The most recent tricky puzzle I’ve heard:
100 people sit in a circle so they can all see each other, but cannot see themselves. Someone walks around putting hats on their head. He has 100 bins, each with a different color of hats inside, and he chooses a hat from an arbitrary bin for each person. Multiple people can have hats from the same bin, and not every bin must necessarily be used.
After looking at everyone else’s hats, everyone in the circle must guess the color of their own hat. They can confer beforehand about how they will guess, but cannot communicate after the hats are put on their heads. Describe a strategy so that exactly one person will guess their hat color correctly.