First, it would be great if you could spend 2 minutes taking part in my quick survey into sleep and dreaming. All you need to do is click here. Many thanks.

On Friday I posted this puzzle….

Two friends are chatting:

John: How old are your children now?

Eric: None of your business

John: Oh come on, it’s for the Friday Puzzle.

Eric: Oh ok. Well, there are 3 of them, and if you multiply their ages together you get the number 36.

John: Can you give me more information?

Eric: OK, the sum of their ages is exactly the number of biscuits we just consumed.

John: That’s still not enough.

Eric: OK, my oldest child likes to watch the ‘Bets you always win’ videos on YouTube.

Eric: Oh ok. Well, there are 3 of them, and if you multiply their ages together you get the number 36.

John: Can you give me more information?

Eric: OK, the sum of their ages is exactly the number of biscuits we just consumed.

John: That’s still not enough.

Eric: OK, my oldest child likes to watch the ‘Bets you always win’ videos on YouTube.

John: OK, now I have worked it out.

How old were each of Eric’s children?

If you have not worked it out, have a go now. For everyone else, the answer is after the break!

There are two combinations that can be multiplied together to 36, and have the same sum: 1-6-6 and 2-2-9. However, the line about the video reveals that there is an oldest child, and so the answer must be 2-2-9. Did you solve it?

Easy, but…cue the argumentatives!

I think this is the original version of the question before the edit which sorted out the identities…

even twins can be distinguished as oldest, younger.

1-4-9?

What’s wrong with 2, 3, and 6?

That’s what I want to know!

it adds up to 9, and given he knew the number of biscuits, he’d of got this as an answer after finding out the sum equals number of biscuits. But he didn’t, meaning there must be a combination of ages that sum to the same value. In fact there is only 2 combinations that sum to the same value. 1-6-6 and 2-2-9. Then the clue about the oldest means 1-6-6 must not be correct because there is twin oldest.

What about 4, 3, 3?

Wait – I get it it!

Could you have 3-3-4?

I don’t get the bit about the biscuits. I thought it was a red herring.

It’s a bit subtle. They both know how many biscuits have been consumed. With this information John still can’t get the ages for sure. Therefore the ages have to be one of the only two sets which add up to the same value. With the next bit of information John now knows which of the two sets (1,6,6 and 2,2,9) is the answer. Don’t know why RW keeps getting the names mixed up though.

Thanks Eddie!

What about 6-3-2 or 36-1-1

1-4-9; 2-3-6; etc

I got a different answer. 2,3,6. The part about how biscuits they had was either left out or over my head completely. There must be tons of other solutions if this restriction is taken out. Did i just miss the restriction?

1-2-18??

Or 9, 4, 1?

Or 12, 3, 1?

I think we need to know how fond they are of biscuits!

The ‘bit about the biscuits’ tells you that the sum is not unique, otherwise that information would be sufficient.

Ahhh of course – thanks Peter

The point about the biscuits is that THAT piece if information wasn’t enough for John to solve the puzzle. (John after all, knows how many biscuits were eaten) so there must be more than one potential solution with the same sum. THEN the extra piece of information resolves the ambiguity

Thanks for this.I completely missed it, but then there is an assumption that John was aware of the quantity of biscuits consumed. I took it to mean that It was not enough info for John because he had not been counting the biscuits (after all who would keep track after 3 or 4 had been eaten?)

How come it starts off with John asking the questions and Eric being cryptic and ends with Eric trying to figure out how old John’s children are? Oh, and thank-you Peter for your explanation of the biscuits; I completely missed that subtle clue and was left muttering to myself that there were “dozens of solutions”

I got lost where Eric’s kids suddenly turn out to be John’s kids

I had 1, 2 and 18. What’s wrong with that?

Ah. Got it. That would have been a unique answer with a sum of 21 biscuits. Doh.

Glad you have got it now Simon.

Would you now be kind enough to explain your apostrophe point from last Friday?

If it was “bets you always win” then I assumed that the child was of gambling age. If it was “bet’s you always win”, then it would have been a name, such as Elizabeth, which made little sense.

Thanks to all who have tried to explain the biscuits but I still don’t get it. Could someone explain why 4-3-3 is wrong? Maybe I’ll get it then. (It would mean they ate ten biscuits. No?)

I think it’s the line “That’s not enough” which is meant to tell us that John has worked out there is more than one solution which adds up to the number if biscuits they had.

Your solution (same as mine) is unique and so cannot be correct or John would’ve got it.

The only solution that had two sets with the same total is the one RW has given.

The numbers which, when multiplied together, make 36, are:

1,1,36 (total = 38)

1,2,18 (21)

1,3,12 (16)

1,4,9 (14)

2,2,9 (13)

2,3,6 (11)

3,3,4 (10)

6,6,1 (13)

[I think I got them all?]

Only two of these have the same total.

The key clue is “the sum of their ages is exactly the same as the amount of biscuits we ate”

John still does not know. That means that the totals must be the same. Only two options have that – 6,6,1 and 2,2,9.

Lastly, Eric talks about his oldest child. If he has an oldest child, there’s an assumption his 6 year old children are considered “the same age” (no “they were born 11 months apart” or “one twin is slightly older” pedantry). This leaves the 9,2,2 option for his children.

Thank you, Appocomaster. I get it now.

I wouldn’t have got that on my own in the next twenty years!

4-3-3 adds up to 10 and, of three numbers that multiply together to make 36, is the only combination that does so. If John and Eric had eaten 10 biscuits, and of course John knows how many biscuits they’ve eaten, he’d have been able to work out how old Eric’s children were from the second piece of information. But he had to wait for the third piece of information, as the number of biscuits they’d eaten gave two sets of three numbers that multiply together to make 36, i.e. 13.

