document.write( "Question 765059: 3. Two mathematician graduates bump into each other while shopping at Vishal’s. They haven't seen each other in over 20 years.
\n" ); document.write( "The first graduate says to the second: \"How have you been?\"
\n" ); document.write( "The second replies: \"Great! I got married and I have three daughters now.\" First: \"Really? How old are they?\"
\n" ); document.write( "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...\"
\n" ); document.write( "First: \"Right, ok... Oh wait... Hmm, I still don't know.\"
\n" ); document.write( "Second: \"Oh sorry, the oldest one just started to play the piano.\" First: \"Wonderful! My oldest child is the same age!\"
\n" ); document.write( "how old was the first graduates child? \n" ); document.write( "
Algebra.Com's Answer #465932 by ramkikk66(644)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Product of ages is 72. Sum is the number on the building\r\n" );
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document.write( "We try the possible combinations of the product of ages and also the corresponding\r\n" );
document.write( "sum.\r\n" );
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document.write( "72,1,1 - sum = 74\r\n" );
document.write( "36,2,1 - sum = 39\r\n" );
document.write( "18,2,2 - sum = 22\r\n" );
document.write( "18,4,1 - sum = 23\r\n" );
document.write( "9,8,1  - sum = 18\r\n" );
document.write( "9,4,2  - sum = 15\r\n" );
document.write( "8,3,3  - sum = 14\r\n" );
document.write( "6,6,2  - sum = 14\r\n" );
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document.write( "Now here's the trick. The 2nd mathematician was NOT able to guess the ages\r\n" );
document.write( "even after checking the sum. From the table above, you see that all the possible\r\n" );
document.write( "combinations have unique sums except (9,4,2) and (8,3,3) which have the same\r\n" );
document.write( "sum. So the door number must be 14 and the mathematician is still not able to\r\n" );
document.write( "find which is the right combination.\r\n" );
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document.write( "3rd clue refers to \"oldest\" child which means that (6,6,2) is not possible - \r\n" );
document.write( "because there are 2 children with the same age of 6 and you can't refer to one\r\n" );
document.write( "as the \"oldest\".\r\n" );
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document.write( "Hence the right combination is (8,3,3)\r\n" );
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document.write( "The ages are 8, 3 and 3.\r\n" );
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