Guessing Haircuts

Logic Level 2

Six prisoners standing in a line are equally likely to be given either a \(\color{blue}{\text{good}}\) haircut or a \(\color{red}{\text{bad}}\) haircut, and each prisoner can only see the haircuts of the prisoners in front of them.

After each prisoner is given their haircut, they must guess her own hair situation, starting from the back of the line. They will be given ramen if and only if they ALL guess correctly. If the prisoners can form a strategy to correctly guess all of their haircuts in advance, then what is the optimal strategy and how likely is it to work?

[If your answer is \(X\)%, enter \(X.\)]

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