[rookie1ja]

Children - Back to the Number Puzzles
An easier number puzzle is as follows. Two friends are chatting:
- 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?

Spoiler for Solution:

Children - solution
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). And as we learned further that 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.

[sokrin]

What about the combination of 1-4-9? It's still 36 and the number of beers drunk was never mentioned.

[rookie1ja]

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What about the combination of 1-4-9? It's still 36 and the number of beers drunk was never mentioned.

That's not correct because 1-4-9 makes sum of 14 from which can be made by only 1 unique combination of 3 numbers which make the product of 36. As written in the puzzle:

Quote

- The sum of their ages is exactly the number of beers we have drunk today.
- That is still not enough.

So the sum can be made of at least 2 combinations of 3 numbers which make the product of 36. And that's why there was another hint needed. Just let me know if that makes sense to you.

[qazqaz]

if he had that many beers, wouldnt he be drunk, and shouting gibberish?

[pibseast]

What about the answer 2, 3, 6
the product is 36
there is an oldest
and 12 beers for 2 people is not a lot on St. Patrick's Day

[rookie1ja]

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What about the answer 2, 3, 6
the product is 36
there is an oldest
and 12 beers for 2 people is not a lot on St. Patrick's Day

2, 3, 6 gives a unique sum (there are no other 3 numbers giving that sum of 12 and product of 36) which does not fit the said, does it:

Quote

- The sum of their ages is exactly the number of beers we have drunk today.
- That is still not enough.

[pibseast]

I'm a bit slow - pls explain - how does the sum have to be unique?

Thanks

[chubaca]

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I'm a bit slow - pls explain - how does the sum have to be unique?

Thanks

The first clue is that the product is 36. Note that 36=3*3*2*2, so all posible combinations are:

6-3-2 (sum=11)
9-2-2 (sum=13)
4-3-3 (sum=10)
9-4-1 (sum=14)
12-3-1 (sum=16)
18-2-1 (sum=21)
6-6-1 (sum=13)

Note that only 9-2-2 and 6-6-1 give the same amount when added. Obviously, the second man must know how many beers thay have drunk, so he knows the sum. If he cannot decide yet it's only because the sum is 13 and there are two combinations that add up to 13. Knowing that there is one older than the rest is enough to solve the problem.

[larryhl]

lol, smart mathematicians/logicians drinking beer.

[Yuckiducky]

Wait...Peter is asking how old Thomas' children are but the teaser question asks how old Peter's children are. We do not know!