Two men met in a road side. One man said “I’ve three daughters. Can you say me the age of my eldest daughter? ”. For this the other man said “I want more information”. Again the first man said “Product of their ages gives 36”. Second man said “Need more information”. Now the first man said “The sum of their ages is equal to one of the door numbers in this street”. The second man was confused and again said “Need more information”. For this the first man said “My eldest daughter wears a red dress”. Hearing this second man said the correct answer. What is the answer?

• The ages are 2, 2, and 9.
  
  Solution: There are only so many ways that three numbers can have a product of 36:
  1×1×36 = 36
  1×2×18 = 36
  1×3×12 = 36
  1×4×9 = 36
  1×6×6 = 36
  2×2×9 = 36
  2×3×6 = 36
  3×3×4 = 36
  
  It’s got to be one of these, but we don’t know which one. The second clue is about the sum of their ages:
  
  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
  
  The 2nd man might know the door numbers of the houses in that street, so the only way that this clue didn’t help him is if the sum is 13, b'cause apart from 13 we do not any sum that is repeated, but we have 13 twice and hence he asked for 3rd clue. So we know the ages are either
  1, 6, and 6, or 2, 2, and 9.
  The third clue makes a reference to the oldest daughter, so the ages must be 2, 2, and 9. b'cause if its 1, 6, 6 then he would mention that 2 daughters would be wearing red dress.
  (It’s true that there could still be an “oldest” daughter in the case of 1, 6, and 6, since they could be few min apart and both be 6 yrs. But since the 1st man gave this as a clue, we can assume that it’s pointing towards the 2, 2, and 9 solution.)
  
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