append(nil,L,L). append([H|L1],L2,[H|L3]) :- append(L1,L2,L3).

mother(gaia,cronos). mother(rhea,zeus). mother(rhea,hades). father(zeus,pollux). father(cronos,zeus). father(ouranos,cronos). father(zeus,helene). father(zeus,castor). parent(X,Y) :- father(X,Y). parent(X,Y) :- mother(X,Y). grandparent(X,Z) :- parent(X,Y),parent(Y,Z).

valid([]). valid([Head|Tail]) :- all_different(Head), valid(Tail). neq(1,2). neq(1,3). neq(1,4). neq(2,3). neq(2,4). neq(3,4). neq(2,1). neq(3,1). neq(4,1). neq(3,2). neq(4,2). neq(4,3). not_member(X,[]). not_member(X,[Head|Tail]) :- neq(X,Head), not_member(X,Tail). all_different([]). all_different([Head|Tail]) :- not_member(Head,Tail), all_different(Tail). mem(X,[X|T]). mem(X,[Y|T]) :- mem(X,T). all_within([],_). all_within([Head|Tail],L) :- mem(Head,L), all_within(Tail,L). unif(X,X). sudoku(Puzzle, Solution) :- unif(Solution, Puzzle), unif(Puzzle, [S11, S12, S13, S14, S21, S22, S23, S24, S31, S32, S33, S34, S41, S42, S43, S44]), all_within(Solution, [1,2,3,4]), unif(Row1 ,[S11, S12, S13, S14]), unif(Row2 ,[S21, S22, S23, S24]), unif(Row3 ,[S31, S32, S33, S34]), unif(Row4 ,[S41, S42, S43, S44]), unif(Col1 ,[S11, S21, S31, S41]), unif(Col2 ,[S12, S22, S32, S42]), unif(Col3 ,[S13, S23, S33, S43]), unif(Col4 ,[S14, S24, S34, S44]), unif(Square1 ,[S11, S12, S21, S22]), unif(Square2 ,[S13, S14, S23, S24]), unif(Square3 ,[S31, S32, S41, S42]), unif(Square4 ,[S33, S34, S43, S44]), valid([Row1, Row2, Row3, Row4, Col1, Col2, Col3, Col4, Square1, Square2, Square3, Square4]).

append(nil,L,L). append([H|L1],L2,[H|L3]) :- append(L1,L2,L3). select3(X, [X|Tail], Tail). select3(Elem, [Head|Tail], [Head|Rest]) :- select3(Elem, Tail, Rest). select([A|As],S):- select3(A,S,S1),select(As,S1). select([],_). next_to(A,B,C):- left_of(A,B,C). next_to(A,B,C):- left_of(B,A,C). left_of(A,B,C):- append(_,[A|[B|_]],C). member(X,[X|T]). member(X,[Y|T]) :- member(X,T). unif(X,X). zebra(Owns, Hs):- unif(Hs, [h(_,norwegian,_,_,_),_,h(_,_,_,milk,_),_,_]), select([h(red,englishman,_,_,_),h(_,swede,dog,_,_), h(_,dane,_,tea,_),h(_,german,_,_,prince)],Hs), select([h(_,_,birds,_,pallmall),h(yellow,_,_,_,dunhill), h(_,_,_,beer,bluemaster)],Hs), left_of(h(green,_,_,coffee,_),h(white,_,_,_,_),Hs), next_to(h(_,_,_,_,dunhill),h(_,_,horse,_,_),Hs), next_to(h(_,_,_,_,blend),h(_,_,cats, _,_),Hs), next_to(h(_,_,_,_,blend),h(_,_,_,water,_),Hs), next_to(h(_,norwegian,_,_,_),h(blue,_,_,_,_),Hs), member(h(_,Owns,zebra,_,_),Hs).