Find the number n such that the following alphanumeric equation:

   KYOTO
   KYOTO
 + KYOTO
   TOKYO

has a solution in the base-n number system.

(Each letter in the equation denotes a digit in this system, and different letters denote different digits)

(In reply to Proof of solution by Eradicator)

3k<n, which implies k0. Thus o=0. From second and third digits we observe 3*t=k*n+y and from 2 leftmost digits then let a represent the carry over to the leftmost digit we derive a*n=3*y and t=a+3*k. I won't bore anyone with rote subsitution, this is sufficient to show n=9.

Posted by Eradicator on 2003-09-21 14:36:15