A dialog between two mathematicians:


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?



How did he know?

Credit: USC mathematician Solomon W. Golomb