Mathematical Chess

By Dr George Ho

Mathematical chess is a two-player educational and entertaining game played on ten digit pieces (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) and six operator pieces (addition, subtraction, multiplication, division, power, and root). The chessboard is a grid made up of nine vertical and nine horizontal lines. It is flexible and suitable for all students from middle and high schools to universities.

The excessive use of electronic calculators and games has caused a negative impact on the alertness of the minds and the numerical abilities of students at all levels. Dr Ryan said, In numeracy, the young teenage student in 2003 was approximately a quarter of a grade level behind his or her counterpart in 1964. This was reported in the article Grade Worse Than in 1960s (SMH, 11 February 2008).

Students love challenges and competitions. Dr Robert C. Ferguson writes, A learning environment organised around games has a positive effect on students attitudes towards learning (Teachers Guide: Research and Benefits of Chess, 11 October 2006).

The above statements drive the implementation of this mathematical chess game. Like European chess and Chinese chess, mathematical chess teaches strategy planning, problem-solving, memory improvement, decision-making, concentration, perseverance, observation, analysis, and organisation skill. Mathematical chess itself also promotes numerical abilities, mental alertness, and speedy calculation.

The numeracy performance of students in many countries has not improved since 1960, not because of the incompetence of the teachers, but because an educational game interesting and challenging enough to attract students attention did not exist. Mathematical chess can help resolve this drawback.

The authors dream is to see mathematical chess become a popular game in all middle and high schools, and to see the love and passion of mathematics flowering in the minds of young people around the world.

• Language: English
• Publisher: Xlibris AU
• Release date: Jun 28, 2017
• ISBN: 9781543401622

Dr George Ho

Dr George holds a Bachelor of mathematics (1965) and a Doctorate es Sciences (March 1975) at the University of Sciences in Saigon, Vietnam. He spent 7 years in high school teaching mathematics for Year 12 students (1962-1969). He came to Australia in 1980 and finished the Graduate Diploma in Data Processing with Distinction at the NSW Institute of Technology, Sydney, in 1982. His last position was as a project leader at the Credit Reference Association of Australia (CRAA). He retired in 2006.

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Copyright © 2017 by Dr George Ho.

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Rev. date: 07/12/2017

Xlibris

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www.Xlibris.com.au

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Contents

Chapter 1: Chess Components

Objectives

Chessboard

Chess Pieces

Digit Pieces

Operator Pieces

Chapter 2: Initial Chess Display

Phase 1: ‘Select now!’ Phase

Step 1: The Four Conditions

Step 2: Levels of Difficulty

Remarks

Phase 2: ‘Prepare now!’ Phase

Step 1: Placing the Operator Pieces

Step 2: Placing the Digit Pieces

Remarks

Phase 3: ‘Play now!’ Phase

Samples of Initial Chess Displays

Chapter 3: Chess Definitions

Operator Pair

Digit Pair

Attached Digits

Partial Sums

Partial Differences

Partial Products

Partial Quotients

Partial Powers

Partial Roots

Table of Squares, Cubes, and Roots

Single Attached Digit

Chapter 4: Mathematical Chess Rules

R01: One Move in a Turn

R02: Power of the Operator Piece

R03: Rule of Two Alone Digit Pieces on a Line.

R04: Rule of the Operator Pair.

R05: Rule of the Digit Pair

R06: Rule of the Partial Values

R07: Multiple Removals from the Operator Pieces

R08: Extended Effect of the Operator Pieces

R09: Removals from the Digit Pieces

R10: Multiple Removals from the Digit Pieces

R11: Extended Effect of the Digit Pieces

R12: Removals without Moving

The Importance of the Digit Piece 0

a) For the Addition Operator

b) For the Subtraction Operator

c) For the Multiplication Operator

d) For the Division Operator

e) For the Power Operator

f) For the Root Operator

How Does a Mathematical Chess Game Finish?

Flexibility of the Mathematical Chess

Conclusion

My Dream

About the Author

To my wife, C.T.N. Minh, for her support, patience, and inspiration.

To my children, H.T.M. Tam, H.H. Hiep, H.H. Tri, and H.T.M. Chau.

In memory of my beloved parents, H.V. Gia and T.T. Tong.

H.V. Hoa

Preface

Mathematical chess is a two-player educational and entertaining game played on ten digit pieces (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) and six operator pieces (addition, subtraction, multiplication, division, power, and root). The default chessboard is a grid made up of nine vertical and nine horizontal lines equally separated.

A chess piece can move freely on any horizontal or vertical line provided it is not obstructed by other chess pieces. A move of a chess piece can result in the removal of the opponent’s digit