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?

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.``````