# What is the ages of the Children

A life insurance agent knocks on a door. A woman answers and he tries to sell her a policy. He asks her how many children she has and their ages. She replies: "I have three children, but I will not even listen to your sales pitch unless you guess their ages."

She gave him a clue: "The product of their ages is equal to 36."

The insurance salesman jots down some figures and replies, "I do not have enough information to answer yet".

The lady replies, "Okay, here is clue number 2: If you go the house next door (points to it), the sum of their ages is the same as the house number".

The salesman goes next door, looks at the number, jots down a few more things and then returns to say, "I still don't have enough information".

The lady then replies, "Okay, your third and final clue: My eldest is learning to play the piano!!"

The salesman replied with the answer, it was correct, he gave his sales pitch, she bought a policy. What were their ages (assume all ages are whole numbers)?

Clue one gives all possible combinations of three ages that multiply to 36, which are:
1 1 36
2 2 9
2 6 3
4 3 3
1 4 9
1 6 6
1 2 18
1 3 12

Clue two still doesn't give the insurance person enough information, meaning that there must be (at least) two combinations adding to the same number. This leaves us with the two combinations:

2 2 9
1 6 6