/* MAGIC, Magic Square */

 /* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */

 /* In recreational mathematics, a magic square of order n is an

    arrangement of n^2 numbers, usually distinct integers, in a square,

    such that n numbers in all rows, all columns, and both diagonals sum

    to the same constant. A normal magic square contains the integers

    from 1 to n^2.

    (From Wikipedia, the free encyclopedia.) */

 param n, integer, > 0, default 4;

 /* square order */

 set N := 1..n^2;

 /* integers to be placed */

 var x{i in 1..n, j in 1..n, k in N}, binary;

 /* x[i,j,k] = 1 means that cell (i,j) contains integer k */

 s.t. a{i in 1..n, j in 1..n}: sum{k in N} x[i,j,k] = 1;

 /* each cell must be assigned exactly one integer */

 s.t. b{k in N}: sum{i in 1..n, j in 1..n} x[i,j,k] = 1;

 /* each integer must be assigned exactly to one cell */

 var s;

 /* the magic sum */

 s.t. r{i in 1..n}: sum{j in 1..n, k in N} k * x[i,j,k] = s;

 /* the sum in each row must be the magic sum */

 s.t. c{j in 1..n}: sum{i in 1..n, k in N} k * x[i,j,k] = s;

 /* the sum in each column must be the magic sum */

 s.t. d: sum{i in 1..n, k in N} k * x[i,i,k] = s;

 /* the sum in the diagonal must be the magic sum */

 s.t. e: sum{i in 1..n, k in N} k * x[i,n-i+1,k] = s;

 /* the sum in the co-diagonal must be the magic sum */

 solve;

 printf "\n";

 printf "Magic sum is %d\n", s;

 printf "\n";

 for{i in 1..n}

 {  printf{j in 1..n} "%3d", sum{k in N} k * x[i,j,k];

    printf "\n";

 }

 printf "\n";

 end;