% Find all 3 by 3 magic squares. 10 times faster!
% d(D) is for digit
d(1). d(2). d(3). d(4). d(5). d(6). d(7). d(8). d(9).
% a row has 3 different digits that add up to 15
row(X,Y,Z):-d(X),d(Y), X=\=Y, Z is 15 - X - Y, d(Z), d(Z),X=\=Z, Y=\=Z.
% was row(X,Y,Z):-d(X),d(Y), X=\=Y, d(Z),X=\=Z, Y=\=Z, X+Y+Z=:=15.

col(X,Y,Z):-X=\=Y, Y=\=Z, X=\=Z, X+Y+Z=:=15.

diag(X,Y,Z):-X=\=Y, Y=\=Z, X=\=Z, X+Y+Z=:=15.
% make sure that there are no other duplicate digits
offdiag(X,Y,Z):-X=\=Y, Y=\=Z, X=\=Z.

printrow(A,B,C):-write(A),write(B),write(C),nl.

out(A,B,C,D,E,F,G,H,I):-nl,
	printrow(A,B,C),
	printrow(D,E,F),
	printrow(G,H,I).

go:-go(More).
go(More):-More=more,
	row(A,B,C),
	row(D,E,F),
	G is 15-A-D, H is 15-B-E,
	row(G,H,I), 
	col(A,D,G),col(B,E,H),col(C,F,I),
	diag(A,E,I), diag(G,E,C),
	offdiag(A,H,F), offdiag(C,D,H),offdiag(G,B,F),offdiag(I,D,B),
	out(A,B,C,D,E,F,G,H,I).