Opgave 1
2.4
-------------------------------
crosswd(V1,V2,V3,H1,H2,H3) :-
        word(H1,_,A,_,B,_,C,_),
        word(H2,_,D,_,E,_,F,_),
        word(H3,_,G,_,H,_,I,_),
                                                                                  
        word(V1,_,A,_,D,_,G,_),
        word(V2,_,B,_,E,_,H,_),
        word(V3,_,C,_,F,_,I,_).
-------------------------------
explanation:
The following variables have to match:
 _ _ _
_A_B_C_
_D_E_F_
_G_H_I_
 _ _ _
                                                                                  
Where _ is a character which doesn't have to match and a letter is a character which does have to match. The letters are read both vertically and horizontally, thus ABC, DEF and ADG BEH etc.

3.2
greater_than(suc(1),0).
greater_than(suc(X),0) :- greater_than(X,0).
greater_than(suc(X),suc(Y)) :- greater_than(X,Y).

4.3
twice([], []).
twice([H|T],[H,H|Y]) :- twice(T,Y).

5.3
addone([], []).
addone([H|T],[K|Y]) :- addone(T,Y), K is H + 1.

Opgave 2
trans1(0,0).
trans1(suc(X),K) :- trans1(X,Y), K is Y + 1.