Here's a Pete Winkler classic:
You are playing a game against your adversary Bob. There are four indistinguishable coins on a tray, say in positions North, West, South, and East, each starting as either heads or tails according to Bob's liking. Bob can always see the tray, and you never can. A single turn consists of the following:
1. You ask Bob to flip any number of coins by referring to their position.
2. Bob rotates the tray to his liking (you do not get to know how the tray is being rotated, and he must rotate it by a multiple of 90°).
You win the game if you make all of the coins heads after finitely many turns, and Bob wins if you give up. There is a strategy that guarantees your victory. What is it?
Example and bonus question below the cut.
















