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;; Author: Carlos Perilla
;; Date: 25-10-2013

;; See: http://programmingpraxis.com/2009/06/12/feynmans-puzzle/

;; Your task is to solve Feynman’s Puzzle. 
;; http://programmingpraxis.files.wordpress.com/2009/06/r3brp.jpg

(require-library amb)
(import amb)
(use srfi-1)
(define (required x) (amb-assert x))
(define (build-decimal list) (fold (lambda (x acc) (+ (* acc 10) x)) 0 list))
(let ((a (amb 0 1 2 3 4 5 6 7 8 9))
      (b (amb 0 1 2 3 4 5 6 7 8 9))
      (c (amb 0 1 2 3 4 5 6 7 8 9))
      (d (amb 0 1 2 3 4 5 6 7 8 9))
      (e (amb 0 1 2 3 4 5 6 7 8 9))
      (f (amb 0 1 2 3 4 5 6 7 8 9))
      )
  (required (not (= a b)))
  (required (not (= a c)))
  (required (not (= a d)))
  (required (not (= a e)))
  (required (not (= a f)))
  (required (< e d))
  (required (= (modulo (quotient  (* (+ (* 1000 d) (* e 100) (* a 10) f)
                                     (+  (* 100 b) (* 10 a) c) ) 100) 10) a))
  (required (= (modulo (* d (+  (* 100 b) (* 10 a) c)) 100)  (+ (* 10 a) a) ))
  (required (= (modulo (* e (+  (* 100 b) (* 10 a) c)) 10) a ))
  (required (= (modulo (quotient (* a (+  (* 100 b) (* 10 a) c)) 100) 10) a ))
  (list  (list b a c)  (list d e a f)))