Further Hardness Results for Stephen’s Sausage Roll

Abstract

Stephen’s Sausage Roll is a relatively unstudied puzzle game with a fascinating set of mechanics for computational hardness problems. The only past results are from a class project in MIT’s 6.5440 class of Fall 2023, which only dealt with two specific subsets of the mechanics restricted to two-dimensional forms of the game [1]. This project presents a more complete characterization of problems based off of Stephen’s Sausage Roll, and provides solutions for a significant portion. In particular, both variants of Stephen’s Sausage Roll considered in prior work can be solved by one of these results.