x_1+x_2+x_3+x_4+x_5+x_6=29

(defun copy-array (a)
  (do ((b (make-array (length a)))
       (i 0 (1+ i)))
      ((= i (length a)) b)
    (setf (aref b i) (aref a i))))

(defun pprint-hash (stream fmt colon at)
  (declare (ignore colon at))
  (maphash
   #'(lambda (k v)
       (format stream "~s => ~s~&" k v)) fmt))

(defun summands-of (n m)
  (let ((result (make-hash-table :test #'equal)))
    (labels ((summands-internal (remaining iterations &optional so-far)
               (if (zerop (- m iterations))
                   (let ((keys (or (gethash so-far result) 1)))
                     (setf (gethash so-far result) keys)
                     so-far)
                   (do* ((step (ceiling remaining (- m iterations)))
                         (i remaining (1- i))
                         collected)
                        (nil)
                     (when (and (car so-far) (> i (car so-far)))
                       (setq i (car so-far)))
                     (when (< i step) (return collected))
                     (mapc
                      #'(lambda (x)
                          (setq collected (cons x collected)))
                      (summands-internal
                       (- remaining i)
                       (1+ iterations)
                       (cons i so-far)))))))
      (summands-internal n 0))
    result))

(defun summands-of-order-matters (n m)
  (let ((result (make-hash-table :test #'equal)))
    (labels ((summands-internal (remaining iterations &optional so-far)
             (if (zerop (- m iterations))
                 (let* ((so-far (progn (incf (car so-far) remaining) so-far))
                          (keys (or (gethash so-far result) 1)))
                     (setf (gethash so-far result) keys)
                     so-far)
                   (do ((i remaining (1- i))
                         collected)
                        ((> 0 i) collected)
                     (mapc
                      #'(lambda (x)
                          (setq collected (cons x collected)))
                      (summands-internal
                       (- remaining i)
                       (1+ iterations)
                       (cons i so-far)))))))
      (summands-internal n 0))
    result))

(defun remove-if-hash (hashtable tester)
  (maphash
   #'(lambda (x y)
       (when (funcall tester x y)
         (remhash x hashtable))) hashtable)
  hashtable)

(defun assignment-15-2-filter (x y)
  (declare (ignore y))
  (let ((odds 0))
    (dolist (i x (/= odds 3))
      (when (< i 2) (return t))
      ;; (format t "odds ~d, ~s~&" odds x)
      (when (oddp i) (incf odds)))))

(defun multiply-powers (powers)
  (if (not (cdr powers)) powers
      (let ((a (car powers))
            (b (cadr powers))
            (c (make-hash-table)) d e)
        (dolist (i a)
          (dolist (j b)
            (setq d (+ (cdr i) (cdr j)))
            (if (gethash d c)
                (incf (gethash d c) (* (car i) (car j)))
                (setf (gethash d c) (* (car i) (car j))))))
        (maphash #'(lambda (x y) (setq e (cons (cons y x) e))) c)
        (multiply-powers (cons e (cddr powers))))))

;; 792
(format t "powers: ~s~&"
        (multiply-powers '(((1 . 2) (1 . 4) (1 . 6) (1 . 8) (1 . 10) (1 . 12)
                            (1 . 14) (1 . 16) (1 . 18))
                           ((1 . 2) (1 . 4) (1 . 6) (1 . 8) (1 . 10) (1 . 12)
                            (1 . 14) (1 . 16) (1 . 18))
                           ((1 . 2) (1 . 4) (1 . 6) (1 . 8) (1 . 10) (1 . 12)
                            (1 . 14) (1 . 16) (1 . 18))
                           ((1 . 3) (1 . 5) (1 . 7) (1 . 9) (1 . 11) (1 . 13)
                            (1 . 15) (1 . 17))
                           ((1 . 3) (1 . 5) (1 . 7) (1 . 9) (1 . 11) (1 . 13)
                            (1 . 15) (1 . 17))
                           ((1 . 3) (1 . 5) (1 . 7) (1 . 9) (1 . 11) (1 . 13)
                            (1 . 15) (1 . 17)))))

(format t "~/pprint-hash/" (summands-of 29 6))

;; 278256 - don't try this at home!
(format t "~/pprint-hash/" (summands-of-order-matters 29 6))
(format t "count: ~d~&"
        (hash-table-count (summands-of-order-matters 29 6)))

;; 1057
(format t "~/pprint-hash/"
        (remove-if-hash
         (summands-of 29 6) #'assignment-15-2-filter))
(format t "count: ~d~&"
        (hash-table-count (summands-of 29 6)))
;; 74
(format t "count: ~d~&"
        (hash-table-count
         (remove-if-hash
          (summands-of 29 6) #'assignment-15-2-filter)))

;; 15840
(format t "~/pprint-hash/"
        (remove-if-hash
         (summands-of-order-matters 29 6)
         #'assignment-15-2-filter))
(format t "count: ~d~&"
        (hash-table-count (remove-if-hash
         (summands-of-order-matters 29 6)
         #'assignment-15-2-filter)))