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?
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 age--either 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 2015-10-31 07:59:05