variable knight's tour through arbitrarywourld

knight's tour is a thought experiment where you imagine a chess piece stepping on every board square exactly once. this game is kind of like that, except you can choose your own custom rise over run (slope), and also instead of a chessboard i just kinda made some shit up.

what is the maximum score? how many different scores are possible? i have absolutely no idea. share your research with your friends or the comment section below and maybe we can come closer to solving these mysteries,