Enumeration on Convex Configurations of Lucky Puzzle
Thanatnon Keelapang, Supanut Chaidee, Piyashat Sripratak, Teeradej Kittipassorn, Tomoko Taniguchi, Ryuhei Uehara · Experimental Mathematics · 2025
This paper proposes mathematical and computational approaches for enumerating the convex configuration of Lucky Puzzle, a silhouette puzzle formed to be a rectangle, different from other traditional square silhouette puzzles. This study demonstrates the existence of 49 silhouette solutions, out of which 21 configurations have been classified as convex composable solutions. The possibilities of convex arrangements were also verified using BurrTools, a puzzle solver that provides information on each silhouette’s difficulty. The geometric characteristics of the puzzle have been proven to successfully eliminate any silhouette that is not possible to be composed by Lucky puzzle pieces.