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Daughters’ ages

Ages of the daughters

Daughters' ages

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 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!”

How old are the daughters ?

Solution: We know that there are 3 daughters whose ages multiply to 72. The possibilities can be :

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 second man still can’t figure out what their ages are, so that means that the sum of the ages (or building number) must be 14 since that is the only sum that has more than one possibility.
Thus the possibilities can be :
2,6,6 or 3,3,8
Then the man found out that there is the oldest daughter, which cancels out “2,6,6” since the two oldest over here are twins, that’s not possible.
Therefore, the daughters’ ages must be 3 years, 3 years, and 8 years.