University Interscholastic League A+ Chess Puzzle Contest • Answer
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A Combinatorial Game Theoretic Analysis of Chess Endgames
A COMBINATORIAL GAME THEORETIC ANALYSIS OF CHESS ENDGAMES QINGYUN WU, FRANK YU,¨ MICHAEL LANDRY 1. Abstract In this paper, we attempt to analyze Chess endgames using combinatorial game theory. This is a challenge, because much of combinatorial game theory applies only to games under normal play, in which players move according to a set of rules that define the game, and the last player to move wins. A game of Chess ends either in a draw (as in the game above) or when one of the players achieves checkmate. As such, the game of chess does not immediately lend itself to this type of analysis. However, we found that when we redefined certain aspects of chess, there were useful applications of the theory. (Note: We assume the reader has a knowledge of the rules of Chess prior to reading. Also, we will associate Left with white and Right with black). We first look at positions of chess involving only pawns and no kings. We treat these as combinatorial games under normal play, but with the modification that creating a passed pawn is also a win; the assumption is that promoting a pawn will ultimately lead to checkmate. Just using pawns, we have found chess positions that are equal to the games 0, 1, 2, ?, ", #, and Tiny 1. Next, we bring kings onto the chessboard and construct positions that act as game sums of the numbers and infinitesimals we found. The point is that these carefully constructed positions are games of chess played according to the rules of chess that act like sums of combinatorial games under normal play. -
Touring Problems – a Mathematical Approach
TOURING PROBLEMS – A MATHEMATICAL APPROACH VIPUL NAIK Abstract. The article surveys “touring”, a problem of “fun” math, and employs serious techniques to attack it. The text is suitable for high school students interested in Olympiad mathematics, as well as undergraduate students studying combinatorics and discrete math- ematics. It can be used to introduce the concept of a graph. A sequel to this article, on a similar analysis for “tiling” problems, shall also appear soon. 1. Prebeginnings 1.1. The knight’s tour. Chess pieces, with their variously defined moves, are a rich source of puzzles in recreational mathematics. Chess puzzles include the following types : • Nonattacking pieces puzzle : Given a piece with some moves defined, place as many copies of this piece as possible so that no two can kill each other. The proto- typical example of this is the eight queens problem – placing eight queens on the chessboard so that no two can kill each other. • Board domination puzzle : Given a piece with some moves defined, place as few copies of the piece as possible so that every square is either covered by some copy or is under direct attack by a copy of the piece. • Touring puzzle : Given a piece with some moves defined, construct a tour of the entire chessboard with that piece. The only nontrivial case of this for a standard chess piece is the knight’s tour. Each of these problems revolves around a piece, with certain moves defined for that piece. Instead of standard chess pieces, we may sometimes be interested in defining chess pieces with somewhat different moves. -
UIL Text 111212
UIL Chess Puzzle Solvin g— Fall/Winter District 2016-2017 —Grades 4 and 5 IMPORTANT INSTRUCTIONS: [Test-administrators, please read text in this box aloud.] This is the UIL Chess Puzzle Solving Fall/Winter District Test for grades four and five. There are 20 questions on this test. You have 30 minutes to complete it. All questions are multiple choice. Use the answer sheet to mark your answers. Multiple choice answers pur - posely do not indicate check, checkmate, or e.p. symbols. You will be awarded one point for each correct answer. No deductions will be made for incorrect answers on this test. Finishing early is not rewarded, even to break ties. So use all of your time. Some of the questions may be hard, but all of the puzzles are interesting! Good luck and have fun! If you don’t already know chess notation, reading and referring to the section below on this page will help you. How to read and answer questions on this test Piece Names Each chessman can • To answer the questions on this test, you’ll also be represented need to know how to read chess moves. It’s by a symbol, except for the pawn. simple to do. (Figurine Notation) K King Q • Every square on the board has an “address” Queen R made up of a letter and a number. Rook B Bishop N Knight Pawn a-h (We write the file it’s on.) • To make them easy to read, the questions on this test use the figurine piece symbols on the right, above. -
