One day a friend visited my house and asked me the ages of my three sons. I replied that the product of my son's ages is 36 and the sum of their ages is equal to my house number. My friend who has a sharp and logical mind, requested me for another hint. I then told him that my eldest son has blue eyes! Following this he quickly told me their ages.

A. 1 year, 1 year and 36 years

C. 2 years, 2 years and 9 years

B . 1 year, 4 years and 9 years

D . 3 years, 3 years and 4 years

The correct answer is C The explanation for the answer is: The product of the ages of the three children is 36. Thus, their possible ages and the sum of their ages are: 1 year, 1 year, 36 years; Sum = 38 1 year, 3 years, 12 years; Sum = 16 1 year, 4 years, 9 years; Sum = 14 1 year, 6 years, 6 years; Sum = 13 2 years, 2 years, 9 years; Sum = 13 2 years, 3 years, 6 years; Sum = 11 3 years, 3 years, 4 years; Sum = 10 The reason for the friend `s confusion was that there are two age groups that have the same sum of the ages, i.e., 13. When he was told that the eldest son has blue eyes, he immediately ruled out the set of 1 year, 6 years and 6 years as in this case, the eldest children have the same age. Thus, only one possibility remained, i.e., the ages of the children are 2 years, 2 years and 9 years. Therefore, the correct answer is C.