Project Euler Problem 491, Common Lisp

Project Euler Problem 491

;gnu clisp 2.49

(defun other-list (alist)
    (loop for i fixnum from 9 downto 0
             collect (let ((q (find i alist :key 'cdr))) (if q (cons (- 2 (car q)) i) (cons 2 i)))))

(let ((num (vector 13168189440000 11851370496000 10534551552000)))
(defun count-possibilities (alist)
   (/ (aref num (or (car (find 0 alist :key #'cdr)) 0)) ; numerator is 10!^2 (no 0’s), 0.9*10!^2 (1 zero) or 0.8*10!^2 (2 0‘s)
      (expt 2 (+ (count 2 alist :key #'car) (- 10 (length alist)))))))

(defun list-possible-sums (&key (d 0) (ndigits 0) (sum 0) (seq))
   (cond
      ((> sum 45) Nil)
      ((= ndigits 10) (if (zerop (rem (- 89 sum) 11)) (list (count-possibilities seq))))
      ((= 10 d) Nil)
      (t (nconc (list-possible-sums :d (1+ d) :ndigits ndigits :sum sum :seq seq)
                     (list-possible-sums :d (1+ d) :ndigits (1+ ndigits) :sum (+ d sum) :seq (acons 1 d seq))
                     (list-possible-sums :d (1+ d) :ndigits (+ ndigits 2) :sum (+ (* 2 d) sum) :seq (acons 2 d seq))))))

(pprint (reduce #'+ (remove-duplicates (list-possible-sums) :test 'equal)))


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