Excellent probability (ish) puzzler from Car Talk:
Three Slips of Paper
RAY: This is from Norm Leyden from Franktown, Colorado. The date on it is 1974–I’m a little behind.
Three different numbers are chosen at random, and one is written on each of three slips of paper. The slips are then placed face down on the table. The objective is to choose the slip upon which is written the largest number.
Here are the rules: You can turn over any slip of paper and look at the amount written on it. If for any reason you think this is the largest, you’re done; you keep it. Otherwise you discard it and turn over a second slip.
Again, if you think this is the one with the biggest number, you keep that one and the game is over. If you don’t, you discard that one too.
TOM: And you’re stuck with the third. I get it.
RAY: The chance of getting the highest number is one in three. Or is it? Is there a strategy by which you can improve the odds?
SPOILER: Answer found here, with an excellent illustration of the solution.