The 2 Friends Riddle
Here is a little problem for you...
A person is walking down the street, when he sees a mate across the road whom he hasn't
spoken to in years...
- Hello Steve... long time no see... how are things with you?
- Hi there... Not bad at all! I got married and now I've got three kids.
- You're kidding me! How old are they?
- Well, why don't you guess... ;-) I'll give you a hint - The product of their ages is equal to 36.
- Hmm that is tough... I'll need another hint...
- You got it! The sum of their ages is equal to the total number of windows on the building across.
- Damn... I'm so close... but I still need another hint!
- Ok then... That is the last one though - My oldest kid has blue eyes!
- Ahhh I see !!! Well now I know the ages of your kids!
The question obviously is: How old are the three kids...
It's not a joke. It has a well sustained mathematical answer.
Check out below for the solution.
Solution:
First, the problem is meaningful only is all the ages are integers.
You must assume that! The next step is to go ahead and use the first condition,
that the product of the sons' ages is 36. This gives just 8 options:
age 1 |
age 2 |
age 3 |
sum |
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 |
Among these options is the correct solution. We must choose. Calculations
of the sum (the fourth column) show the only possible numbers of windows
in the house. If the sum were 38, 21, 16, 14, 11, or 10, Igor would have
been able to solve the problem immediately. He was unable to do so only
because the number of windows in the house (and the sum of the ages) was
13! Because of this, he did not have a unique solution until Pavel informed
him of the hair color of his "oldest son." If the ages are 1,
6, and 6, there are older sons but not an older son, and the ambiguity
is resolved:
Friend's sons are 2, 2, and 9 years old.
Author unknown
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