Related papers: Coin-Moving Puzzles
This paper extends the work started in 2002 by Demaine, Demaine and Verill (DDV) on coin-moving puzzles. These puzzles have a long history in the recreational literature, but were first systematically analyzed by DDV, who gave a full…
Here, we present a variant of the sliding coins game. Two coins are placed on distinct squares of a semi-infinite linear board with squares numbered $0, 1, 2, dots, $. Two players take turns and move a coin to a lower unoccupied square.…
The move-minimizing puzzles presented here are certain types of one-player combinatorial games that are shown to have explicit solutions whenever they can be encoded in a certain way as diamond-colored modular or distributive lattices. Our…
We propose a new kind of sliding-block puzzle, called Gourds, where the objective is to rearrange 1 x 2 pieces on a hexagonal grid board of 2n + 1 cells with n pieces, using sliding, turning and pivoting moves. This puzzle has a single…
We define a variant of the two-dimensional Silver Dollar game. Two coins are placed on a chessboard of unbounded size, and two players take turns choosing one of the coins and moving it. Coins are to be moved to the left or upward…
We study a popular puzzle game known variously as Clickomania and Same Game. Basically, a rectangular grid of blocks is initially colored with some number of colors, and the player repeatedly removes a chosen connected monochromatic group…
In the "Game about Squares" the task is to push unit squares on an integer lattice onto corresponding dots. A square can only be moved into one given direction. When a square is pushed onto a lattice point with an arrow the direction of the…
We analyze Solo Chess puzzles, where the input is an $n \times n$ board containing some standard Chess pieces of the same color, and the goal is to make a sequence of capture moves to reduce down to a single piece. Prior work analyzes this…
For any odd integer $n\geq3$ a board (of size $n$) is a square array of $n\times n$ positions with a simple rule of how to move between positions. The goal of the game we introduce is to find a path from the upper left corner of a board to…
Given a set of coins arranged in a line, we remove heads-up coins one at a time and flip any adjacent coins after each removal. The coin-removal problem is to determine for which arrangements of coins it is possible to remove all of the…
We consider the problem of determining the minimum number of moves needed to solve a certain one-dimensional peg puzzle. Let N be a positive integer. The puzzle apparatus consists of a block with a single row of 2N+1 equally spaced holes…
Notes on the Spinpossible puzzle game. We give a mathematical description of the game, prove some elementary bounds on the length of optimal solutions, and consider variations of the game which place restrictions on the set of permitted…
In this paper we give a mathematical model for a game that we call picture cube puzzle and investigate its properties. The central question is the number of moves required to solve the puzzle. A mathematical discussion is followed by the…
This paper studies sequential quantum games under the assumption that the moves of the players are drawn from groups and not just plain sets. The extra group structure makes possible to easily derive some very general results characterizing…
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 present a perspective on quantum games that focuses on the physical aspects of the quantities that are used to implement a game. If a game is to be played, it has to be played with objects and actions that have some physical existence.…
In the paper it is proven that the two-players turn-based stochastic game "Risk or Safety" has a unique solution. Both players need to play the same strategy if they want to maximize their winning chances. An analytical method based on the…
This paper examines multiplayer symmetric constant-sum games with more than two players in a competitive setting, including examples like Mahjong, Poker, and various board and video games. In contrast to two-player zero-sum games,…
This paper models games where the strategies are nodes of a graph G (we denote them as G-games) and in presence of coalition structures. The cases of one-shot and repeated games are presented. In the latter situation, coalitions are assumed…
This paper proves that push-pull block puzzles in 3D are PSPACE-complete to solve, and push-pull block puzzles in 2D with thin walls are NP-hard to solve, settling an open question by Zubaran and Ritt. Push-pull block puzzles are a type of…