Related papers: Evolomino is NP-complete
We analyze the computational complexity of several new variants of edge-matching puzzles. First we analyze inequality (instead of equality) constraints between adjacent tiles, proving the problem NP-complete for strict inequalities but…
We show that the classical game LaserTank is $\mathrm{NP}$-complete, even when the tank movement is restricted to a single column and the only blocks appearing on the board are mirrors and solid blocks. We show this by reducing $3$-SAT…
We prove that the classic 1994 Taito video game, known as Puzzle Bobble or Bust-a-Move, is NP-complete. Our proof applies to the perfect-information version where the bubble sequence is known in advance, and it uses just three bubble…
We prove computational intractability of variants of checkers: (1) deciding whether there is a move that forces the other player to win in one move is NP-complete; (2) checkers where players must always be able to jump on their turn is…
Various forms of sorting problems have been studied over the years. Recently, two kinds of sorting puzzle apps are popularized. In these puzzles, we are given a set of bins filled with colored units, balls or water, and some empty bins.…
We prove that Hamiltonicity in maximum-degree-3 grid graphs (directed or undirected) is ASP-complete, i.e., it has a parsimonious reduction from every NP search problem (including a polynomial-time bijection between solutions). As a…
We prove that the 2017 puzzle game ZHED is NP-complete, even with just 1 tiles. Such a puzzle is defined by a set of unit-square 1 tiles in a square grid, and a target square of the grid. A move consists of selecting an unselected 1 tile…
This paper investigates the popular card game UNO from the viewpoint of algorithmic combinatorial game theory. We define simple and concise mathematical models for the game, including both cooperative and uncooperative versions, and analyze…
Using the notion of visibility representations, our paper establishes a new property of instances of the Nondeterministic Constraint Logic (NCL) problem (a PSPACE-complete problem that is very convenient to prove the PSPACE-hardness of…
This paper presents a novel and straight formulation, and gives a complete insight towards the understanding of the complexity of the problems of the so called NP-Class. In particular, this paper focuses in the Searching of the Optimal…
A polynomial algorithm is obtained for the NP-complete linear ordering problem.
We show that the decision versions of the puzzles Knossos and The Hour-Glass are complete for NP.
In this paper we show that the Mastermind Satisfiability Problem (MSP) is NP-complete. The Mastermind is a popular game which can be turned into a logical puzzle called Mastermind Satisfiability Problem in a similar spirit to the…
We prove that the classic falling-block video game Tetris (both survival and board clearing) remains NP-complete even when restricted to 8 columns, or to 4 rows, settling open problems posed over 15 years ago [BDH+04]. Our reduction is from…
This chapter deals with the exact enumeration of certain classes of self-avoiding polygons and polyominoes on the square lattice. We present three general approaches that apply to many classes of polyominoes. The common principle to all of…
A polyomino is called a development if it can make a box by folding edges of unit squares forming the polyomino. It is known that there are developments that can fold into a box (or boxes) in multiple ways. In this work, we conducted a…
Icosoku is a challenging and interesting puzzle that exhibits highly symmetrical and combinatorial nature. In this paper, we pose the questions derived from the puzzle, but with more difficulty and generality. In addition, we also present a…
Modern board games are a rich source of interesting and new challenges for combinatorial problems. The game Nmbr9 is a solitaire style puzzle game using polyominoes. The rules of the game are simple to explain, but modelling the game…
Many popular puzzle and matching games have been analyzed through the lens of computational complexity. Prominent examples include Sudoku, Candy Crush, and Flood-It. A common theme among these widely played games is that their generalized…
Based on a previous generalization by the author of Latin squares to Latin boards, this paper generalizes partial Latin squares and related objects like partial Latin squares, completable partial Latin squares and Latin square puzzles. The…