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Incredible, but solvable (Posted on 2015-10-30) Difficulty: 4 of 5
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.

No Solution Yet Submitted by Ady TZIDON    
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Hints/Tips re(3): comp. aided solution -- HINT | Comment 6 of 11 |
(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
  Posted by Ady TZIDON on 2015-10-31 04:16:13

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