# Riddle

This riddle, which I got from Professor Dan Ariely’s site (h/t TC), took me and my roommate a little too long to solve, but it was very satisfying to figure out. SPOILER ALERT: I left the solution in the comments, but don’t cheat!

Two Chinese men meet on the street. The first asks the second how his family is, and the second answers: “They’re great. I have three sons. They all have their birthday today. The sum of their ages is 13. The product of their ages is the number of that house across the street.”

The next day they meet again, and the first man tells the second: “I almost have it, but I need one more piece of information before I can tell you how old your children are.” The second answers: “Oh, my oldest son plays the violin.” The first man says: “Okay, I’ve got it.”

The question is: what are the ages of the children?

See the comments for the solution.

Photo via Eleaf’s Flickr (CC).

1 Comment

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### One response to “Riddle”

1. ceisenhood

Since I’m getting a lot of traffic from Google searches looking for the answer to the riddle, I’ll leave the solution here in the comments.

First, it’s helpful to make a list of all of the possible age combinations.

Here’s the age combos that sum to 13 along with the product of those ages:

1.1.11 – 11
1.2.10 – 20
1.3.9 – 27
1.4.8 – 32
1.5.7 – 35
1.6.6 – 36
2.2.9 – 36
2.3.8 – 48
2.4.7 – 56
2.5.6 – 60
3.3.7 – 61
3.4.6 – 72
3.5.5 – 75
4.4.5 – 80

We know that the man knows that the product of the ages is the “number of that house across the street.” The only way he would be unable to immediately know what their ages were is if the number was 36, which has two possible age combos (1.6.6 or 2.2.9).

But, in the 2nd paragraph, the first man gets the last bit of info he needs – the second man has an older son. Therefore, he couldn’t have two older twins, eliminating 1.6.6 and leaving us with the answer:

The ages are 2, 2, and 9.

Great riddle!