(labels ((power-set (list)

"Return a list of all subsets of elements in the list."

(loop with length = (length list)

for flags from 0 below (ash 1 length)

collect (loop for index from 0 below length

when (logbitp index flags)

collect (elt list index))))

(optional-masks (bits num-bits)

"Return a list of masks indicating previous row optional cards."

(loop for i from 0 to (- num-bits 2)

for mask = #b11 then (ash mask 1)

unless (logtest mask bits)

collect (ash 1 i)))

(previous-rows (bits num-bits)

"Return all valid card existence bit flags for the previous row."

(loop with all-bits-on = (1- (ash 1 (1- num-bits)))

for masks in (power-set (optional-masks bits num-bits))

collect (logandc2 all-bits-on (reduce #'logior masks))))

(pyramid-flags (&rest row-flags)

"Return a PYRAMID-FLAGS given card existence bits for each row."

(reduce #'logior (mapcar #'ash row-flags '(0 1 3 6 10 15 21)))))

(let ((all '()))

;; for all possible combinations of cards on the bottom row, calculate

;; all possible combinations of cards for each previous row, then combine

;; them all into PYRAMID-FLAGS values

(dotimes (r7 (ash 1 7) (sort (coerce all 'vector) #'<))

(dolist (r6 (previous-rows r7 7))

(dolist (r5 (previous-rows r6 6))

(dolist (r4 (previous-rows r5 5))

(dolist (r3 (previous-rows r4 4))

(dolist (r2 (previous-rows r3 3))

(dolist (r1 (previous-rows r2 2))

(push (pyramid-flags r1 r2 r3 r4 r5 r6 r7) all)))))))))))