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# Children

## 63 posts in this topic

Ahh I missed part two of your solution when trying to figure this out.

when one man said to the other "The sum of their ages is exactly equal to the number of beers we've drunk"

I thought, "well after 11 beers, I woudn't remember how many I've had, either..."

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Okay all your soulutions were great, But my children and I sat and read all of the posts and Heres the answer

amw8181 you were on the right track... with the twins but you left out the 3rd ..

.that makes it Triplets 3x12=36

Peter drank 6 Beers Thomas drank 6 Beers = 12 Beers all togather

12 is the age of the Triplets

12+12+12=36

Ohhh Yesss the RED HAT so they knew who was the oldest out of the 3

ITS BEEN FUN

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Okay all your soulutions were great, But my children and I sat and read all of the posts and Heres the answer

amw8181 you were on the right track... with the twins but you left out the 3rd ..

.that makes it Triplets 3x12=36

Peter drank 6 Beers Thomas drank 6 Beers = 12 Beers all togather

12 is the age of the Triplets

12+12+12=36

Ohhh Yesss the RED HAT so they knew who was the oldest out of the 3

ITS BEEN FUN

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.

Re both of these postings, the word PRODUCT means multiplication. Therefore these ages are impossible

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What about 1-1-36. Its product is 36, its is a possible drinking amount, and there is a eldest child.

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I'm SOOO confused about the math part of this question but when the oldest child wears a red hat, I think about the Red Hat Club. That would be that the oldest is over 50 though... Could you multiply every number as itself? Like if the age is 52 years, 5X2=10.

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Where/when was it established that the sum of the ages had to be a unique solution?

love it

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Only 18 year olds can drink.

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Hi - I've come into this one a bit late but I have read all the responses and I still am still unable to see anything in the question that suggests that the sum of the ages cannot be unique from the sum of any other possible combination of the ages. Can anyone out there please explain? My immediate thought was 2, 3 & 6 and I don't see why this, or any of the other combinations giving a product of 36, is not an acceptable solution.

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Hi - I've come into this one a bit late but I have read all the responses and I still am still unable to see anything in the question that suggests that the sum of the ages cannot be unique from the sum of any other possible combination of the ages. Can anyone out there please explain? My immediate thought was 2, 3 & 6 and I don't see why this, or any of the other combinations giving a product of 36, is not an acceptable solution.

sum of the 3 numbers can not be unique ... so to use your "solution" ... 2+3+6=11 ... you can not split 11 into other 3 numbers that would make a product of 36, can you?

so if I knew that we drank 11 beers and the product was 36, then I would know the ages ... however, I did not know the ages (because we did not drink 11 beers)

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The answer could be 4,3,3 or 9,2,2. The Older son is wearing the red hat indicates that the other two children are of the same age or "twins". The sum of the beers if two people are taking at a time would be a even number and it can be 10 so 4,3,3 would be the answer to me.

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gees ole' granny of 9 here and I thought I was smarter than a 5th grader...oh well. When someone figures this out, PLEASE POST!, otherwise I will be awake all night ...

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gees ole' granny of 9 here and I thought I was smarter than a 5th grader...oh well. When someone figures this out, PLEASE POST!, otherwise I will be awake all night ...

The answer is in the initial post. Click on the Spoiler for Solution bit.

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What if he has a baby that 0.5 years old?

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i say 6- 6- 1 and 9-2-2 are both right.

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... Ok, after reading the first two pages, I finally figured it out.. lol!

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

- 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!

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

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

good job ... that was my line of thinking as well

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So it's 9 2 2 ? Whoa I really needed alot of time on that, what a great puzzle, I worked out every possiable solution for forever. Wonderful. Honestly though the 6 6 1 and 9 2 2 was the hardest to decifer which was which. I look forward to more of your puzzles.

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I'm pretty sure having a 36 year old son and twin one year olds is biologically impossible. Saying Hypotheticly that the wifes menapause is about 50. Subtract 36 and you get 14. So, Having a son at the age of 14 is A.) In some cases impossible due to late growth hormones B.)Abortion anyone? or C.) Probably to avoid embarassment and future stress handed the baby off to foster/orphan care.

The world may never 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!

Actually, Thomas is asking how old Peter's children are.

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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!

no its not look

- 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?

Those are the actual sentences the friends told each other. so i doubt they are saying there own name before the start talking. so when the first sentence say Peter, how old are your children? it is just Thomas clarifying who he is talking to.

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Letâ€™s start with the known product â€“ 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.

Hey even though the two 6 yr olds are twins one is still older, so really either one is still an option

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This was a very good one.

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Why has no body noted that children can be born 9, 10 or 11 months apart and still be the same number of years old (since years is always rounded down)? Therefore the answer 1,6,6 does not require twins, and there would be a clear older brother.

An example just to be as clear as possible - one child just turned 6, the "oldest" child will be turning 7 next month but is still 6 now.

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But the oldest wore a "red" hat, implying that, perhaps, he's a professional, like a fireman. Then the ages of the children would need to be 1-2-18, so that the oldest could be old enough to be a fireman. The number of beers they drank then would be 21, one drank ten and the other eleven. I imagine they're both drunk by now.