Hats in a line
100 prisoners stand in a line; each wears a red or blue hat and can see all hats in front of them but not their own or those behind. Starting from the back, each must say "red" or "blue"; correct guesses survive, and everyone hears every guess. Playing optimally, how many can be guaranteed to survive?
Show hints (2)+
- The first speaker can encode one bit of global information.
- Parity of red hats lets everyone else deduce their own color.
Answer
Reveal answer →Final answer
99
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