For Your Mathematicians: IBM Research: Ponder This
Link: IBM Research: Ponder this
There is an archive of old problems and solutions going back to May 1988.
You are cordially invited to match wits with some of the best minds in IBM Research.
Seems some of us can't see a problem without wanting to take a crack at solving it. Does that sound like you? Good. Forge ahead and ponder this month's problem. We'll post a new one every month, and allow a month for you to submit solutions (we may even publish submitted answers, especially if they're correct). We usually won't reply individually to submitted solutions but every few days we will update a list of people who answered correctly. At the beginning of the next month, we'll post the answer.
I must confess that I have had a look at a few of the problems and the ones I looked at I would not have been able to solve. I did think that some here might like the site though.