Prepare....


A student asks a teacher about the teachers kids' ages. The teacher replies: "The product of their ages is 36 and the sum of their ages is your house number."

The student thinks, and replies, "I need more information." The teacher says, "Oh, and the oldest plays piano."

What are the three kids' ages?

Nice one! But didn't we have a topic for these?

I'm not sure. Maybe, but I'm pretty new here and still sorta exploring the boards.

2-2-9

what the.....

so explain, why?

All the possible ages are:

1 1 36
1 2 18
1 3 12
1 4 9
1 6 6
2 2 9
2 3 6
3 3 4

Those sum to 38, 21, 16, 14, 13, 13, 11, and 10, respectively. Since just knowing their sum was NOT enough information to figure it out, that means it must have been one of the two with sum 13, i.e. 1 6 6 or 2 2 9. But then we find out that there is an OLDEST one, which 1 6 6 does not have. So it's 2 2 9.

Exactly this. I love this one.

Not necessarily, the question is poorly worded. It is quite possible that there could be two kids that are both 6 years old but were born months apart (at least nine probably).

Also, there was a thread for these kinds of puzzles: http://twistypuzzles.com/forum/viewtopic.php?f=18&t=19093 .

Alex

True, but this is not an issue unless a six-year old can play piano?

http://www.youtube.com/watch?v=vUx4t4W4eVY

Alex

Quick search and found this. I wonder if she has a special piano with smaller keys so she can do bigger spans. It must be hard playing with such small hands.

*edit* Ah, APJ beat me to it.

My nephew isn't as good as the girl APJ linked to, but he started playing piano at four and can play several classical pieces very well, and he's only five.

Also, isn't it necessary to know the student's address? This could be almost any of those combinations without that piece of information. This isn't a good riddle because it doesn't have a set answer. A riddle should have an answer that can be arrived at without straying outside the boundaries of the riddle or creating circumstances not given by the riddle. That's just my opinion.

- Billy

No, it's only necessary to know that knowing the address isn't enough, since only no. 13 leaves more than one option. All other options would be unique and thus sufficient.

The "riddle" doesn't say that it can't be a solution that results in a sum that matches a sum that is also possible. So that means that every combination is technically a correct answer...even both of the combinations resulting in the sum of 13. To me, this is not a riddle.

- Billy

No, but it clearly indicates that knowing both the product and the sum is not enough for the student (the fact that we don't know the address/sum is irrelevant):
So it can only be one of two possible combinations that happen to have both the same product (36) AND the same sum (13), since the student would be able to work out the answer directly (without requesting additional info) if his address was anything other than 13. On that basis, the riddle provides all the info you need to find the unique solution.

Well, not necessarily. As AJP pointed out, it's possible to have two children with the same year age but one be older by nine or ten months. So, it could be 1-6-6 or 2-2-9. Since it's supposed to be a "logic riddle" I'll concede on that point, but it doesn't give all of the information needed to come to a unique solution under technical circumstances. I understand why the answer is what is, and understood before I read other comments, but I still don't like the.....limits of the "riddle." They just don't account for all of the real situations that exist.

Anyway, good chat. Thanks!

- Billy

I really like it. Good one

(hopefully it can be fixed to only have one answer )

Actually, it does. The only reason that the student would need to ask for more information is if there are 2 possible solutions.

The teacher says the oldest plays piano, therefore there has to be an oldest, therefore 2-2-9.

If you REALLY wanted to get picky about it, I could go into fractions. Maybe the youngest is 1/4 year old?

The point of riddles isn't to get around them, it's to solve them as they are presented.

I started at 5.

No, it doesn't. My friend Paul is 28 and his little brother, Brian, is also 28. They are considered the same age even though Brian was born ten months after Paul. They would have fallen into this predicament. I said that I'll except the answer but I don't agree that this is a true riddle because there are technically multiple answers. I understand that it's just for fun and I nitpicked too much. Thanks!

- Billy

In the spirit of riddles, I believe it is. But, define it as you may, what we're arguing over is purely semantics.

It's still an interesting logic puzzle, whether riddle or not.

Maybe the teacher instead could say "two of them are twins"

Rewrite riddle:

Teacher says: "The product is 36, and the sum is your house number. And oh, by the way, don't bother figuring it out. Their ages are 9, 2, and 2. It really wouldn't be worth your time."