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)

Answer:

base 9, meaning 0,1,2,3,4,5,6,7,8

t=5
o=0
k=1
y=6

kyoto
kyoto
kyoto
--------
tokyo



long term logic version to send to puzzle club:

assume each variable is distinct.

there are two cases that can be explored.
because o+o+o=o, then o=0 or o=N/2

case 1
o=0

t+t+t=k*N^1 + y 3t=k*N^1 + y
y+y+y=x*N^1 3y=x*N^1
k+k+k+x=t 3k+x=t

then

y=(x*N^1)/3
3t=k*N^1 + (x*N^1)/3
t=(k*N^1)/3 + (x*N^1)/9
t=(3(k*N^1) + x*N^1)/9
t=((3k+x) N^1)/9
N^1=9t/(3k+x)

N^1=9(3k+x)/(3k+x)
N^1=9

so base 9 works for case 1

from this, variables are easy to determine.

case 2 later, too many variables...

Posted by desiree on 2003-09-22 22:37:40