Hint to Puzzle #34: Man With 3 Daughters of Different Ages

34. A man has three daughters. A second, intelligent man, asked him the ages of his daughters. The first man told him that the product of their ages (them all multiplied together,) was 36. After thinking the second man was unable to find the answer and asked for another clue. The first man replies the sum of their ages is equal to his house door number. Still the second man was unable to answer and asked for another clue. The first man told him that his youngest daughter had blue eyes, and suddenly second man gave the correct answer. Explain how?

three girls sum of ages is door number I have two hints for this puzzle. The first is conceptual and the other practical.

The first hint is that instinctively we want to be the second man in the puzzle. We can't solve the puzzle that way but we don't need to. We are a third man and we gain information from the first and the second, in particular the fact that he can or can't solve the puzzle at a particular point is telling.

Write down all the combinations of 3 numbers that have a product of 36 and then begin eliminating them based on the information from both men.

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