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
- The Hundred Lockers 5.0/10
Source: Classic hat-guessing puzzle in wide circulation; the parity strategy is standard in the literature. Statement written for AxiomIQ.