(Defun Convert-State-to-String  (state)  
   ; recall a state is a list of the form:
   ;       (  (1 2 3) (4 5 6) (7 8 0)) ) here I represent blank as a 0
   ; let's convert it to a string (not a number, but a string)
   ; first we copy the state so we don't destroy it inadvertently..this is "cstate" below
   ; return-string will be the converted state to a string with a capital S at the beginning

 (let  (  (cstate (append (copy-list (first state)) (copy-list (second state)) (copy-list (third state)) ) )
          (returned-string "S" ) 
                                 ) ;close the let's local variable defs.
  (loop
   (if (null cstate) (return returned-string))
   (setf returned-string
         (concatenate 'string returned-string (subseq "012345678" (first cstate) (1+ (first cstate)))))
   (setf cstate (rest cstate))
   );loop
  ) ;let
 )  ;defun

;Now that that is done, we want to convert the character representation of the state to
;a symbol...Here we use LISP's intern function for that purpose. 

(defun Convert-State-to-Symbol (state)
   (intern  (Convert-State-to-String  state)))

;now...we'll use LISP's internal hash table to store this symbol, and thus store our
;states for us...and I will use property lists to indicate that the state has been visited.
;an example

(setf state '( (7 8 0) (1 2 3) (4 5 6)))

(setf (get (Convert-State-to-Symbol state) 'Visited)  T)

;later, if I want to know whether I have visited a state before, I do it this way:



(if
 (get (Convert-State-to-Symbol state) 'Visited)  (print "indeed I have...") )