The Oldest Plays the Piano

The possible ages ( factors of 72 ) and their sums are shown below:
Ages: - Sum of ages:
1 1 72 - 74
1 2 36 - 39
1 3 24 - 28
1 4 18 - 23
1 6 12 - 19
1 8 9 - 18
2 2 18 - 22
2 3 12 - 17
2 4 9 - 15
2 6 6 - 14
3 3 8 - 14
3 4 6 - 13
We can deduce from the man’s confusion over the building number that this wasn’t enough information to solve the problem. The chart shows the sum 14 twice for two different age possibilities, which would explain how knowing the building number alone would not have given him the answer. The clue that the “oldest one” started to play the piano rules out “2 6 6” as an answer, because there is no “oldest”. Since the first grad was certain with the piano clue, the first grad’s oldest daughter is 8. I’ll leave it up to the reader to figure out why this doesn’t necessarily mean the second grad’s oldest daughter was also 8.