neighbours(devon,cornwall).
neighbours(devon,dorset).
neighbours(devon,somerset).
neighbours(avon,somerset).
neighbours(avon,wiltshire).
neighbours(avon,gloucestershire).
neighbours(dorset,wiltshire).
neighbours(somerset,wiltshire).
neighbours(gloucestershire,wiltshire).
neighbours(dorset,somerset).
neighbours(dorset,hampshire).
neighbours(hampshire,wiltshire).
neighbours(hampshire,berkshire).
neighbours(hampshire,sussex).
neighbours(hampshire,surrey).
neighbours(sussex,surrey).
neighbours(sussex,kent).
neighbours(london,surrey).
neighbours(london,kent).
neighbours(london,essex).
neighbours(london,hertfordshire).
neighbours(london,buckinghamshire).
neighbours(surrey,buckinghamshire).
neighbours(surrey,kent).
neighbours(surrey,berkshire).
neighbours(oxfordshire,berkshire).
neighbours(oxfordshire,wiltshire).
neighbours(oxfordshire,gloucestershire).
neighbours(oxfordshire,warwickshire).
neighbours(oxfordshire,northamptonshire).
neighbours(oxfordshire,buckinghamshire).
neighbours(berkshire,wiltshire).
neighbours(berkshire,buckinghamshire).
neighbours(gloucestershire,worcestershire).
neighbours(worcestershire,herefordshire).
neighbours(worcestershire,warwickshire).
neighbours(bedfordshire,buckinghamshire).
neighbours(bedfordshire,northamptonshire).
neighbours(bedfordshire,cambridgeshire).
neighbours(bedfordshire,hertfordshire).
neighbours(hertfordshire,essex).
neighbours(hertfordshire,cambridgeshire).
neighbours(hertfordshire,buckinghamshire).
neighbours(buckinghamshire,northamptonshire).
distance(plymouth,exeter,42).
distance(exeter,bournemouth,82).
distance(bristol,taunton,43).
distance(bristol,gloucester,35).
distance(torquay,exeter,23).
distance(plymouth,torquay,24).
distance(bristol,bath,13).
distance(exeter,taunton,34).
distance(penzance,plymouth,78).
distance(taunton,bournemouth,70).
distance(bournemouth,salisbury,28).
distance(taunton,salisbury,64).
distance(salisbury,bath,40).
distance(bath,gloucester,39).
distance(bournemouth,bath,65).
distance(truro,penzance,26).
distance(plymouth,truro,52).
distance(shaftesbury,salisbury,20).
distance(sherbourne,shaftesbury,16).
distance(dorchester,bournemouth,28).
distance(salisbury,winchester,24).
distance(exeter,sherbourne,53).
distance(sherbourne,taunton,29).
distance(bath,cirencester,32).
distance(cirencester,cheltenham,16).
distance(cheltenham,gloucester,9).
distance(dorchester,sherbourne,19).
distance(bath,shaftesbury,33).
distance(winchester,bournemouth,41).
distance(exeter,dorchester,53).
distance(athens,bristol,60).
county(bristol,avon).
county(taunton,somerset).
county(salisbury,wiltshire).
county(bath,avon).
county(bournemouth,dorset).
county(gloucester,gloucestershire).
county(torquay,devon).
county(penzance,cornwall).
county(plymouth,devon).
county(exeter,devon).
county(winchester,hampshire).
county(dorchester,dorset).
county(cirencester,gloucestershire).
county(truro,cornwall).
county(cheltenham,gloucestershire).
county(shaftesbury,dorset).
county(sherbourne,dorset).


size([],0).
size([X|Tail],N) :- size(Tail,N1),
                    N is N1+1.
 

% Answer to question (i)

give(County) :- 
                 bagof(X,neighbours(X,County),L),
                 size(L,N),
                 N>=3
                 ;
                 bagof(X,neighbours(County,X),L),
                 size(L,N),
                 N>=3.


% Answer to question (ii) 


distance1(Town):-
                 distance(bristol,Town,D),
                 D<65.

distance2(Town):-
                  distance(Town,bristol,D),
                  D<65.

printlist(List):-
                 findall(Town,distance1(Town),List1),
                 findall(Town,distance2(Town),List2),
                 conc(List1,List2,List).

% Answer to question (iii) 

not(P):-
         call(P),!,fail
         ;
         true.


member(X,[X|T]).

member(X,[H|T]):-
                  member(X,T).

adjacent(X,Y):-
                neighbours(X,Y)
                ;
                neighbours(Y,X).


path(A,Z,Path):-
                 path1(A,[Z],Path).

path1(A,[A|Path1],[A|Path1]).

path1(A,[Y|Path1],Path):-
                          adjacent(X,Y),
                          not(member(X,Path1)),
                          path1(A,[X,Y|Path1],Path).