euler15.clj

; Problem 15
; Starting in the top left corner of a 22 grid, there are 6
; routes (without backtracking) to the bottom right corner.
; 
; How many routes are there through a 2020 grid?
; 

(def facts (lazy-cat [1] (map * facts (rest natnums))))

(defn solve [gridsize]
  (let [gz (dec gridsize)]
     (/ (nth facts (+ gz gridsize))
	(* (nth facts gz)
	   (nth facts gz)))))

(def answer (solve 20))
; => 137846528820