I was readking In Code by Sara Flannery last night. Its a book about cryptography and it had this really good math puzzle in it and I was wondering if anyone could solve it. I couldn't but thankfully she gave the solution in the book and I can't believe I didn't get it. Here is the puzzle:

An insurance salesman knocks on the door of a home in a housing development. When the woman answers the door he asks "How many children do you have?" She replies "Three." When he asks "What are there ages?" She decides that he is to cheeky and refuses to him. After he apologizes for his apparent rudeness he asks for a hint about the children's ages. She says "If you multiply their three ages you get 36." (Their ages are exact numbers). He thinks for a while and then asks for another hint. When she says "The sum of the ages is the number of the house next door" the salesman quickly hops the fence to determine this number. This done, he returns to the lady and asks for a final hint. "All right", she responds "the eldest of my children plays piano." He then knows there ages, do you?

Anyone willing to give this a go?

An insurance salesman knocks on the door of a home in a housing development. When the woman answers the door he asks "How many children do you have?" She replies "Three." When he asks "What are there ages?" She decides that he is to cheeky and refuses to him. After he apologizes for his apparent rudeness he asks for a hint about the children's ages. She says "If you multiply their three ages you get 36." (Their ages are exact numbers). He thinks for a while and then asks for another hint. When she says "The sum of the ages is the number of the house next door" the salesman quickly hops the fence to determine this number. This done, he returns to the lady and asks for a final hint. "All right", she responds "the eldest of my children plays piano." He then knows there ages, do you?

Anyone willing to give this a go?