Finding Checkmate in N Moves in Chess Using Backtracking And
Finding Checkmate in N moves in Chess using Backtracking and Depth Limited Search Algorithm Moch. Nafkhan Alzamzami 13518132 Informatics Engineering School of Electrical Engineering and Informatics Institute Technology of Bandung, Jalan Ganesha 10 Bandung [email protected] [email protected] Abstract—There have been many checkmate potentials that has pieces of a dark color. There are rules about how pieces players seem to miss. Players have been training for finding move, and about taking the opponent's pieces off the board. checkmates through chess checkmate puzzles. Such problems can The player with white pieces always makes the first move.[4] be solved using a simple depth-limited search and backtracking Because of this, White has a small advantage, and wins more algorithm with legal moves as the searching paths. often than Black in tournament games.[5][6] Keywords—chess; checkmate; depth-limited search; Chess is played on a square board divided into eight rows backtracking; graph; of squares called ranks and eight columns called files, with a dark square in each player's lower left corner.[8] This is I. INTRODUCTION altogether 64 squares. The colors of the squares are laid out in There have been many checkmate potentials that players a checker (chequer) pattern in light and dark squares. To make seem to miss. Players have been training for finding speaking and writing about chess easy, each square has a checkmates through chess checkmate puzzles. Such problems name. Each rank has a number from 1 to 8, and each file a can be solved using a simple depth-limited search and letter from a to h. -
Chess & Bridge
2013 Catalogue Chess & Bridge Plus Backgammon Poker and other traditional games cbcat2013_p02_contents_Layout 1 02/11/2012 09:18 Page 1 Contents CONTENTS WAYS TO ORDER Chess Section Call our Order Line 3-9 Wooden Chess Sets 10-11 Wooden Chess Boards 020 7288 1305 or 12 Chess Boxes 13 Chess Tables 020 7486 7015 14-17 Wooden Chess Combinations 9.30am-6pm Monday - Saturday 18 Miscellaneous Sets 11am - 5pm Sundays 19 Decorative & Themed Chess Sets 20-21 Travel Sets 22 Giant Chess Sets Shop online 23-25 Chess Clocks www.chess.co.uk/shop 26-28 Plastic Chess Sets & Combinations or 29 Demonstration Chess Boards www.bridgeshop.com 30-31 Stationery, Medals & Trophies 32 Chess T-Shirts 33-37 Chess DVDs Post the order form to: 38-39 Chess Software: Playing Programs 40 Chess Software: ChessBase 12` Chess & Bridge 41-43 Chess Software: Fritz Media System 44 Baker Street 44-45 Chess Software: from Chess Assistant 46 Recommendations for Junior Players London, W1U 7RT 47 Subscribe to Chess Magazine 48-49 Order Form 50 Subscribe to BRIDGE Magazine REASONS TO SHOP ONLINE 51 Recommendations for Junior Players - New items added each and every week 52-55 Chess Computers - Many more items online 56-60 Bargain Chess Books 61-66 Chess Books - Larger and alternative images for most items - Full descriptions of each item Bridge Section - Exclusive website offers on selected items 68 Bridge Tables & Cloths 69-70 Bridge Equipment - Pay securely via Debit/Credit Card or PayPal 71-72 Bridge Software: Playing Programs 73 Bridge Software: Instructional 74-77 Decorative Playing Cards 78-83 Gift Ideas & Bridge DVDs 84-86 Bargain Bridge Books 87 Recommended Bridge Books 88-89 Bridge Books by Subject 90-91 Backgammon 92 Go 93 Poker 94 Other Games 95 Website Information 96 Retail shop information page 2 TO ORDER 020 7288 1305 or 020 7486 7015 cbcat2013_p03to5_woodsets_Layout 1 02/11/2012 09:53 Page 1 Wooden Chess Sets A LITTLE MORE INFORMATION ABOUT OUR CHESS SETS.. -
A Beginner's Guide to Coaching Scholastic Chess
