USC mathematician Solomon W. Golomb offered this problem in the Pi Mu Epsilon Journal, Fall 1971 (page 241):
Ted: I have two numbers x and y, where x + y = z. The sum of the digits of x is 43 and the sum of the digits of y is 68. Can you tell me the sum of the digits of z?
Fred: I need more information. When you added x and y how many times did you have to carry?
Ted: Let’s see. … It was five times.
Fred: Then the sum of the digits of z is 66.
Ted: That’s right! How did you know?