lockpicking-logic.clj

(ns number-puzzles.core
  (:refer-clojure :exclude [==]) ;; Prevent ns conflict
  (:require [clojure.core.logic :refer :all]))

(run* [q]
      (fresh [a b c variants]
             (== [0 1 2 3 4 6 7 8] variants)
             (membero a variants)
             (membero b variants)
             (membero c variants)

             ;; [6 8 2] One digit is right and in its place
             (fresh [comb]
                    (== comb [6 8 2])
                    (conde [(== [a 8 2] comb)
                            (nafc membero b comb)
                            (nafc membero c comb)]
                           [(== [6 b 2] comb)
                            (nafc membero a comb)
                            (nafc membero c comb)]
                           [(== [6 8 c] comb)
                            (nafc membero b comb)
                            (nafc membero a comb)]))

             ;; [6 1 4] One digit is right but in the wrong place
             (fresh [comb]
                    (== comb [6 1 4])
                    (conde [(== [6 a 4] comb)]
                           [(== [6 1 a] comb)]
                           [(== [b 1 4] comb)]
                           [(== [6 1 b] comb)]
                           [(== [c 1 4] comb)]
                           [(== [6 c 4] comb)]))

             ;; [2 0 6] Two digits are right but both are in the wrong place
             (fresh [comb]
                    (== comb [2 0 6])
                    (conde [(== [2 a b] comb)]
                           [(== [2 c b] comb)]
                           [(== [2 c a] comb)]
                           [(== [c 0 b] comb)]
                           [(== [b 0 a] comb)]
                           [(== [c 0 a] comb)]
                           [(== [c a 6] comb)]
                           [(== [b c 6] comb)]
                           [(== [b a 6] comb)]))

             ;; [7 3 8] All digits are wrong           
             (fresh [comb]
                    (== comb [7 3 8])
                    (nafc membero a comb)
                    (nafc membero b comb)
                    (nafc membero c comb))

             ;; [3 8 0] One digit is right but in the wrong place
             (fresh [comb]
                    (== comb [3 8 0])
                    (conde [(== [3 a 0] comb)]
                           [(== [3 8 a] comb)]
                           [(== [b 8 0] comb)]
                           [(== [3 8 b] comb)]
                           [(== [c 8 0] comb)]
                           [(== [3 c 0] comb)]))

             (== q [a b c])))