相关论文: Analysis of the picture cube puzzle
Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and…
This puzzle, often called the "Reverse the Triangle Puzzle," appears regularly in puzzle books. Four rows consisting of 1 coin in row 1, 2 coins in row 2, 3 coins in row 3, and 4 coins in row 4 form the shape of a triangle. What is the…
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…
A setup is proposed to play a quantum version of the famous bimatrix game of Prisoners' Dilemma. Multi-slit electron diffraction with each player's pure strategy consisting of opening one of the two slits at his/her disposal are essential…
This paper presents the quantile cube, a novel three-dimensional summary representation designed to analyze external load using GPS-derived movement data. While broadly applicable, we demonstrate its utility through an application to data…
In problem-solving, a path towards solutions can be viewed as a sequence of decisions. The decisions, made by humans or computers, describe a trajectory through a high-dimensional representation space of the problem. By means of…
We discuss the problem of finding critical sets in graphs, a concept which has appeared in a number of guises in the combinatorics and graph theory literature. The case of the Sudoku graph receives particular attention, because critical…
In this work, we develop a graphical model to capture team dynamics. We analyze the model and show how to learn its parameters from data. Using our model we study the phenomenon of team collapse from a computational perspective. We use…
Capacitated network bargaining games are popular combinatorial games that involve the structure of matchings in graphs. We show that it is always possible to stabilize unit-weight instances of this problem (that is, ensure that they admit a…
In this paper we study a single player game consisting of $n$ black checkers and $m$ white checkers, called shifting the checkers. We have proved that the minimum number of steps needed to play the game for general $n$ and $m$ is $nm + n +…
The Decodoku project seeks to let users get hands-on with cutting-edge quantum research through a set of simple puzzle games. The design of these games is explicitly based on the problem of decoding qudit variants of surface codes. This…
In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be…
The New York Times (NYT) games have found widespread popularity in recent years and reportedly account for an increasing fraction of the newspaper's readership. In this paper, we bring the computational lens to the study of New York Times…
The power of symbolic computation, as opposed to mere numerical computation, is illustrated with efficient algorithms for studying the generalized gambler's ruin problem in one and two dimensions. We also consider a new generalization of…
This paper consider the possibility of using some quantum tools in decision making strategies. In particular, we consider here a dynamical open quantum system helping two players, $\G_1$ and $\G_2$, to take their decisions in a specific…
In this paper, we consider a game played on a rectangular $m \times n$ gridded chocolate bar. Each move, a player breaks the bar along a grid line. Each move after that consists of taking any piece of chocolate and breaking it again along…
We present several new characterizations of correlated equilibria in games with continuous utility functions. These have the advantage of being more computationally and analytically tractable than the standard definition in terms of…
We investigate a version of Waring's Problem over quaternion rings, focusing on cubes in quaternion rings with integer coefficients. We determine the global upper and lower bounds for the number of cubes necessary to represent all such…
The deduction game is a variation of the game of cops and robber on graphs in which searchers must capture an invisible evader in at most one move. Searchers know each others' initial locations, but can only communicate if they are on the…
Juggling patterns can be described by a sequence of cards which keep track of the relative order of the balls at each step. This interpretation has many algebraic and combinatorial properties, with connections to Stirling numbers, Dyck…