% Find all 3 by 3 magic squares. 10 times faster!
% digit(D) is for digit
digit(1). digit(2). digit(3). digit(4). digit(5). digit(6). digit(7). 
digit(8). digit(9).
% digits can only be used once. Select extracts one digit from Unused list
d(D,OldUnUsed,NewUnUsed):-select(OldUnUsed,D,NewUnUsed).
% a row has 3 digits that add up to 15
row(X,Y,Z,OldUnused, NewUnused):-d(X,OldUnused, U),d(Y,U,U2), 
	Z is 15 - X - Y, d(Z,U2,NewUnused).
% 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+Z=:=15.

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

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,
	UnUsed=[1,2,3,4,5,6,7,8,9],
	row(A,B,C,UnUsed,UnUsed2),
	row(D,E,F,UnUsed2,UnUsed3),
	G is 15-A-D, H is 15-B-E,
	row(G,H,I,UnUsed2,UnUsed4), 
	col(A,D,G),col(B,E,H),col(C,F,I),
	diag(A,E,I), diag(G,E,C),
	out(A,B,C,D,E,F,G,H,I).