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alphamet.gms : Alphametics - a Mathematical Puzzle

Alphametics are a type of mathematical puzzle. Given a set of
words, written down as a long-hand addition, find the mapping
between letters and digits (values). For example:

    G E O R G I A             8 4 6 5 8 0 2
      O R E G O N     ->        6 5 4 8 6 3
    V E R M O N T             1 4 5 9 6 3 7
    -------------           ---------------
  V I R G I N I A           1 0 5 8 0 3 0 2

Additional information can be found at:

http://www.gams.com/modlib/adddocs/alphametdoc.htm
References:
Large Model of Type: MIP
$title Alphametics - A Mathematical Puzzle (ALPHAMET,SEQ=170) $ontext Alphametics are a type of mathematical puzzle. Given a set of words, written down as a long-hand addition, find the mapping between letters and digits (values). For example: G E O R G I A 8 4 6 5 8 0 2 O R E G O N -> 6 5 4 8 6 3 V E R M O N T 1 4 5 9 6 3 7 ------------- --------------- V I R G I N I A 1 0 5 8 0 3 0 2 Additional information can be found at: http://www.gams.com/modlib/adddocs/alphametdoc.htm Brooke, A, Kendrick, D, and Meeraus, A, GAMS: A User's Guide. The Scientific Press, Redwood City, California, 1988. $offtext set i letters /g,e,o,r,i,a,n,v,m,t/; alias (i,j); abort$(card(i) <> 10) "set i should contain 10 letters"; set k slices /1*8/ lead(i) /g,o,v/; parameter lhs(k,i) input count for each letter in slice / 1.(a,n,t) 1 2.(i,o,n) 1 3.g 2 , 3.o 1 4.(r,e,m) 1 5.o 1 , 5.r 2 6.e 2 , 6.o 1 7.(g,v) 1 /; parameter rhs(i,k) result / (v.8,i.7,r.6,g.5,i.4,n.3,i.2,a.1) 1.0 / variables z sum of carries - some objective x(i,j) assignment of digits or values to letters y(i) assigned value c(k) carry; binary variables x; integer variables c; equations obj some objective eq(k) defines addition for each slice ydef(i) assigned value x1(i) assignment constraint one x2(j) assignment constraint two ld(i) bound on lead letters; obj.. z =e= sum(k, c(k-1)); eq(k).. c(k-1) + sum(i, lhs(k,i)*y(i)) =e= sum(i, rhs(i,k)*y(i)) + 10*c(k)$(ord(k)<>card(k)); ydef(i).. y(i) =e= sum(j, (ord(j) - 1)*x(i,j)); x1(i).. sum(j, x(i,j)) =e= 1; x2(j).. sum(i, x(i,j)) =e= 1; ld(lead).. y(lead) =g= 1; model m /all/; option optcr=1,optca=100; solve m using mip minimizing z;