daughter's ages

Problem:
Two MIT math grads bump into each other at Fairway on the upper west side. they haven'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.. hmm, 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?

Solution: Start with what you know. you know there are 3 daughters whose ages multiply to 72. let's look at the possibilities...

Ages:            Sum of 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

after looking at the building number the man still can't figure out what their ages are (we're assuming since he's an MIT math grad, he can factor 72 and add up the sums), so the building number must be 14, since that is the only sum that has more than one possibility.

finally the man discovers that there is an oldest daughter. that rules out the "2 6 6" possibility since the two oldest would be twins. therefore, the daughters ages must be "3 3 8".