The Real McCoy!

Enjoyed watching Texas winning over OU 28-10. Colt McCoy (Quarter Back) and his team will be bringing the 10-gallon Gold Cowboy Hat to Austin again!

Solution:
The only combinations of three ages whose product is 36 are: 1x1x36, 1x2x18, 1x3x12, 1x4x9, 1x6x6, 2x2x9, 2x3x6, and 3x3x4. Except for two of the combinations, all their sums are different. Say that you ask the sister her age. If her age were the same as any of those sums, you would know the ages of the brothers. But because you need to know that the oldest brother usually wears his baseball cap backward, her age must be the sum of that’s shared by two combinations: 13 (1, 6, 6 or 2, 2, 9). Only one of these two combinations has an “oldest” brother, which means 2, 2, and 9 years in the answer.