diff -r d59bea55db9b -r c445c931472f examples/magic.mod --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/examples/magic.mod Mon Dec 06 13:09:21 2010 +0100 @@ -0,0 +1,54 @@ +/* MAGIC, Magic Square */ + +/* Written in GNU MathProg by Andrew Makhorin */ + +/* 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;