Blake,

From the statement that the product of their ages is 36 the possibilities of the three individual ages 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

From the statement that the sum equals the house number it is possible to eliminate all but two possibilities. The sums of the rest are unique and would allow for an immediate answer. For example if the house number were 16 the ages must be 1, 3, and 12. The two remaining possibilities are 2, 2, and 9; or 1, 6, and 6.

After the clue that the oldest has red hair you can eliminate 1, 6, and 6 because the oldest two have the same age thus there is no oldest son. The only remaining posibility is 2, 2, and 9.

Answer

Their ages are 2, 2, and 9

You were correct maybe next time something much more difficult.

Do you know the 12 ball oddball problem?

Alan