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2+2=4 is true (Posted on 2014-06-22) Difficulty: 3 of 5
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.
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No Solution Yet Submitted by Ady TZIDON    
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Some Thoughts possible solution | Comment 1 of 2

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

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