Hats with 100 colors
100 prisoners each receive a hat labelled with a number in (repeats allowed). Each sees everyone's hat but their own. Simultaneously, all write down a guess of their own number. If at least one is correct, all go free. Find a strategy that always wins.
Show hints (2)+
- Have each prisoner assume a different value for the total sum mod 100.
- Exactly one assumed residue matches the truth.
Answer
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