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.)
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::
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.
Yes, I agree with the answer. Let me pour something,...
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