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I know I can get the answer for this puzzle but I'm struggling to see how to solve it.

Every letter represents a different number (0-9):

    PLAYS  +   WELL   =======    BETTER 

So far I know that:

  • B = 1 (has to be)
  • P = 9 (because P + 1 ≥ 10)
  • E = 0 (9 + 1 = 10)
  • L + W ≥ 10
  • A + 1 = T

How do I continue from here? I can't find any more hints:

    1 1     9LAYS  +   W0LL   =======    10TT0R 
  • 0
    In general these kinds of problems are Constraint Satisfaction Problems(CSP) http://en.wikipedia.org/wiki/Constraint_satisfaction_problem. And a CSP solver will solve them.2012-10-15

1 Answers 1

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Following from the comments, including mine. There are only four possible combinations for the trio of $(A,T,Y)$: $(2,3,4), (3,4,2), (4,5,2), (4,5,3)$.

The first two are impossible because the possible values left for R and S keep the tens column from summing to 0. The third case gives both L and W as 7 or 8. That leaves 3 and 6 for R and S, the only combination of those four numbers that would work in the rightmost column is $L=7, S=6, R=3$. This gives you your final answer:

    97426  +   8077    ======    105503 
  • 0
    Wow, it's pretty complicated. Thanks for the help!2012-10-15