Sudoku

TITLE
  Sudoku;

INDEX
   row  := 1..9;
   coln := row;
   num  := 1..9;
   box  := 1..9;

DATA
    FixedValues[row,coln] := DATAFILE("sudoku.dat");

    BoxAssign[row,coln] := (

        1, 1, 1,  2, 2, 2,  3, 3, 3,
        1, 1, 1,  2, 2, 2,  3, 3, 3,
        1, 1, 1,  2, 2, 2,  3, 3, 3,

        4, 4, 4,  5, 5, 5,  6, 6, 6,
        4, 4, 4,  5, 5, 5,  6, 6, 6,
        4, 4, 4,  5, 5, 5,  6, 6, 6,

        7, 7, 7,  8, 8, 8,  9, 9, 9,
        7, 7, 7,  8, 8, 8,  9, 9, 9,
        7, 7, 7,  8, 8, 8,  9, 9, 9);

INDEX
    BoxComp[row,coln,box] WHERE (BoxAssign = box);

BINARY VARIABLES
   Assign[row,coln,num];

MODEL

   MAX TotalAssign = SUM(row,coln,num: Assign);

SUBJECT TO
   SingleCell[row,coln]: SUM(num: Assign) = 1;

   SingleRow[row,num]: SUM(coln: Assign) = 1;

   SingleCol[coln,num]: SUM(row: Assign) = 1;

   SingleBox[box,num]: SUM(row,coln IN BoxComp: Assign) = 1;

   FixValue[row,coln,num] WHERE (FixedValues[row,coln] = num):

       num*Assign = FixedValues;

END