A man has 3 cards face down on a table. One is a jack and two are aces. He knows the order but you do not. You can ask him one yes or no question, but when you do you have to point to one of the cards. If you point to an ace, he will tell the truth, if you point to the jack, he will randomly say yes or no. You have to find one of the aces.
Point to the middle card and say, "Is the card to the right an ace?" If the answer is yes, then the card on the right is an ace. If the answer is no, the card on the left is an ace. This solution works because if you're pointing to an ace then he's obviously telling the truth and if you're pointing to the jack the answer doesn't matter anyway because you will pick one of the other two which are both aces.
Today's brain teaser courtesy of Braingle.com.