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## Question

Two friends met,the first one asked his friend:

sorry I forget your children`s ages...how old are they?

"if you multiply their ages,you`ll get 36" replied the other.

Hmmmm...still I can not guess.

and if you add their ages together, you`ll get your house number.

ok....the old one has black hair ,where as the last two are twins.

How old are those children?

Edited by wolfgang

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Umm

Since house number is usually a whole number (even though I have seen halves), the ages will be in whole years. Twins are 2, older, black haired kid is 9. Address is 13.

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2,2,9

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It's easier if you write out possibilities.

so three numbers multiplied to get 36:

1,1,36

1,2,18

1,3,12

1,4,9

1,6,6

2,2,9

2,3,6

3,3,4

I think thats everything. Let me know if there are more.

Then we get 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

2,3,6=11

3,3,4=10

Now,the second friend would have guessed the ages of his children by now; since the sums (house numbers) are all different. But since he still cannot figure it out, it must be the two sets of numbers (1,6,6 and 2,2,9) that have the same sum.

And finally, since he said "oldest one", the oldest cannot be twins. 1,6,6 is impossible, therefore the ages are 2,2 and 9.

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Why not 3,3, and 4 ?

Ahh, OK. I can see above. I sent my post before reading it. It looks like I cannot remove it now.

2,2,9

Edited by Eta

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Also, he said the oldest had black hair, and a four-year-old would not have black hair.

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and wolfgang, you should remove the twins part. It just makes it easier.

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I don't think the question as stated is limited to 3 children. It says "the last two are twins".

This would allow..

1,1,2,2,9 sum 15

1,1,4,9 sum 15

I believe this satisfies the criteria of the question and follows the logic of Aaryan's solution.

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TYounghb, youre right. Wolfgang, you need to specify. I've seen puzzles like this-they all say that friend #2 has 3 children.

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so my point is that there is not a unique solution unless it is limited to 3 children.

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I guess this can be done with more ease. We need two numbers (older and younger)with product 36. Possibilities are;

9 x 4

12 x 3

12 x 2

The younger ones are twins so we break the 'small' number in the above options.

9 x 2 x 2 = 36 - possible

12 x 3 x 1 - not possible

12 x 2 x 1 - not possible

We have our answer. Older one is 9 and younger twins are two. The puzzle is restricted to three kids. More combinations will only mean another set of an year old twins and multiplying them with other numbers wont change the equation.

Hair color, door number, etc. are waste information.

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There is a reason the question is put the way it is. You don't know that the younger ones are twins unless you do the long way.

Edited by Aaryan

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Never mind. either I read the riddle wrong, or wolfgang edited it, making it say that the younger ones are twins. That simplifies it way too much.

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One of my favorites - already

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