Explorer is absolutely right and there is no flaw in this question. With the several possible factors of 36 : 36*1*1 (sum=38) 18*2*1 (sum=21) 9*4*1 (sum=14) 9*2*2 (sum=13) 6*6*1 (sum=13) 6*3*2 (sum=11) 4*3*3 (sum=10) There is only one scenario when the census taker is not sure of the ages (i.e. when the sum=13). He obviously knows the address of the next house (even though we dont), and he would be able to tell for sure (even though we would not) if the sum was anything but 13. Since the lady had "an oldest child", he can tell that it is 9,2,2 instead of 6,6,1.