One day a friend visited my house and asked me the ages of my threesons. I replied that the product of my son's ages is 36 and the sum of theirages 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 blueeyes! Following this he quickly told me their ages.Tell me how old are my three sons?

Question

anonymous · Answer

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

In this case, every combination of possible ages has a unique sum of ages - except for two cases, both of which have 13 as the sum. Since the friend could not figure out the ages after looking at the house number, the house number must be 13, because then, the ages could be either 1, 6, 6 or 2, 2, 9. 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.