% Six by six chessboard problem, see "http://www.perlmonks.org/?node_id=821272"
% Finite domain constraint programming variaton

:- use_module(library(clpfd)).

row(R) :-
	length(R, 6), 
	R ins 0 .. 1,
	row1(R).
	
row1([X0, X1, X2, X3, X4, X5]) :-
	X0 + X1 + X2 + X3 + X4 + X5 #= 3.

/*
differ([X0, X1, X2, X3, X4, X5], [Y0, Y1, Y2, Y3, Y4, Y5], P) :-
	(X0 #\= Y0) #\/ (X1 #\= Y1) #\/ (X2 #\= Y2) #\/ ... % nah, I'll typo this somewhere
*/
vdiffer(Xs, Ys) :-
	zip(lambda(arg(X, Y, N), N = (X #\= Y)), Xs, Ys, Ns),
	foldrz(lambda(arg(M, N, Q), Q = (M #\/ N)), 0, Ns, P),
	P.

pairwise_vdiffer([]).
pairwise_vdiffer([H | T]) :-
	for(lambda_close(H, Hi, arg(K), vdiffer(Hi, K)), T),
	pairwise_vdiffer(T).

boardp(B) :-
	length(B, 6),
	for(lambda(arg(R), row(R)), B), 
	transpose(B, BT),
	for(lambda(arg(C), row1(C)), BT),
	pairwise_vdiffer(B),
	pairwise_vdiffer(BT).

board(B) :- 
	boardp(B), 
	concat(B, Bfl), 
	[R0 | _] = B,
	labeling([leftmost], R0),
	write(board_debug0([R0])), nl,
	labeling([leftmost], Bfl).

nboard(N) :-
	findall(x, board(_B), L),
	length(L, N).

main :-
	nboard(N), write(N), nl.	


/*