% -----------------------------------------------
%                    Exercice 4
%           Florian Lepot & Maxime Fabre
% -----------------------------------------------

% Question 1
% -------------------------

?- choisir(X, [1,2,3]).
X = 1 ;
X = 2 ;
X = 3.



% Question 2
% -------------------------

?- permutation([1,2,3], [X,Y,Z]).
X = 1,
Y = 2,
Z = 3 ;
X = 2,
Y = 1,
Z = 3 ;
X = 2,
Y = 3,
Z = 1 ;
X = 1,
Y = 3,
Z = 2 ;
X = 3,
Y = 1,
Z = 2 ;
X = 3,
Y = 2,
Z = 1 ;
false.



% Question 3
% -------------------------

?- generer(L).
L = [2, 4, 3, 5, 1, 6] ;
L = [4, 3, 5, 1, 6, 2] ;
L = [1, 4, 5, 2, 3, 6] ;
L = [4, 5, 2, 3, 6, 1] ;
L = [3, 2, 5, 4, 1, 6] ;
L = [1, 5, 3, 4, 2, 6] ;
L = [5, 3, 4, 2, 6, 1] ;
L = [2, 5, 4, 1, 6, 3] ;
L = [5, 4, 1, 6, 3, 2] ;
L = [3, 5, 1, 6, 2, 4] ;
L = [5, 2, 3, 6, 1, 4] ;
L = [5, 1, 6, 2, 4, 3] ;
L = [3, 4, 2, 6, 1, 5] ;
L = [4, 1, 6, 3, 2, 5] ;
L = [4, 2, 6, 1, 5, 3] ;
L = [2, 3, 6, 1, 4, 5] ;
L = [3, 6, 1, 4, 5, 2] ;
L = [1, 6, 2, 4, 3, 5] ;
L = [6, 2, 4, 3, 5, 1] ;
L = [6, 1, 4, 5, 2, 3] ;
L = [1, 6, 3, 2, 5, 4] ;
L = [6, 3, 2, 5, 4, 1] ;
L = [2, 6, 1, 5, 3, 4] ;
L = [6, 1, 5, 3, 4, 2] ;
false.



% Question 4
% -------------------------

?- tester([2, 4, 4, 5, 1, 6]).
false.

?- tester([2, 4, 3, 5, 1, 6]).
true.



% Question 5
% -------------------------

?- solution([2, 4, 3, 5, 1, 6]).
true.

7 ?- solution([2, 4, 4, 5, 1, 6]).
false.



% Question 6
% -------------------------

?- nbsolutions(S).
S = 1.