Solution to the three daughters

What are their ages?

A woman had three daughters. A second woman asked her the ages of her daughters. The first woman told her that the product of their ages was 36. After thinking the second woman was unable to find the answer and asked for another clue. The first woman replied that the sum of their ages was equal to the second woman’s house number. Still unable to find the ages, the second woman asked for another clue. The first woman told her that her youngest daughter had blue eyes, and the second woman knew the ages. What were they?

Solution:

The only possible ages whose product is 36 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). The sums of these ages are: 38, 21, 16, 14, 13, 13, 11,10. Since the second woman knows her own house number the house number must be 13 because this is the only case when there is an ambiguity. Hence the possible ages are (1,6,6) or (2,2,9). The final statement tells her that there is a “youngest” daughter, which leaves only one possibility – (1,6,6) for the ages of the daughters.