The right color

It was execution day in the kingdom of Ferristy. But also, by coincidence, it was a national holiday. Thus it was that the king decided to spare the life of one condemned man. He took three men who were to be killed and placed them in a circle facing each other. Then he blindfolded them. Next, he placed a daub of blue paint on the forehead of each. Finally, he said, “On the forehead of each of you I have placed a spot of either blue or yellow paint. At least one of the spots will be blue. I am now going to remove your blindfolds and let you look at the paint on each other’s foreheads. The first man to tell me what color I have placed on him will be freed. But it will not be advisable to guess. If you guess wrong I will have you tortured before you are killed.” He then removed the blindfolds. The prisoners looked at each other’s heads, and one cried, “My color is blue!” Can you tell what chain of logic he used to be fairly certain he had gotten the right color?

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Lets call the man A. He reasoned that if his color were yellow, B would have promptly figured that his was blue. For if As had been yellow, B would know that C would rapidly call out, My color is blue! This is so because if C had seen yellow on both As and Bs heads, he would immediately know his was blue.

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