Solution
The Census Taker
Show the problem again
A census taker asks a woman the ages of her three children. She says their ages multiply to 36 and sum to the house number next door. The census taker checks the house number and says that's still not enough information. She adds: "My oldest child likes ice cream." What are the three ages?
Worked solution
The ages are 2, 2, and 9. Among factorizations of 36, only two share a sum: 1+6+6 = 13 and 2+2+9 = 13; the ambiguity tells us the house number is 13. The final clue's content is irrelevant; what matters is that an "oldest" child uniquely exists, ruling out (1, 6, 6) with its twin elders. The ages are 2, 2, 9.
Source: Classic 'ages of three children' deduction puzzle in wide circulation; no traceable original source. Statement written for AxiomIQ.