A puzzle by Princeton mathematician John Horton Conway:
Last night I sat behind two wizards on a bus, and overheard the following:
A: I have a positive integral number of children, whose ages are positive integers, the sum of which is the number of this bus, while the product is my own age.
B: How interesting! Perhaps if you told me your age and the number of your children, I could work out their individual ages?
A: No.
B: Aha! AT LAST I know how old you are!
Rem: Taking in account the fatherhood limitations, this is uniquely solvable.
(In reply to
re(3): comp. aided solution  HINT by Ady TZIDON)
The answer does NOT propagate to 13, as can be seen on the next two sets:
13 36 3 1 6 6
13 36 3 2 2 9
13 48 5 1 1 3 4 4
13 48 5 1 2 2 2 6
So at the aha! stage, B, not knowing the product or sum, but only the bus number, A not having told him anything except that knowing the three data items would still not give the overall answer, would still not know A's ageeither 36 or 48. On the other hand, even without knowing the details, just from the metainformation and bus number, B can deduce the age from the bus number's being 12.

Posted by Charlie
on 20151031 07:59:05 