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# Children

62 replies to this topic

### #1 rookie1ja

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Posted 30 March 2007 - 07:43 PM

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?

This old topic is locked since it was answered many times. You can check solution in the Spoiler below.
Pls visit New Puzzles section to see always fresh brain teasers.

Spoiler for Solution

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### #2 sokrin

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Posted 17 April 2007 - 04:38 PM

What about the combination of 1-4-9? It's still 36 and the number of beers drunk was never mentioned.
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### #3 rookie1ja

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Posted 19 April 2007 - 07:42 AM

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:

- 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.
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### #4 qazqaz

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Posted 28 April 2007 - 09:18 PM

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

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Posted 29 April 2007 - 04:33 AM

the product is 36
there is an oldest
and 12 beers for 2 people is not a lot on St. Patrick's Day
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### #6 pibseast

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Posted 30 April 2007 - 02:20 AM

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

Thanks
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### #7 chubaca

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Posted 01 June 2007 - 04:57 AM

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.
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### #8 larryhl

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Posted 07 June 2007 - 01:35 PM

lol, smart mathematicians/logicians drinking beer.
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### #9 Yuckiducky

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Posted 15 June 2007 - 06:19 PM

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

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Posted 19 June 2007 - 01:14 PM

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

Umm, no. Thomas is asking Peter how old his children are...
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