A census taker shows up at a house to do an interview. He ia asking all of the normal questions when he gets to the part about other people living in the home. He asks the homowner how old the 3 children are. The homeowner answers that the product of their ages is 36. The census takes says "that does not tell me much"! Then the homeowner says that the sum of their ages is the same as the house address. The census taker checks the address and says "this is getting ridiculous, just tell me the ages"!. The homowner says "the oldest likes strawberry ice cream". "Ok", says the census taker, "that is what I wanted to know" as he wrote down the ages of the children. The question is what are the ages of the children?
There is plenty of info ;-) Also, nothing was said anywhere about the sex of the children, just the ages. Also nothing about twins (or not) or anything else. Just that there are 3 and the answers by the homeowner.
The first answer given by the homeowner obviously didn't tell much as there are many three digit products that equal 36. When the second answer was given, It would have given the answer, except that there must have been still multiple answers even though we don't know the address. If you add up the different sets of three that multiply to 36, you find that there are two that add to 13 and the rest are unique. (this tells us that the address was 13, but it doesn't matter what the number is, just that there are more than one of them)
The two that add to 13 are 1,6, and 6 and 2,2, and 9. When the homeowner said that the oldest likes the ice cream, that gave the answer because 2,2,9 is the combination with an oldest. (I am not going to argue that one twin had to be a few minutes older ;-))
2,2 and 9 was what I was going to guess initially, but tried to get you to first confirm twins by my round about question about sex.
But your answer stated "If you add up the different sets of three that multiply to 36, you find that there are two that add to 13 and the rest are unique. (this tells us that the address was 13". Why couldn't it be one of the combinations whose sum was unique and not 13?
because the census taker still could not answer the question. If it had been one of the unique ones, he would have known at the second answer. I didn't want to answer the part about the twins because there is sufficient info in the original problem to solve it. ;-)