Question 73
An evil wizard imprisons $n$ mathematicians. He has $n$ colors and puts a hat of one of the $n$ colors on each person; hats may have the same color. Each mathematician sees everyone else’s hat but not their own. They must simultaneously announce their own hat colors. If at least one guesses correctly, all are freed. They may agree on a strategy before seeing any hats.
Give a strategy that guarantees their release.
Give a strategy that guarantees their release.