In what bases the cryptarithmetic puzzle TOO + TOO = FOR has a unique solution?

case A: each letter could be any digit, including 0.
case B: T could be any digit, except 0.
.

Start with case B. There must be 4 distinct values; T,O,F,R, plus 0, making 5. No base less than 5 qualifies. Base 5 causes T and R to have the same value. Base 6 and base 7 produce unique solutions, bases 8 and up produce multiple solutions.

In case A, T=0 iff F=1. No base less than 4 qualifies. All bases greater than 3 produce a solution. So only bases 4 and 5 produce unique solutions, since bases 6 and 7 already have a different solution.

Edited on June 22, 2014, 10:11 am

Posted by broll on 2014-06-22 10:09:20