prologcryptarithmetic-puzzle

Using Prolog to solve a brain teaser (Master Mind)


A friend from work shared this with our whatsapp group:

This lock has a 3 digit code.
Can you guess it using only these hints?

If you had to solve this using Prolog how'd you do it?

We solved it using something akin to a truth table. I'm curious however, how would this be solved in Prolog?


Solution

  • Straightforward coding of the check predicate:

    check( Solution, Guess, NValues, NPlaces ) :-
        Solution = [A,B,C],
        Guess   = [X,Y,Z],
        findall( t, (member(E, Guess), member(E, Solution)), Values ),
        length( Values, NValues ),
        ( A=X -> V1    is 1    ; V1      is 0  ),
        ( B=Y -> V2     is 1+V1 ; V2      is V1 ),
        ( C=Z -> NPlaces is 1+V2 ; NPlaces is V2 ).
    

    Then simply transcribe the clues, no creativity involved:

    puzzle( [A,B,C] ):-
        findall( X, between(0,9,X), XS ),
        select(A,XS,RA), select(B,RA,RB), member(C,RB),
        /* "291": one digit is right and in its place
           "245": one digit is right but in the wrong place
           "463": two digits are right but both are in the wrong place
           "578": all digits are wrong
           "569": one digit is right but in the wrong place */
        check( [A,B,C], [2,9,1], 1, 1 ),
        check( [A,B,C], [2,4,5], 1, 0 ),
        check( [A,B,C], [4,6,3], 2, 0 ),
        check( [A,B,C], [5,7,8], 0, 0 ),
        check( [A,B,C], [5,6,9], 1, 0 ).
    

    Running it:

    23 ?- time( puzzle(X) ).
    /* 13,931 inferences, 0.000 CPU in 0.000 seconds (?% CPU, Infinite Lips) */
    X = [3, 9, 4] ;
    /* 20,671 inferences, 0.000 CPU in 0.000 seconds (?% CPU, Infinite Lips) */
    false.