/* MAGIC, Magic Square *//* Written in GNU MathProg by Andrew Makhorin <mao@mai2.rcnet.ru> *//* 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;