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**