% Harry Potter and the seven potions

perm([],[]).
perm(X,[Y|Z]):-select(Y,X,R),perm(R,Z).

puzzle(Potions):- Potions=[P1,P2,P3,P4,P5,P6,P7],
	perm(Potions, [forward,back,wine,wine,poison,poison,poison]),
 % First clue -- Each wine bottle has poison on the left
	P1\==wine,
	(P2\==wine; P1=poison),
	(P3\==wine; P2=poison),
	(P4\==wine; P3=poison),
	(P5\==wine; P4=poison),
	(P6\==wine; P5=poison),
	(P7\==wine; P6=poison),
 % Second clue -- the ends are different
	P1\==P7,
 %   Neither end moves you forward
	P1\==forward, P7\==forward,
 % Third clue -- look at the drawing for the biggest and smallest
	Dwarf=P3, Giant=P2, Dwarf\==poison, Giant\==poison,
 % Fourth clue -- second left and second on the right are the same
	P2==P6.

solve(S):-setof(P,puzzle(P),S),member(T,S), write(T),nl,fail.