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(2): computer aided solution -- continued by Charlie)
Your output provides a correct answer, which you have overlooked.
Your answer does not provide the ages,- if ( 48,4) was said loud and clear no one could distinguish between
12 48 4 1 3 4 4
12 48 4 2 2 2 6
-(copied from your table.)
Two important remarks:
a. At least 3 children is a must to warrant an ambiguity.
b. By adding an extra 1 year old child to the above example we "propagate" the ambiguity into bus number 13, since the product stays unchanged, and the sum increases by one:
13 48 5 1 1 3 4 4
13 48 5 1 2 2 2 6
Therefore for buses over 12 - no way to reconstruct the ages- a dual combination (for age 48) exists. Extending the program for higher bus values was redundant.
The correct answer my friend is written in the wind - you will easily recover it from your table.
I believe that the "fatherhood limitations" do not disturb the uniqueness of this beautiful puzzle .
Edited on October 31, 2015, 4:36 am
re(3): comp. aided solution -- HINT
