative to get the interview moving toward areas that are likely to have good outcomes for you. For example, you are interviewing for a risk management job and you need to talk to someone about exotic options. If you know nothing about exotic options, but notice that he/she went to the same college as you did, what should you be discussing - a primer on exotic options or How 'bout them Tigers? If you are writing on the board, you have no opportunities to be manipulative.