The Monty Hall Problem New York Times
Can't recall now where I first heard this, but it completely engrossed me at the time --and I am not much given to such puzzles. The challenge is one of those non-intuitive results that statistics gives us to a situation we all think to be perfectly obvious: Does it matter if you change your mind once Monty Hall opens a door on Lets Make a Deal?

Here, the times has turned the problem into a cool little animated interactive which lets you play for yourself.

Alas, it doesn't go the step further of doing an interactive with the math behind the problem.