Problem: How old are the daughters?

[chantillylace]

Not an easy one! This is from a Microsoft Interview.

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?

[Raevoyn]

My brain is not working properly at the moment ... what is the number of the building over there?

[chantillylace]

It took a while but this is what I figured out - cld be wrong tho!

Factors of 72 = 1x72, 2x36, 3x24, 4x18, 6x12, 8x9

So now I needed to break down the pairs of factors into three so that I could still arrive at the same product of 72. The easiest way to do that was to find the square root of one of the numbers in my existing pairs. It only states that one child is older so I'm just going to assume that the other two are twins, which I think is how the other man arrives at his answer with only that additional info.

So based on that, I know that the single number needs to be higher than the two numbers I get from finding the square root.

So, the following numbers have square roots:

36 = 6 + 6 (+ 2) Not possible as the twins are younger
18 = 9 + 9 (+ 4) Not possible as the twins are younger
9 = 3 +3 (+ 8) Only possible solution, if I am still assuming that the younger two are twins.

So final answer

3 x 3 x 8 = 72
3 + 3 + 8 = 14 (the number of the building I presume)

[FerrariSucks]

why did that take you so long

[chantillylace]

It was the coming up with the twins shit! Otherwise there were too many options.