"Age of childen" is fun because at first you stumble over the hint with the oldest child playing piano and wonder how that could have anything to do with the ch

"Age of childen" is fun because at first you stumble over the hint with the oldest child playing piano and wonder how that could have anything to do with the children's ages. So, there are three kids and the product of their ages is 36. Assuming that ages are integers, this gives us the following possibilities: (a) 1 1 36 (b) 1 2 18 (c) 1 3 12 (d) 1 4 9 (e) 1 6 6 (f) 2 2 9 (g) 2 3 6 (h) 3 3 4 The sum of their ages is the neighbor's house number. So let's see what the above age distributions sum up to: (a) 38 (b) 21 (c) 16 (d) 14 (e) 13 (f) 13 (g) 11 (h) 10 The fact that the insurance agent still doesn't know the answer after returning from the neighbor's house means that it must be either (e) or (f) as those are the only two possibilities that sum up to the same value and thus are ambiguous. But then the mother mentions that her oldest kid plays the piano, and of course it's not so much the piano that gives us the hint, but the fact that she has one oldest kid: in (e) there would be two oldest kids. Therefore the answer is (f): two of the kids are 2 and one is 9 years old.