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Logic Puzzles 7.0/10

One Hundred Hats

100 prisoners stand in a line, each wearing a red or blue hat, seeing only the hats in front of them. From the back of the line forward, each must guess their own hat color aloud; correct guesses live. They may agree on a strategy beforehand. What is the maximum number of prisoners who can be guaranteed to survive?

Related problems & prerequisites

Worth solving first

Source: Classic hat-guessing puzzle in wide circulation; the parity strategy is standard in the literature. Statement written for AxiomIQ.