Problem Solving of Mathematical Games

Artificial Intelligence, 2002

In this article we present an overview on the state of the art in games solved in the domain of twoperson zero-sum games with perfect information. The results are summarized and some predictions for the near future are given. The aim of the article is to determine which game characteristics are predominant when the solution of a game is the main target. First, it is concluded that decision complexity is more important than state-space complexity as a determining factor. Second, we conclude that there is a trade-off between knowledge-based methods and brute-force methods. It is shown that knowledge-based methods are more appropriate for solving games with a low decision complexity, while brute-force methods are more appropriate for solving games with a low state-space complexity. Third, we found that there is a clear correlation between the first-player's initiative and the necessary effort to solve a game. In particular, threat-space-based search methods are sometimes able to exploit the initiative to prove a win. Finally, the most important results of the research involved, the development of new intelligent search methods, are described.  2001 Published by Elsevier Science B.V.

2004

Curriculum Integration, 2013

In the last few years, the authors have been carrying out a study involving elementary school students from 3rd to 6th years of schooling. The main goal of this study is to identify the possible relationships between the ability to identify patterns and the ability to play games, in particular mathematical games. The research methodology is quantitative and most of the analysis is concerned with the verification of correlation between variables. The analysis takes into account seven factors (besides the ability of pattern recognition) identified through a factor analysis carried out on data. With these tools, the authors have been able to differentiate games according to the different measurements. In this chapter, they disclose the important steps of this research as well as the results and main conclusions reached so far.

Australian Mathematics Teacher, 2005

2006

2006

Over the last few years have witnessed a growing recognition of the educational potential of computer games. However, it is generally agreed that the process of designing and deploying TEL resources generally and games for mathematical learning specifically is a difficult task. The Kaleidoscope project," Learning patterns for the design and deployment of mathematical games", aims to investigate this problem. We work from the premise that designing and deploying games for mathematical learning requires the assimilation and ...

2016

Introduction We present here an analysis of the game of Spot It! that can be used as background information for the purpose of leading a math circle around the game. In this paper we present an algorithmic/numerical approach that is complementary of the geometric approach given in [1]. The presentation here follows the progression of solving the puzzle for simple cases first and culminating in the solution of the original game.

Communications of the ACM, 2010

The widespread adoption of the Internet and the emergence of the Web changed society's relationship with computers. The primary role of a computer evolved from a stand-alone, well-understood machine for executing software to a conduit for global communication, content-dissemination, and commerce. The algorithms and complexity theory community has responded to these changes by formulating novel problems, goals, and design and analysis techniques relevant for modern applications. Game theory, which has studied deeply the interaction between competing or cooperating individuals, plays a central role in these new developments. Research on the interface of theoretical computer science and game theory, an area now known as algorithmic game theory (AGT), has exploded phenomenally over the past ten years.

2020

The game method is a non-standard method for computing the truth value of a given sentence in a given structure. This method is applicable on sentences of prenex form. We remark that every sentence can be presented in a prenex form.

Topics in the Theory of Computation, Selected Papers of the International Conference on ‘Foundations of Computation Theory’, FCT '83, 1985

We develop a Logic in which the basic objects of concern are games, or equivalently, monotone predicate transforms. We give completeness and decision results and extend to certain kinds of many-person games. Applications to a cake cutting algorithm and to a protocol for exchanging secrets, are given.