First, the problem is meaningful only is all the ages are integers. You must assume that! The next step is to go ahead and use the first condition, that the product of the sons' ages is 36. This gives just 8 options:
| age 1 | age 2 | age 3 | sum |
| 1 | 1 | 36 | 38 |
| 1 | 2 | 18 | 21 |
| 1 | 3 | 12 | 16 |
| 1 | 4 | 9 | 14 |
| 1 | 6 | 6 | 13 |
| 2 | 2 | 9 | 13 |
| 2 | 3 | 6 | 11 |
| 3 | 3 | 4 | 10 |
Among these options is the correct solution. We must choose. Calculations of the sum (the fourth column) show the only possible numbers of windows in the house. If the sum were 38, 21, 16, 14, 11, or 10, Igor would have been able to solve the problem immediately. He was unable to do so only because the number of windows in the house (and the sum of the ages) was 13! Because of this, he did not have a unique solution until Pavel informed him of the hair color of his "oldest son." If the ages are 1, 6, and 6, there are older sons but not an older son, and the ambiguity is resolved:
Pavel's sons are 2, 2, and 9 years old.