Problem of the Week-6: The Three Sons

Two men meet on the street. They haven't seen each other for many years. They talk about various things, and after some time one of them says, "Since you are a professor of mathematics, I'd like to give you a problem to solve. You know, today's a special day for me: All 3 of my sons celebrate their birthday this very day! So, can you tell me how old each of them is?" "Sure," answers the mathematician, "but you'll have to tell me something about them."

"Ok, I'll give you some hints," replies the father of the 3 sons. "The product of the ages of my sons is 36." "That's fine," says the mathematician, "but I'll need more than this."

"The sum of their ages is equal to the number of windows in this building," says the father, pointing at the structure next to them. The mathematician thinks for some time and replies,

"My oldest son has blue eyes," says the man. "Oh, this is sufficient!" exclaims the mathematician, and he gives the father the correct answer: the ages of his 3 sons.

Explain how the mathematician arrived at the answer. (There is a logical solution to this problem)

Posted: 4/5/04

Submit your answers (by e-mail or hard copy) before 4 pm on 4/16/04 to Noah Aydin.

Mathematics Dept.