Most mathematicians have encountered the Problem of the Three Prisoners. Kraitchik gives the problem and the solution as follows:

“Three unsuccessful revolutionists managed to escape across the border, where they were interned in the lockup of a small town. The sheriff’s sympathies lay with the prisoners, and he sought a way to let them go free. One day he came into the jail brandishing three white discs and two black ones and said to the prisoners : ‘On the back of each of you I shall pin one of these discs. None of you can see his own disc, though you can see your companions ! If any of you guesses correctly that his own disc is white he will receive his freedom. If not, he will be detained indefinitely.’ With this he pinned a white disc on the back of each and left them in the care of a guard. How can each of the prisoners, A, B, and C, guess whether his disc is white?