# Traveling Salesman Puzzle

A salesman knocks on the door of a house.

When a woman answers the door, he asks her how many children she has.

She replies, “3”.

He then asks their ages.

Offended, she replies obscurely, “The product of their ages is 36.”

He says that he needs more information.

She replies, “The sum of their ages is the address of the house next door.”

Even though he is a gifted amateur mathematician, he explains that this is still not enough information.

She replies, “My oldest plays the piano.”

He says “Thank you.”, and writes their name in his notebook.

What are the ages (integer years) of the three children?

My solution:

Possible ages of 3 kids whose product is 36 (I*J*K=36) are:

(1 1 36), (1 2 18), (1 3 12), (1 4 9), (1 6 6), (2 2 9), (2 3 6), (3 3 4)

Sums of these possible age sets are:

(I+J+K) = 38, 21, 16, 14, 13, 13, 11, 10

That you need to know that there is an oldest child (who plays piano) suggests that you need to decide between (1 6 6) and (2 2 9) which both sum to 13.

My answer for kids ages are 2, 2, and 9.