(5) Quora

Question: There's a mathematician flying to Frankfurt. On board he encounters a middle aged woman who challenges him to test his skills. She gives him the following 2 clues: He has to guess her daughters' ages.

• The product of my 3 daughters' ages is 36.
• The sum of my daughters' ages is your seat number.

The mathematician is unable to solve it and asks for a final hint.

• My youngest daughter has blue eyes.

The moment he hears the last clue, he is able to tell the ages correctly. Find the ages of the three daughters.

Solution: 

1. Using the first clue,
   a*b*c = 36, Possibilities are:
   (1 - 1 - 36)
   (1 - 2 - 18)
   (1 - 3 - 12)
   (1 - 4 - 9)
   (1 - 6 - 6)
   (2 - 2 - 9)
   (2 - 3 - 6)
   (3 - 3 - 4)
2. Using the second clue. You don't really know the seat number, but we would sum the possibilities anyway to see if it leads us a way.
   (a + b + c) = Seat Number
   (1 + 1 + 36) = 38
   (1 + 2 + 18) = 21
   (1 + 3 + 12) = 16
   (1 + 4 + 9) = 14
   (1 + 6 + 6) = 13
   (2 + 2 + 9) = 13
   (2 + 3 + 6) = 11
   (3 + 3 + 4) = 10
   Now logic says, if Mathematician's seat number would have been 11, he would have said the answer and wouldn't have required a third clue. He would need a third clue only in case of a confusion/doubt. We have two possibilities pointing towards 13.
3. Third clue - The youngest daughter has blue eyes.
   (1 + 6 + 6) = 13
   (2 + 2 + 9) = 13 - Twin sisters - cannot decide youngest.

Hence, the required ages are 1, 6 and 6. This was a que

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_- Steve