% -----------------------------------------
% Exercice 4
% @author "Alexis Fouché" <contact@alexisfouche.net>
% -----------------------------------------

% == 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.