Snipperclips: Cutting Tools into Desired Polygons using Themselves

TL;DR

This paper investigates the computational complexity of creating target shapes in the puzzle game Snipperclips through a sequence of snip operations, providing bounds on the number of steps needed for various game variants.

Contribution

It formalizes the problem of shape creation in Snipperclips, analyzes its computational complexity, and establishes bounds on the number of operations required for different variants.

Findings

Determined the conditions under which target shapes can be formed.

Bounded the number of snip operations needed for various game variants.

Analyzed the complexity of the shape creation problem.

Abstract

We study Snipperclips, a computer puzzle game whose objective is to create a target shape with two tools. The tools start as constant-complexity shapes, and each tool can snip (i.e., subtract its current shape from) the other tool. We study the computational problem of, given a target shape represented by a polygonal domain of $n$ vertices, is it possible to create it as one of the tools' shape via a sequence of snip operations? If so, how many snip operations are required? We consider several variants of the problem (such as allowing the tools to be disconnected and/or using an undo operation) and bound the number of operations needed for each of the variants.