But, the YouTube terms of service say users must be 13 years or older, so they have to be 18,2,1

1 4 9 if they were sharing biscuits they would of eaten and even umber!!

So, 2 2 9 gives an odd number. 3 3 4 would work as well.

Sorry, Anne. I wrote that before realising you’d read Appocomaster’s excellent explanation.

Thanks Pogo! Much appreciated.

One of the cleverest puzzles I’ve seen since I’ve been visiting (about a year now, I reckon, or thereabouts). I suppose those who went higher than A Level in Maths got it easily, but I gave up at that point… and clearly don’t remember much of what I learnt there!

It doesn’t say they ate an equal number each. Even if John ate 1 and Eric ate 12, they still jointly are 13 🙂

OK, I was stumped by this one but now get it. It’s a really nice little logical puzzle because in order to work out the answer you have to put yourself in the shoes of John – I’ll try and explain…

First, as we all did, figure out the various combinations of three numbers which multiply to 36, at this point none of us know which of the combinations is the right one.

Next the clue is given that the sum of the ages amounts to the number of biscuits consumed, and here’s where we have to put ourselves in John’s shoes – John knows the number of biscuits yet he still can’t work out the ages, so this must mean that there must be two or more combinations which add up to the number of biscuits eaten (otherwise he would know the answer straight away). If you check the various possible combinations only two of them have an equal sum (1+6+6 and 2+2+9 both equal 13).

Ignoring the fact that it is possible for someone to have two six year olds, one of which is older, the rest should be self explanatory.

Jethro: cheers! A really useful bunch of replies. I have learned something new this week!

Ah, Appocomaster got there before me!

A full explanation may be found here:

http://en.wikipedia.org/wiki/Ages_of_Three_Children_puzzle

Substituting certain statements accordingly.

I don’t think the answer fits the clues. the combinations to get 36 would be

1-4-9

2-2-9

1-2-18

1-1-36

1-6-6 etc.

however those two had biscuits together meaning they would most likely have had equal number of biscuits. so the sum should be even. moreover there is am oldest child big enough to watch a YouTube video. so the best answer that fits is 1-4-9 in my opinion.

then again I could be missing something

There is no requirement on having an equal number of biscuits – just a known number of biscuits. If you scroll up, it’s been explained in more detail a couple of times how this helps to narrow things down.

Your approach is very fair though!

Thanks Appocomaster,

of all the explanations given, yours I could understand.

I got this right in about 2 secs and having read the comments now have absolutely no idea why I was right

A proper puzzle! Cheers!

What about 2,3 and 6?

Read Jethro’s explanation, it’s the best worded I think. Appomaster explains it completely too.

I really enjoyed this puzzle. I read it in the morning and solved it in the evening while brushing my teeth. (I mentioned some time ago in another context that I have all my best ideas while brushing my teeth.)

Why couldn’t they be 2, 3 and 6?

Got it! The answer is 2,2, and 9

Well done Huge!

Unfortunately Richard’s explanation is not sufficient to understand the answer. The key to this puzzle is that the participants themselves are likely to know how many biscuits that they ate, but nevertheless could not work out the answer. What we conclude from that, is that the sum of the ages must be non-unique. The only non-unique sums are those taht Richard mentions. There are quite a lot of hlogic puzzles using this “they couldn’t work it out using the information they had” technique which allows us to draw conclusions despite not having the information they had. It becomes quite easy once you understand the trick.

I actually started with the last clue, wondering what it was there for and concluding that there must be two possible solutions, one of which has no oldest child. From there it was easy.

Oh, I gave up on this puzzle too quickly, thinking it was some kind of language thing. Great puzzle, wish I’d given it more time.

parents of twins keep track of which one is oldest, even if by a few minutes. this can lead to absurd real-life situations, such as my chinese friends with twins who are constantly telling the older child to watch over the younger, presumably out of a strong cultural affinity and focus on the “oldest” child.

since most twins i know have different (sometimes, very different) personalties from their twin, it’s perfectly reasonable for one twin to like videos and the other to not.

Thanks ctj

Are you going to to spill the beans on the “two valid solutions” you mentioned on Friday?

No No No. Youtube’s minimum viewing age is 13. So we know the oldest child must at least 13. So the answer must be 18-2-1. The bit about the biscuits just shows that Eric wasn’t keeping track of his biscuits. Now just wait until Google finds out someone underage is viewing Youtube. They’re going to be quite surprised, I assure you!

2, 3 and 6 were the ages I ended up with, which also fills all criteria.

no it doesn’t –

Eric: OK, the sum of their ages is exactly the number of biscuits we just consumed.

John: That’s still not enough.

see earlier replies for explanation

It doesn’t say why that doesn’t help and those explanations assume that it doesn’t help because there are multiple values for some of of the possible sums of children.

It is therefore an equal assumption to assume that John has no idea how many biscuits they ate between them as the extra information wasn’t volunteered. In fact, considering Erics deliberately obtuse manner of speaking, it is more likely that John was concentrating on other things than how many biscuits they consumed between them.

See Eric being a dick about answering a regular question, for evidence.

John wasn’t counting – so Eric’s reply didn’t help him; I’ll give it to you that that’s a possible reading. Although perhaps John would have said “that doesn’t help” rather than “it’s still not enough”,

However the fact that Eric’s third statement about his eldest did then give John the definitive answer needs to be factored in (ignoring all the other factors about Youtube minimum age and elder twins)

Confused. Let me know the correct answer please

The official answer: 2, 2, 9, is best explained in Jethro’s comment above