I'll try to explain what everyone's confused about...

Let's start with the beginning:

- 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 ...

Let's find out the combinations (from youngest to oldest):

1 - 1 - 36 (sum is 38)

1 - 2 - 18 (sum is 21)

1 - 3 - 12 (sum is 15)

1 - 4 - 9 (sum is 14)

1 - 6 - 6 (sum is 13)

2 - 2 - 9 (sum is 13)

2 - 3 - 6 (sum is 11)

3 - 3 - 4 (sum is 10)

I think everyone is all right with this so far. Now the tricky part.

Here's the thing. The trick isn't so much math related. It's READING RELATED. Note the next two lines...

- The sum of their ages is exactly the number of beers we have drunk today.

**- That is still not enough.**

Most people are concentrating on the first line, but the SECOND LINE is EQUALLY important. Thomas knows how many beers they have drunk in that day. He sums up the number of beers and finds that the information Peter gives him is "still not enough". Therefore this indicates that the sum of their ages CANNOT BE UNIQUE and that as of right now, there must be two or more answers that sum up to the same number and their product is 36.

Therefore, the only two possible answers are:

1 - 6 - 6 (sum is 13)

2 - 2 - 9 (sum is 13)

(Note: This has nothing to do with Thomas suspecting twins of any sort)

Lastly:

- OK, the last thing is that my oldest child wears a red hat.

So this part gets controversial, but the main message is that there is only 1 oldest. If we're only comparing years (not minutes, or hours of difference), then there remains only one possible answer...

His children are 2, 2 and 9 years old.

I think this puzzle was pretty well written. Keep up the good work!