The answer is 2, 2, and 9.
List all the factors of 36:
Factors Sum
| 6 * 6 * 1 | 13 |
| 4 * 9 * 1 | 14 |
| 2 * 18 *1 | 21 |
| 3 *12 * 1 | 16 |
| 6 * 2 * 3 | 11 |
| 4 * 3 * 3 | 10 |
| 2 * 9 * 2 | 13 |
Notice: Two sets have sums of 13 which is why the Census-taker could not determine the answer. But as soon as the lady says: "the oldest plays the piano, then it must be 2, 9, 2, which is the combination of the two that has an older sibling.