In This World - Problem of the Day

CNN News Clip

"Niels, where are you going?" asked Sammy. "I'm going to the barber for a shave," answered Niels. "You know, Niels, Alfredo, the barber, does a very good business. He shaves those men and only those men who do not shave themselves." "Come on, Sammy, that's impossible! Who do you think shaves him?"

The study of sets and relationships among sets can lead us to a consideration of questions such as this. Consider the following Barber's Rule: Alfredo shaves those men and only those men who do not shave themselves. If he shaves himself, according to the Barber's Rule, he does not shave himself. On the other hand, if he does not shave himself, then, according to the Barber's Rule, he shaves himself!