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!”

How old are the daughters ?

See Solution : Daughter's agesWe know that 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 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. 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”.

Aaron says

3,3,8

Abdulhameed Ansari Sikkandar says

3,4,6

no career says

one of the best puzzle I came across on this site

Rohit says

why is 2 6 6 ruled out?? You can have 2 births in same year without being twins…

Progs says

how is 14 is the building number??

puzzlersworld says

If it was not 14 then First guys would know the ages without any doubt as seen in by the possibilities(in explanation section), but it is only number 14 where there are more than one possibilities, so thats why he was confused.

Zeest says

Hey man need more puzzles,ur explainations are awesome.

puzzlersworld says

Thanks Zeest, We will post some more logical puzzles soon, i hope you have tried other Logical Puzzles and Interview Puzzles.