Single-Player and Two-Player Buttons & Scissors Games
  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 $F \leq 3$. 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. 
Kyle Burke, Erik D. Demaine, Harrison Gregg, Robert A. Hearn, Adam   Hesterberg, Michael Hoffmann, Hiro Ito, Irina Kostitsyn...
cs.CC math.CO