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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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re(4): comp. aided solution -- HINT | Comment 7 of 11 |
(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
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