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## Kids ages

Posted by Chris on July 8, 2010 – 4:07 pm

A and B have the following conversation:

A: How old are your three kids?
B: The product of their ages is 36.
A: I still don’t know their ages.
B: The sum of their ages is the same as your house number.
A: I still don’t know their ages.
B: The oldest one has red hair.
A: Ah, now I know their ages.

How old are the kids?

Assume the kids ages are a whole number of years.

If you remember this from the old site, please don’t post the answer straight away.

This post is under “Tom” and has 13 respond so far.

### 13 Responds so far- Add one»

1. 1. Nathan Said：

The prime factors of 36 are 2,2,3,3. Since there is no mention of twins, I assume that they all have unique ages. The ages of the children are then 2,3, and 6.

2. 2. Chris Said：

Hi Nathan. There are twins.

3. 3. Leela_astro Said：

Hey there!
Well that was a pretty easy and fun one. The key phrases are the second “I still don’t know their ages” and “The oldest one”. If you make a list of all the triple products that give 36, you’ll get a list of 8 triplets. Now if you calculate the sums, there is only one pair of the same sum, hence the first key phrase. Now, considering the second key phrase, you get to decide which one it is . And the answer is…. (drum roll please)
Twins at the age of two and a 9 year-old redhead.

4. 4. cheater Said：

there can be:
2,3,6
2,2,9
1,1,36
3,3,4

5. 5. Chris Said：

2,2,9 it is. I’ll post the full reasoning in 10 or so hours from now (unless someone beats me to it). But Leela_astro clearly has done it correctly.

6. 6. cheater Said：

why can be 2,3,6 and the older one (6 years) has red hair?

7. 7. Chris Said：

You’ll see later on. Re-read Leela_astro’s response for a clue.

8. 8. Euclid's Brother Said：

As Leela_Astro says, there are only 8 possible combination of ages that can have a product of 36. Here they are, with their sums:

1,1,36 = 38
1,2,18 = 21
1,3,12 = 16
1,4,9 = 14
1,6,6 = 13
2,2,9 = 13
2,6,3 = 11
3,3,4 = 10

They all have unique sums except for two. And since the sum matches his own house number, the only reason he couldn’t determin was because his house# is 13 which has 2 possible combination of ages. Both of which have twins.

1,6,6 = 13
2,2,9 = 13

Since the oldest one has red hair, then that one is not one of the twins, therefore, it must be 2,2,9.

Also note, since we were to assume whole number ages, then one twin can’t be older than the other. So he coudn’t have meant that one of the twins was red-headed.

9. 9. Chris Said：

Thanks EB. Nice explanation. I’m quite sure that Leela_astro had used exactly the same reasoning.

10. 10. Anonymous Said：

Chris,

Thanks for posting these puzzles from the old site.

A couple of great puzzles from the old site I would like to see posted are (the details may be off as these are coming from my foggy memory):

-The sheep herder wills his sheep to his 3 sons, no son may receive more than 9 sheep and the sum of the sheep is whispered into each of their ears, each is questioned if they know how many sheep they are to get. After 2? rounds of “I don’t know” one of the sons (the middle one?) knows the answer. (there may have been a condition that oldest receives at least as many as middle son and middle son receives at least as many as youngest son)

-A and B are trying to guess eachothers number. A knows the sum of A+B and B knows the product A*B. The sequence goes something like: A says I don’t know your number. B says I knew that. A says now I know. B says I do too.

Cam

11. 11. Chris Said：

Hi Cam. I’m not sure about the sheep one, but I’ll see if I can dig it up. You must be a glutton for punishment for wanting the other one (the two logicians/mathematicians were called P and S, for product and sum) – I’m sure I can find that one. I nearly posted it a week back, but as I hadn’t seen much of you, and hadn’t met slavy, I thought it would be too hard for most people (I didn’t complete it myself, LOL).

There are fair number of very good puzzles on the old site. I definitely intend to steal many of them. But I will space them out.

12. 12. Haily Said：

the product of the ages of the twin girls and their youngest brother is 36.
How old are each of the children?

13. 13. Chris Said：

Hi Haily,
1,1,36
2,2,9
3,3,4
6,6,1

Not that your question has got much to do with the posted problem.

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