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Children

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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.

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.

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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.

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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:

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

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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 :)

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

Thanks

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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.

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lol, smart mathematicians/logicians drinking beer.

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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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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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Consider the possibility that two of the children are 6, they're nearly identical twins but the slightly older one (a minute or two older) wears a red hat so that Peter can tell them apart. The third child is one. And Peter and Thomas have each drunk a 6-pack. So, 6 x 6 x 1 works.

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OK, so then it's 6-6-1?

6*6*1=36

6+6+1=13

And the oldest child wears a red hat to distinguish himself from his twin, no?

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wat about the number of beers?

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True. The number of beers only work if you think of their ages logically and not being a couple of minutes different.

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I dont understand something,

If me and a sibling were both six what would stop one of us wearing a red hat and one of us wearing a different coloured hat or no hat at all?

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robadob:

In the riddle it says:

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

Now, if you and your sibling were both 6, if your father said this, it doesn't make sense as there are two oldest children. This last statement points out that there is only one "oldest".

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Answer must be 2 2 and 9

:lol:

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Possible combinations for the age of the children are:

(4,3,3), (9,2,2), (9,4,1), (6,6,1), (12,3,1), (18,2,1), (36,1,1), (6,3,2)

Now, the hint is sum of the ages is being told and correct ages can't be guessed. So, the possible choices left are:

(9,2,2), (6,6,1).

Now, the hint is oldest is wearing a Red hat. So, the only answer left is:

(9,2,2)

which is our answer.

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It took me a sec, but I understand the need for the sum's to be unique. Without them being unique the last parameter would be obsolete or another would have to be there to replace it.

Great puzzle!

-Axilla

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

- That is still not enough."

When Peter says "That is still not enough" in reply to Thomas's statement. He is assuming that a couple of them are twins(Which as profound as it may sound is just an assumption).

i still have my doubts for what made him conclude that they're twins, for, they don't have to be.

why cant they be a 9-4-1 or 2-3-6 or 4-3-3 (in case they are twins)?

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is there any reason why we are multipling the answer let's add 11+15+10 that will give u the sum of 36 we could also assume that the oldest is 15 and why is he wearing a red hat. Is it possible that he could work or play a sport? What profession would you have to wear a hat for (fast food)! And in most states u have to be at least 14 to work.

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In the riddle it says:

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

Now, if you and your sibling were both 6, if your father said this, it doesn't make sense as there are two oldest children. This last statement points out that there is only one "oldest".

I disagree; having had 3 sets of twins in my grade school and high school class, I know that at least some parents refer to their "younger" and their "older" twin, and I would presume that most do. It may not be obvious to others, but to a parent, the younger and older son has the same sentimental meaning for twins as it does for any other set of children.

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:icon_eek: Does the type of hat the son is wearing have anything to do with the answer? Is he wearing the hat backwards like a teenager? Is it a fishing hat or perhaps a dunce cap because he has been bad in class? These are tough questions that I believe must be answered! :P

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18 – 1 – 2

Works best because an 18 year old is more likely to wear a hat then a 9 year old (admins answer) or a 1 and 2 year old which would be his siblings. The sum is 21 how many beers they drank that day (they started early) and the product is 36. The sum did not answer the question so he had to give another clue.

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18 – 1 – 2

Works best because an 18 year old is more likely to wear a hat then a 9 year old (admins answer) or a 1 and 2 year old which would be his siblings. The sum is 21 how many beers they drank that day (they started early) and the product is 36. The sum did not answer the question so he had to give another clue.

sum of their ages can not be unique (respecting the "product = 36" condition and doubts which were clarified only after "the oldest child sentence") ... so what other combination of 3 numbers that have product of 36 and sum of 21 do you know?

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