I enjoy collecting good logic riddles, and I thought some of y'all forumites might enjoy them as well.
No "lateral thinking" here--there's no hiding bad assumptions in the problem description or flavor and no tricking your way around them.
I'll start with what I think is my very favorite:
An evil overlord has captured you and, as evil overlords are wont to do, he forces you to play a game to win your freedom.
The overlord shows you a turntable with four bowls on it, one at each compass point. You are blindfolded and the bowls are set to some unknown orientation: some face up, others face down. Each round of the game works like this: You put your hands above two of the compass points. The overlord then rotates the turntable in any way he wishes (but always stopping at the compass points; there are only four possible orientations for it). You then lower your hands onto the bowls that are now beneath your hands and are allowed to flip both, one, or neither of them. If all four of the bowls are now in the same orientation--either all face up or all face down--the overlord announces your victory, you immediately win and go free. Otherwise you play another round; however, after 10 rounds, if you still haven't won, the overlord will send you to a horrible fate. The overlord wants this to happen, of course, so he will use his ability to rotate the turntable to thwart you if possible.
What strategy can you use to guarantee victory?
Hint 0: A solution exists.
Hint 1: 10 rounds is far more than necessary. In the worst case, you can do it in 7 rounds. As the faithful, perspicacious, and virtuous followers of this thread have noticed, my original clue was incorrect.
Hint 2: You don't need to realize that you've won to win.
Hint 3: Amazingly, the solution also works if the bowls are replaced with coins, and you are wearing gloves so you can't determine heads from tails.
Hint 4: How must the bowls be oriented in order to force a victory on your next move? How can you cause that situation to exist?
As a postscript, Hint 3 is one of my favorite hints of any riddle, because at first glance it only seems to make the problem harder.