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+/* QUEENS, a classic combinatorial optimization problem */
+
+/* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */
+
+/* The Queens Problem is to place as many queens as possible on the 8x8
+   (or more generally, nxn) chess board in a way that they do not fight
+   each other. This problem is probably as old as the chess game itself,
+   and thus its origin is not known, but it is known that Gauss studied
+   this problem. */
+
+param n, integer, > 0, default 8;
+/* size of the chess board */
+
+var x{1..n, 1..n}, binary;
+/* x[i,j] = 1 means that a queen is placed in square [i,j] */
+
+s.t. a{i in 1..n}: sum{j in 1..n} x[i,j] <= 1;
+/* at most one queen can be placed in each row */
+
+s.t. b{j in 1..n}: sum{i in 1..n} x[i,j] <= 1;
+/* at most one queen can be placed in each column */
+
+s.t. c{k in 2-n..n-2}: sum{i in 1..n, j in 1..n: i-j == k} x[i,j] <= 1;
+/* at most one queen can be placed in each "\"-diagonal */
+
+s.t. d{k in 3..n+n-1}: sum{i in 1..n, j in 1..n: i+j == k} x[i,j] <= 1;
+/* at most one queen can be placed in each "/"-diagonal */
+
+maximize obj: sum{i in 1..n, j in 1..n} x[i,j];
+/* objective is to place as many queens as possible */
+
+/* solve the problem */
+solve;
+
+/* and print its optimal solution */
+for {i in 1..n}
+{  for {j in 1..n} printf " %s", if x[i,j] then "Q" else ".";
+   printf("\n");
+}
+
+end;