How old are the daughters?

Two MIT math graduates bump into each other at Fairway on the upper west side. They hadn't seen each other in over 20 years.
The first grad says to the second: "how have you been?"
Second: "Great! I got married and I have three daughters now"
First: "Really? how old are they?"
Second: "Well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there.."
First: "Right, ok.. oh wait.. hmmmm.., I still don't know"
second: "Oh sorry, the oldest one just started to play the piano"
First: "Wonderful! my oldest is the same age!"

Problem: How old are the daughters?


Anonymous said…
12, 3 and 2. There are only a few combinations of factors that multiply to 72. Only 12, 3 and 2 exlude the possibilty of the first two daughters being twins (for example: 6, 6, 2). Since she indicates "the oldest one", this excludes the possiblity that her first born daughters are twins (although technically they could have been born a day apart, I guess).
Rajneesh Garg said…
...This problem was asked to one of my friends during his interview with M$
glenn said…
1, 6, 12

2, 3, 12

3, 4, 6

1, 3, 24

1, 1, 72 ( not likely )

2, 2, 18

2, 4, 9

3, 3, 8

I feel like we're missing some clues?!?!
Anonymous said…
9, 8, 1

Yep. I'm definitely missing something, possibly the address of the building on the upper west side.
Anonymous said…
The bit about the building number means the solution is one of two (or more) solutions that add to the same value (on the building). The bit about the piano is to decide between them.
Charlie said…
Well, here's why all the clues are necessary. After finding the factors of 72 you'll arrive at the point where 2 sets will add up to the same number. One of which set will have two larger numbers equal. Given the fact that the first guy says "my oldest daughter" you can exclude this and are left with the other set of factors. =)
Anonymous said…
Even between twins there's an elder and a younger twin. My oldest daughter = the elder twin. So how ?
Anonymous said…
and the sum of their ages is my house number.

You`ll see that you have 2 sets with wher e the numbers add up to the same "house number" because if it was any other the solution would be straightforward
Chakra said…
The oldest daughter's age is < 20.
If you have lived in new york, you would know that manhattan as about 12 avenues and that they follow a specific numbering system where the avenue or street number is one of the first one or two digits.
So I wanted to be sure where exactly they were standing. I did a google map search for Fairwar Market, New york. I came up with couple of locations on upper west side. Taken down the addresses. Downloaded Google Earth ( and virtually navigated the neighborhoods of both Fairway markets and found a building with 12 on it. So the answer is 12, 6, 1.

Note: I was the one who gave interview with M$. I was not selected because I was using Google's tools!! Damn M$. :-)
Anonymous said…
Factor 72 out and sum their ages:
1 1 72 74
1 2 36 39
1 3 24 28
1 4 18 23
1 6 12 19
1 8 9 18
2 2 18 22
2 3 12 17
2 4 9 15
2 6 6 14
3 3 8 14
3 4 6 13

The sum of the ages add up to a building number which still confuses the person. So how could that be, well the building number must be sum we get twice "14". The next part says, "My oldest one" indicating that their is only one oldest. Therefore, the the only combo that would work is 3,3,8.

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