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:: Another Age Problem ::

Two old friends hadn't seen each other for a long time when they meet in the streets. 'How are your three sons?' -the first asks. 'Hey, I can't remember their ages'. The other replies, 'Well, the product of their ages is 36. Also the sum of their ages equals to the number of windows in that house over there'. The first one says: 'Listen, I still can't figure out the ages of your sons'. The second replies 'Sorry, I forgot to tell you my oldest son has blue eyes.' At which point the first one figures out the ages of the three sons. Can you do it?

Answer: Begin by writting all the possible set of three numbers that when multiplied give 36. You will notice that their sums add up to different numbers except for the solutions {1,6,6} and {2,2,9} which both add to 13. So the fact that the friend cannot deduce their ages means that the solution does indeed add up to 13. So the last piece of information rules out {1,6,6} as this has no eldest son. Remaining solution is {2,2,9}.

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