Two Cambridge graduates, Peter and Paul, meet for the first time in 20 years.
Peter asks, "How've you been?"
Paul says, "Great! I'm married now and have three daughters."
Peter asks, "How old are they?"
Paul answers, ""The product of their ages is 72, and the sum of their ages is the same as the number on that building over there."
Peter says "Uh... I still don't know."
Paul says, "My oldest just started to play the piano."
Then Peter says, "Really? My oldest is the same age!"

How old are the daughters?

  • 6
    $\begingroup$ Is this a duplicate of this question? $\endgroup$
    – axavio
    Jun 18, 2016 at 20:55

1 Answer 1


There are (ignoring permutations) 12 triples of positive integers with product 72. Of these, there are only two with the same sum:

2,6,6 and 3,3,8.

Peter was able to work out which was the right one from just the information that

there is a unique oldest daughter (note: strictly, this is kinda unsound because you can have two 6-year-old daughters but know which one is older, either by observing which twin was born first or by moving very quickly after the first one)

so the ages must be

3, 3, 8.


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