Computer Board Games of Africa (Algorithms Strategies & Rules) by Prof Johnson Ihyeh Agbinya (2004).pdf

(1208 KB) Pobierz
Computer Board Games
of Africa
(Algorithms, Strategies & Rules)
Prof. Johnson Ihyeh Agbinya
Department of Computer Science
University of the Western Cape, Private Bg X17, Bellville 7535, South Africa
jagbinya@uwc.ac.za
Copyright © 2004
2
This book is dedicated to my deceased parents and uncles Agbinya Awurwu, Onwu Awurwu, Abi
Edeh, Anyuwogbu elders and youths alive who introduced me to the first experiences on African
board games. I can still hear them count as they play "hohe", "heeyeh", "hata", "hene", "kiriwoh".
Without them, this book may have never been written. Keep counting and thinking.
3
Table of Contents
Part One
Chapter One
Terminology
16
Introduction
1.1
Fundamentals of African Board Games
1.1.1
Who is Confused?
1.1.2
Mathematical Strengths
1.2
Short List of Games from Africa
15
16
16
16
17
18
19
20
23
23
24
24
25
25
26
26
26
27
27
27
27
28
29
30
31
31
31
31
32
33
33
1.3
Terminology
1.3.1
Description of Board Games
1.3.2
Moves
1.3.3
Capturing of Seeds
1.3.4
Winning
1.4
References
Chapter 2
Algorithmic Representation
26
2.1
2.2
Introduction
A Move
Even Characteristics of African Board Games
2.3
Game Complexity
2.3.1
State-Space Complexity
2.3.2
Game Tree Complexity
2.3.3
Mutational Complexity
2.4
References
Chapter 3
Mathematics of African Board Games
36
3.1
3.2
3.3
3.4
Introduction
Nonlinear Additive Series (Triangular Numbers in ‘tarumbeta’)
Discrete Self-Organization in Oware
Cellular Automata
Magic Numbers
4
Magic Numbers In Omweso
3.4.1
3.4.1.1 Magic Number 0
3.4.1.2 Magic Number 2
3.4.1.3 The magic number 8
3.4.1.4 Magic Number 9
3.4.1.5 Magic Number 16
3.4.1.6 Magic Number 17
3.4.1.7 Magic Number 25
3.5
Symmetrical Series In Omweso
3.5.1
Symmetrical Odd Integer Square Series
3.5.2
Decreasing Symmetrical Integer Series
3.5.3
Symmetrical Mirror Image Even Series
3.6
References
34
34
35
35
35
36
36
36
37
37
38
38
39
40
40
40
40
40
41
41
41
42
42
42
43
44
47
47
48
Chapter 4
Never Ending Moves
46
4.1
4.2
4.2.1
4.2.2
4.2.3
4.2.4
4.2.5
4.3
4.3.2.3
4.3.2.4
4.4
4.4.1
4.4.2
Introduction
Trivial Never Ending Moves
Complex Never Ending Moves
Kyagaba-32
Ilukor-25 Case 1
Ilukor-25 Case 4
Wernham-28
Jonkers, Uiterwijk and de Voogt-40
A Theorem of Endless Moves
Case 1: Suppose x(0) is a multiple of 16
Case 2: x(0) is not a multiple of 16
Meyer Test of Incongruencies
Meyer Test A
Meyer Test B
5
4.4.3
4.5
Meyer Test C and D
References
49
49
50
50
50
50
54
55
55
55
55
56
56
57
57
58
59
59
60
61
62
62
65
65
65
Chapter 5
Diagonal Count Arrays
5
5.1
5.2
Introduction
Diagonal Count Arrays
References
Chapter Six
Game Defining Matrices
6
6.1
6.2
6.2.1
6.2.2
6.2.3
6.3
Introduction
Matrices Defining Never Ending Moves
Game Set Up Defining Matrices
Junior Group Defining Matrices
Senior Group Defining Matrices
Game Set up with Defining Matrices
References
Part Two
Strategies and Research
7
Introduction
7.2.2
Strategy 2: look at special cases
7.2.3
Strategy 3
7.2.4
Proceeding mathematically
7.3
Complex Never Ending Moves
7.3.1
7.4
Solution
References

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika:

Zgłoś jeśli naruszono regulamin