Games, Puzzles and Math Excursions_Interior.indd 1 12/10/20 10:25 AM Copyright © 2020, Chandru Arni All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording or any information storage and retrieval system now known or to be invented, without permission in writing from the publisher, except by a reviewer who wishes to quote brief passages in connection with a review written for inclusion in a magazine, newspaper or broadcast. Published in India by Prowess Publishing, YRK Towers, Thadikara Swamy Koil St, Alandur, Chennai, Tamil Nadu 600016 ISBN: 978-1-5457-5330-9 Library of Congress Cataloging in Publication Games, Puzzles and Math Excursions_Interior.indd 4 15/10/20 4:51 PM Contents Foreword .............................................................................................xiii Preface .................................................................................................. xv Introduction .......................................................................................xvii About The Author ...............................................................................xix History ................................................................................................xxi What’s in This Book? ........................................................................xxiii Games Unlisted .................................................................................. xxv Paper and Pencil game with Templates ............................................ xxix GAMES ..................................................................................................1 1. Alignment ..................................................................................3 Achi ............................................................................................3 Tic Tac Toe or Noughts and Crosses ............................................4 Nine Men’s Morris ......................................................................6 Picaria .........................................................................................8 Dara ............................................................................................9 Connect Four ............................................................................10 Quarto ......................................................................................11 Go-Moku ..................................................................................13 Arni’s 3 in a row ........................................................................14 2. Connection (Joining Dots or Lines) .......................................15 Dots and Boxes Game ...............................................................15 Sprouts ......................................................................................17 Games, Puzzles and Math Excursions_Interior.indd 5 12/10/20 10:25 AM Games, Puzzles and Math Excursions Sim ...........................................................................................19 Cram .........................................................................................20 Bridg-It .....................................................................................21 3. Territory (Linking or Occupying the Other Side) ..................22 Hex ...........................................................................................22 Pentomino Space .......................................................................24 Twixt .........................................................................................26 Five Field Kono .........................................................................28 Reversi (Othello) .......................................................................29 Arni’s Knights ............................................................................30 Draughts ...................................................................................31 Go .............................................................................................32 4. Deduction Games ....................................................................34 Battleships .................................................................................34 Mastermind ...............................................................................36 Bulls and Cows .........................................................................38 Wallpaper ..................................................................................39 5. Counting Games ......................................................................41 Nim ..........................................................................................41 Game of 31 ...............................................................................46 Moore’s Nim (Nimk) .................................................................48 Wythoff’s Nim ..........................................................................51 Fibonacci Nim ..........................................................................52 Monopile ..................................................................................56 Bulo or TacTix ..........................................................................58 Shut the Box .............................................................................59 6. Non Specific Games .................................................................61 L Game Edward Bono ...............................................................61 Arni Sodoko Game ....................................................................62 Arni’s Move and Rotate Game ...................................................64 Wythoff’s Game ........................................................................66 vi Games, Puzzles and Math Excursions_Interior.indd 6 12/10/20 10:25 AM PUZZLES PRESENTATION ..............................................................69 1. Jars ...........................................................................................71 Decantation ........................................................................71 Target Measure ....................................................................72 2. Alignment Problems ................................................................73 Hearts and Coins ......................................................................73 Jumping Coins ....................................................................73 16 Discs in 4 Piles ...............................................................73 Heart Pairs ..........................................................................74 Hearts Swap ........................................................................74 Invert a Triangle ..................................................................75 5 - Coin Puzzle ....................................................................75 6 - Coin Geometry ..............................................................75 Square Coin Geometry ........................................................76 3. Weight Problems .....................................................................77 Problem # 1 ........................................................................77 Problem # 2 ........................................................................77 Problem # 3 ........................................................................77 Problem # 4 ........................................................................78 Problem # 5 ........................................................................78 Problem # 6 ........................................................................78 Problem # 7 – The Treasure Coup .......................................79 Problem # 8 ........................................................................79 4. Expressing Numbers ................................................................80 The Four Fours Problem (4 4s) ...........................................80 The 1234 Problem ..............................................................81 5. Matchstick Puzzles ..................................................................82 17 Puzzles..................................................................................82 6. Fairy Chess Puzzles ..................................................................87 Sam Loyd’s Classic Puzzle ....................................................87 Chess in a Pistol ..................................................................88 vii Games, Puzzles and Math Excursions_Interior.indd 7 12/10/20 10:25 AM Games, Puzzles and Math Excursions Swap 4 Knights ...................................................................89 Swap 6 Knights ...................................................................89 Knight’s Tour 30 Cells .........................................................89 Another Knight’s Tour 12 cells ............................................90 The Queens Problem ..........................................................90 Can I be the #2 World Chess Champion? ...........................90 7. Cryptarithms ...........................................................................91 Restorations ..............................................................................91 8. Patterns and Series ...................................................................93 Numerical Patterns .............................................................93 What