7 prisoners stand in a line such that they can only see the prisoners in front of them. Each prisoner randomly gets either a great haircut or bad haircut (without them knowing which). Starting from the back of the line, each prisoner must either guess her own hair situation or pass.
In order to win, at least one prisoner must guess correctly, and no prisoners can guess incorrectly.
They can strategize in advance. What is the optimal strategy? How likely is it to work?