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 solution by Christian Perfect)

It looks like you assumed that the letter O equals the number zero. I could prove that if n is odd, letter 0 equals zero. I'll spell zero if I refer to the number

For O times 3 to have a last digit of O, O must either be zero, or exactly half of n. Since O must be an integer, n must be divisible by 2 for O two be half of n. Since n is not even, O must be zero.

Your assumption was correct, but you may have overlooked some solutions. Or you may not have. I think I might try to find other possible solutions. I wonder if n has to be less than or equal to ten...

Posted by Tristan on 2003-09-21 11:39:53