100 prisoners are sent into a room to hear the warden say: "tomorrow I will line you up and put a hat on your head. The hat can be red, green, yellow, …" and he goes on enumerating colors. He then adds: "The executioner will then start from the back of the line and run up to the front, and to every prisoner he will ask what the color of his hat is. If the prisoner guesses the color correctly then he is freed, but if he gets it wrong he will be killed right away.
The following days, the prisoners are lined up, and the warden puts a colored hat on their head. Then, the executioner starts asking question. The unlucky prisoner at the back of the line guesses wrong and is killed. But by some magic, all the other prisoners guess the color of their hat correctly.
How did they do?
PS: I apologize for my English
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