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FreeLilly We'll start with listing all combinations that add up to 13, and add the multiple for the next step too:
11 * 1 * 1 = 11
10 * 2 * 1 = 20
9 * 3 * 1 = 27
9 * 2 * 2 = 36
8 * 4 * 1 = 32
8 * 3 * 2 = 48
7 * 5 * 1 = 35
7 * 4 * 2 = 56
7 * 3 * 3 = 63
6 * 6 * 1 = 36
6 * 5 * 2 = 60
6 * 4 * 3 = 70
5 * 5 * 3 = 75
5 * 4 * 4 = 80
Although we don't know what the multiple is, we do know the guy still isn't sure. Therefore the multiple must leave us with more than one option. The only one doing so is 36, so we can narrow it down to either 9, 2 and 2 or 6, 6 and 1.
That's were the last hint comes in. The harp isn't important, but there is an eldest one. That means we can eliminate 6, 6 and 1 leaving us with 9, 2 and 2 as the correct ages.