% Find all 3 by 3 magic squares.
% Shows the use of a list of variables to keep track of whether
% they have been assumed to have values or not yet.
:-op(100, xfx, not_in).  % a new infix operator. xfx defines associativity
_ not_in [].
D not_in [X | Rest]:- var(X),! , %added to reduce trail
	D not_in Rest.
D not_in [X | Rest]:- nonvar(X), D\==X,!, %added to reduce trail
	 D not_in Rest.

% d(D) is for digit
d(1). d(2). d(3). d(4). d(5). d(6). d(7). d(8). d(9).

% nd(X, D) gets a new and different digit each time, But quickly.
% D is a list of the variables representing digits in problem
nd(Digit,DigitList):- nonvar(Digit),!. 
			% cut added to reduce trail
nd(Digit,DigitList):-
	var(Digit),!, d(X1), X1 not_in DigitList, Digit=X1.

% a row has 3 different digits that add up to 15
row(X,Y,Z, DigitList):-nd(X,DigitList),
	nd(Y,DigitList), 
	nd(Z,DigitList), 
	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,
	DigitList=[A,B,C,D,5,F,G,H,I],
	row(A,B,C,DigitList),
	row(D,5,F,DigitList),
	row(G,H,I,DigitList), 
	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).