## December 7, 2009

### Find the ages of the chidren ?

Many years from now, two classmates met in a street.

The following is part of their discussion.

Student 1: Yes, I'm married and have three wounderful children.
Student 2: That's great! How old are they?
Student 1: Well, the product of their ages is 36.
Student 2: Hmm. That doesn't tell me enough. Give me another clue.
Student 1: OK. the sum of their ages is the number on that building
across the street.
Student 2: (After a few minutes of thinking with the aid of pencil and paper)
Ah ha! I've almost got it but I still need another clue.
Student 1: Very well. The oldest one has red hair.
Student 2: I've got it!

What were the ages of the children of student 1?

Hello World said...

4,3,3

Tiger Woods said...

9,2,2.

13 is the only sum of two sets of three numbers whose product is 36. Therefore, 13 is the number of the building across the street. His children were either 6,6,1 or 9,2,2. When he stated that the oldest one has red hair, the option of 6,6,1 became invalid

Varun said...

9 2 2

my explanation is same as previous one.

Anonymous said...

You could argue that since one twin was born shortly before the other that they were therefore the oldest, but Student 2 clearly doesn't think so since they worked out their ages. So 2,2,9 is certainly correct.

Hey, Tiger! - if your wife won't let you have all of those girls any more, how about sending one or two my way :-)

Anonymous said...

What's wrong with 2, 3, 6? The sum is 11.

I don't know whether street addresses work the same as floor numbers in buildings, but you'll notice there's never a floor 13. That is a cultural bias solely of the US, I would guess.

Anonymous said...

The thing "wrong" with 2,3,6 is that there is only that one answer summing up to 11. Then the ages would have been clear after the house number. 13 is the only sum with two answers (2,2,9 and 1,6,6) and thus requires the tie-breaker...

Anonymous said...

The problem asked for th product. The product of 2, 3, and 6 is 36.
So the ages can be 2, 3, and 6, yes??

StÃ¥le said...

In response to the last Anonymous, yes the product had to be 36.

However, the second clue, which was that the sum of their ages was the number of the building across the street, was not sufficient. If the number had been 11, there is only one set of numbers whose sum is 11 and product is 36, so that can't be it, since student 2 still needed more information.

The information s/he needed was whether the two oldest children were twins or the two youngest ones - 6,6,1 or 9,2,2. When Student 1 said "The oldest one...", that's what made it clear.