Single-Player and Two-Player Buttons & Scissors Games - (Extended Abstract)

We study the computational complexity of the Buttons & Scissors game and obtain sharp thresholds with respect to several parameters. Specifically we show that the game is NP-complete for \(C=2\) colors but polytime solvable for \(C=1\). Similarly the game is NP-complete if every color is used by at most \(F=4\) buttons but polytime solvable for \(F\le 3\). We also consider restrictions on the board size, cut directions, and cut sizes. Finally, we introduce several natural two-player versions of the game and show that they are PSPACE-complete.