Lazy solution

p85.lisp

@@ -0,0 +1,19 @@
+(defun count-rectangles (max-width max-height)
+  (loop with count = 0
+	for width from 1 upto max-width
+	do (loop for height from 1 upto max-height
+		 do (incf count (* (1+ (- max-width width))
+				   (1+ (- max-height height)))))
+	finally (return count)))
+	  
+
+(defun counting-rectangles (&optional target)
+  ;; TODO: Could terminate once height 1 is over target, right?
+  (loop with best-difference = 10000000
+	for width upfrom 1
+	do (loop for height from 1 upto width
+		 for count = (count-rectangles width height)
+		 for difference = (abs (- target count))
+		 do (when (< difference best-difference)
+		      (setf best-difference difference)
+		      (format t "(~a) ~ax~a (~a)~%" difference width height (* width height))))))