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An unusual sales pitch

Clue No. 1: a x b x c = 36

Clue No. 2: The salesman not having enough information after the second clue implies more than one a + b + c sums to the same number - i.e: a1 + b1 + c1 = a2 + b2 + c2

Clue No. 3: "My eldest is learning to play the piano!!" implies there is only one eldest child (not twins).

Therefore 2, 2, 9 is the only possible solution.

a b c Sum Product
1 2 18 21 36
1 3 12 16 36
1 4 9 14 36
1 6 6 13 36
2 2 9 13 36
2 3 6 11 36
3 3 4 10 36

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