BrainDen.com - Brain Teasers

# Children

## 63 posts in this topic

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.

##### Share on other sites

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

##### Share on other sites
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.

##### Share on other sites

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

##### Share on other sites

the product is 36

there is an oldest

and 12 beers for 2 people is not a lot on St. Patrick's Day

##### Share on other sites

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

Thanks

##### Share on other sites
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.

##### Share on other sites

lol, smart mathematicians/logicians drinking beer.

##### Share on other sites

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

##### Share on other sites
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...

##### Share on other sites

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.

##### Share on other sites

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?

##### Share on other sites

wat about the number of beers?

##### Share on other sites

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

##### Share on other sites

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?

##### Share on other sites

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".

##### Share on other sites

Answer must be 2 2 and 9

##### Share on other sites

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)

##### Share on other sites

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

##### Share on other sites

"- 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)?

##### Share on other sites

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.

##### Share on other sites
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.

##### Share on other sites

: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!

##### Share on other sites

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.

##### Share on other sites
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?

##### Share on other sites
This topic is now closed to further replies.