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The example describes the classic crypt-arithmetic puzzle "send more money". A different digit for each letter of the following equation has to be found:

  S E N D
+ M O R E
---------
M O N E Y

To specify the problem for a constraint solver, we have to declare the variables and their domains:

S, E, N, D, M, O, R, Y    {0..9}

In addition, the problem involves the following two constraints:

                    1000 × S + 100 × E + 10 × N + D 
1)                + 1000 × M + 100 × O + 10 × R + E 
      = 10000 × M + 1000 × O + 100 × N + 10 × E + Y

2)    alldifferent({S, E, N, D, M, O, R, Y})

Giving this information to a constraint solver, a solution is produced immediately:

{S = 2, E = 8, N = 1, D = 7, M = 0, O = 3, R = 6, Y = 5}

Notice that there was no solving method given. The solver produced only one solution, but of course all other possible solutions can be listed as well. If special solutions are prefered, an optimization can be applied.

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Last update:
May 19, 2001 by Alexander Nareyek