Using Prolog to solve a password puzzle.

README.md

Password Puzzle

Here has a three-digit password. It satisfies all constraints below:

1. 682: One correct digit in the correct position.
2. 614: One correct digit in the wrong position.
3. 206: Two correct digits, neither in the correct position.
4. 738: No correct digits.
5. 870: One correct digit in the wrong position.

Answer

042

solve-1.pl

pass(Ps) :-
    length(Ps, 1),
    (
        member(h(6, _, _), Ps);
        member(h(_, 8, _), Ps);
        member(h(_, _, 2), Ps)
    ),
    (
        member(h(_, 6, _), Ps);
        member(h(_, _, 6), Ps);
        member(h(1, _, _), Ps);
        member(h(_, _, 1), Ps);
        member(h(4, _, _), Ps);
        member(h(_, 4, _), Ps)
    ),
    (
        member(h(_, 2, 0), Ps),
        \+ member(h(6, _, _), Ps);
        member(h(0, 2, _), Ps),
        \+ member(h(_, _, 6), Ps);
        member(h(0, _, 2), Ps),
        \+ member(h(_, 6, _), Ps);
        member(h(6, 2, _), Ps),
        \+ member(h(_, _, 0), Ps);
        member(h(6, _, 2), Ps),
        \+ member(h(_, 0, _), Ps);
        member(h(_, 6, 2), Ps),
        \+ member(h(0, _, _), Ps);
        member(h(6, _, 0), Ps),
        \+ member(h(_, 2, _), Ps);
        member(h(0, 6, _), Ps),
        \+ member(h(_, _, 2), Ps);
        member(h(_, 6, 0), Ps),
        \+ member(h(2, _, _), Ps)
    ),
    \+ (
        member(h(7, _, _), Ps);
        member(h(_, 7, _), Ps);
        member(h(_, _, 7), Ps);
        member(h(3, _, _), Ps);
        member(h(_, 3, _), Ps);
        member(h(_, _, 3), Ps);
        member(h(8, _, _), Ps);
        member(h(_, 8, _), Ps);
        member(h(_, _, 8), Ps)
    ),
    (
        member(h(_, 8, _), Ps);
        member(h(_, _, 8), Ps);
        member(h(7, _, _), Ps);
        member(h(_, _, 7), Ps);
        member(h(0, _, _), Ps);
        member(h(_, 0, _), Ps)
    ).

solve-2.pl

digit(0).
digit(1).
digit(2).
digit(3).
digit(4).
digit(5).
digit(6).
digit(7).
digit(8).
digit(9).

clue0(A, B, C) :-
    digit(A), digit(B), digit(C).

clue1(A, B, C) :-
    A  = 6, B \= 8, C \= 2;
    A \= 6, B  = 8, C \= 2;
    A \= 6, B \= 8, C  = 2.

clue2(A, B, C) :-
    A = 1, \+ member(B, [6, 4]), \+ member(C, [6, 4]);
    A = 4, \+ member(B, [6, 1]), \+ member(C, [6, 1]);
    B = 4, \+ member(A, [6, 1]), \+ member(C, [6, 1]);
    B = 6, \+ member(A, [1, 4]), \+ member(C, [1, 4]);
    C = 1, \+ member(A, [6, 4]), \+ member(B, [6, 4]);
    C = 6, \+ member(A, [1, 4]), \+ member(B, [1, 4]).

clue3(A, B, C) :-
    A \= 6, B  = 2, C  = 0;
    A  = 0, B \= 6, C  = 2;
    A  = 0, B  = 2, C \= 6;
    A \= 0, B  = 6, C  = 2;
    A  = 6, B \= 0, C  = 2;
    A  = 6, B  = 2, C \= 0;
    A \= 2, B  = 6, C  = 0;
    A  = 6, B \= 2, C  = 0;
    A  = 0, B  = 6, C \= 2.

clue4(A, B, C) :-
    \+ member(A, [3, 7, 8]),
    \+ member(B, [3, 7, 8]),
    \+ member(C, [3, 7, 8]).

clue5(A, B, C) :-
    A = 0, \+ member(B, [7, 8]), \+ member(C, [7, 8]);
    A = 7, \+ member(B, [0, 8]), \+ member(C, [0, 8]);
    B = 0, \+ member(A, [7, 8]), \+ member(C, [7, 8]);
    B = 8, \+ member(A, [0, 7]), \+ member(C, [0, 7]);
    C = 7, \+ member(A, [0, 8]), \+ member(B, [0, 8]);
    C = 8, \+ member(A, [0, 7]), \+ member(B, [0, 7]).

pass(A, B, C) :-
    clue0(A, B, C),
    clue1(A, B, C),
    clue2(A, B, C),
    clue3(A, B, C),
    clue4(A, B, C),
    clue5(A, B, C).