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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(5): comp. aided solution -- HINT | Comment 8 of 11 |
(In reply to re(4): comp. aided solution -- HINT by Charlie)

BTW, it looks as if I am not alone in my solution. A google search for John Horton Conway bus number individual ages, brings up as the top result http://www.futilitycloset.com/2015/04/08/overheard-4/, agreeing with my answer.


Or from http://arxiv.org/pdf/1210.5460.pdf: Now to the answer. The bus number is 12. The only age for which the bus number and the number of children do not define the ages of children is 48. The children ages could be 2, 2, 2, and 6, or on the other hand, 1, 3, 4, and 4. ... If the bus number is 13 or greater, wizard B cannot figure out the age of wizard A.

...  added:

It occurred to me that you missed actually seeing my solution, in bold face at the bottom of the last continuation:

The bus number was 12, as was the sum of A's kids' ages. Their ages' product is 48 and so that's A's age, and he has 4 children. The only thing in doubt is their ages: either 1, 3 and two 4-year olds; or three 2-year olds and a 6 year old.

Edited on October 31, 2015, 8:31 am
  Posted by Charlie on 2015-10-31 08:07:16

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