daughter's ages Here is a list of the possible ages of the daughters and their sums.  Note that the product is 72, and none of the ages is over 20.  (The mathematician hasn't seen his friend in 20 years.) Ages          Sum 1,8,9 =        18 1,4,18  =    23 2,4,9 =        15 2,2,18 =      22 2,6,6 =        14 3,3,8 =        14 Since there is an oldest, then the oldest cannot be a twin.  Then she must be 8 years old, and have two 3-year-old sisters Anonymous Thursday, November 20, 2003 This is a perfect example of importance to read the problem text carefully before one approaches it. It says "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." So there is no contradiction between this statement and possible age of the oldest daughter to be 72. Is there a contradiction between her age and the fact that she "just started to play the piano"? Certainly not! Would you believe that an MIT math grad, which has a 72-year-old daughter "can factor 72 and add up the sums"? Well, he must be about 100 years old, born around 1903, missed the drafts for the First and Second World Wars and probably still is of excellent health. So could he have the oldest daughter of 72 and twins of 1 year old? You obviously say yes - but!! Look around the "Fairway on the upper west side" - is there a single building with the street number equal to 74? No!! That's what the aha!! is about. Otherwise the result is absolutely correct, especially that it matches the published answer. Congratulations! ::applause:: vk Thursday, November 20, 2003 Althought I agree with the published answer completely, the poster should consider saying the two grads haven't met for ... may be 10 years or so. I see that they can be very young when graduating from MIT, but it is 12 years after that they give birth to their first children?! (and then 2 more coming..) Is it typical in America? Well they are geeks obviously. May Bee Saturday, January 10, 2004   Yes, I agree with the answer. Let me pour something,...   When the 1st grad replys "still i dont know"  i.e. there was a co-incidence in the solution,with the 1st hint given and he wanted one more hint. He said like that because:   The multiplication of 3 ages of different combinations have a different  sum, except 2+6+6 =14 and  3+3+8 = 14, i.e. resulting to the same sum(14). No two other combinations sum  doesn't result to the same number like this. With the other hint given we can conclude the answer as 3,3 and 8 are the ages. PradeepKumarReddy Wednesday, February 18, 2004   Fog Creek Home