- Peter, how old are your children?
- Well Thomas, there are three of them and the product of their ages is 36.
- That is not enough...
- The sum of their ages is exactly the number of beers we have drunk today.
- That is still not enough.
- OK, the last thing is that my oldest child wears a red hat.

How old were each of Peter's children?

Answer

2, 2 and 9.
Let’s start with the known product 36. Write on a sheet of paper the possible combinations giving the product of 36. Knowing that the sum is not enough to be sure, there are two possible combinations with the same sum (1-6-6 a 2-2-9). The oldest son wears a hat, it is clear that the correct combination of ages is 2-2-9, where there is exactly one of them the oldest one.

- Peter, how old are your children?
- Well Thomas, there are three of them and the product of their ages is 36.
- That is not enough...
- The sum of their ages is exactly the number of beers we have drunk today.
- That is still not enough.
- OK, the last thing is that my oldest child wears a red hat.

How old were each of Peter's children?

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