A Beginner’s Guide To Coaching Scholastic Chess by Ralph E. Bowman Copyright © 2006 Foreword I started playing tournament Chess in 1962. I became an educator and began coaching Scholastic Chess in 1970. I became a tournament director and organizer in 1982. In 1987 I was appointed to the USCF Scholastic Committee and have served each year since, for seven of those years I served as chairperson or co-chairperson. With that experience I have had many beginning coaches/parents approach me with questions about coaching this wonderful game. What is contained in this book is a compilation of the answers to those questions. This book is designed with three types of persons in mind: 1) a teacher who has been asked to sponsor a Chess team, 2) parents who want to start a team at the school for their child and his/her friends, and 3) a Chess player who wants to help a local school but has no experience in either Scholastic Chess or working with schools. Much of the book is composed of handouts I have given to students and coaches over the years. I have coached over 600 Chess players who joined the team knowing only the basics. The purpose of this book is to help you to coach that type of beginning player. What is contained herein is a summary of how I run my practices and what I do with beginning players to help them enjoy Chess. This information is not intended as the one and only method of coaching. In all of my college education classes there was only one thing that I learned that I have actually been able to use in each of those years of teaching. -
The Complete Guide to Chess
The Complete Guide to Chess Master: Chess Tactics, Chess Openings and Chess Strategies Logan Donovan © Copyright 2015 - All rights reserved. In no way is it legal to reproduce, duplicate, or transmit any part of this document in either electronic means or in printed format. Recording of this publication is strictly prohibited and any storage of this document is not allowed unless with written permission from the publisher. All rights reserved. The information provided herein is stated to be truthful and consistent, in that any liability, in terms of inattention or otherwise, by any usage or abuse of any policies, processes, or directions contained within is the solitary and utter responsibility of the recipient reader. Under no circumstances will any legal responsibility or blame be held against the publisher for any reparation, damages, or monetary loss due to the information herein, either directly or indirectly. Respective authors own all copyrights not held by the publisher. Legal Notice: This eBook is copyright protected. This is only for personal use. You cannot amend, distribute, sell, use, quote or paraphrase any part or the content within this eBook without the consent of the author or copyright owner. Legal action will be pursued if this is breached. Disclaimer Notice: Please note the information contained within this document is for educational and entertainment purposes only. Every attempt has been made to provide accurate, up to date and reliable complete information. No warranties of any kind are expressed or implied. Readers acknowledge that the author is not engaging in the rendering of legal, financial, medical or professional advice. -
Introductions & Basic Rules
Chess Club: Introductions & Basic Rules Club Goals 1. Have fun! 2. Play chess. 3. Get better every week. Introductions & Basic Rules 4. Prepare for competitive play. September 7, 2015 Meeting Schedule Club Officers We meet every other Monday at lunch in Thompson 303. President: Rocco Consiglio The Game Design Club meets on the alternate Mondays Vice-President: Skye Williams in this room. Secretary: William "Tim" Crawford Treasurer: Enoch Gamble At each meeting, you will... 1. Eat your lunch. While you are eating we will have a brief Faculty advisors: presentation or discussion. Prof. George Rudolph 2. Work a short group activity (e.g. chess puzzle or a short Prof. Todd Wittman mini-game). 3. Pair up for friendly scrimmages. This Semester Next Semester At each meeting, we will have a brief presentation while Next semester we will discuss more advanced topics. you are eating lunch. We encourage student presentations, e.g. show us your favorite trap. This semester's goal is to cover the rules of chess. Strategy Openings 1. 9/7: Introductions & Basic Rules Traps Famous chess matches 2. 9/21: Pawns 3. 10/5: Knights & Bishops Variants of Chess 4. 10/19: Rooks & Queens Bughouse Chess Chess 960 5. 11/2: Chess Terminology Chess 4 6. 11/16: Standard Openings 7. 12/7: Scoring & Tournament Rules We will keep our eyes open for local tournaments we can attend. 1 Chess Club: Introductions & Basic Rules Game Night Game Night Board games: Risk, Settlers of Catan, Once a month, the CS department hosts a Game Night on Monopoly, Jenga, Mao, Sentinels of the Multiverse, Chess, Pokemon. -