MAGIC SQUARE LEXICON

1 1276355226959451948471166239226138745096 4148128574026243349811783463372356422554 1681380301873325844214767066657513677102 979152741556735372546177531204360H. D. Heinz & J. R. Hendricks1234567891011121314151617181920 2122232425262712346810121416182022232425 579111317192115 Illustrated48161024204832164 4096212825651210241161204814181211281512 1256164132140961 MAGIC SQUARELEXICON: MAGIC SQUARE LEXICON : ILLUSTRATED 192 224 97 1 33 65 256 160 96 64 129 225 193 161 32 128 2 98 223 191 8 104 217 185 190 222 99 3 159 255 66 34 153 249 72

2 40 35 67 254 158 226 130 63 95 232 136 57 89 94 62 131 227 127 31 162 194 121 25 168 200 195 163 30 126 4 100 221 189 9 105 216 184 10 106 215 183 11 107 214 182 188 220 101 5 157 253 68 36 152 248 73 41 151 247 74 42 150 246 75 43 37 69 252 156 228 132 61 93 233 137 56 88 234 138 55 87 235 139 54 86 92 60 133 229 125 29 164 196 120 24 169 201 119 23 170 202 118 22 171 203 197 165 28 124 6 102 219 187 12 108 213 181 13 109 212 180 14 110 211 179 15 111 210 178 16 112 209 177 186 218 103 7 155 251 70 38 149 245 76 44 148 244 77 45 147 243 78 46 146 242 79 47 145 241 80 48 39 71 250 154 230 134 59 91 236 140 53 85 237 141 52 84 238 142 51 83 239 143 50 82 240 144 49 81 90 58 135 231 123 27 166 198 117 21 172 204 116 20 173 205 115 19 174 206 114 18 175 207 113 17 176 208 199 167 26 122 All rows, columns.

3 And 14 main diagonals sum correctly in proportion to length 16 4x4 MAGIC squares. H. D. Heinz & J. R. Hendricks48161024204832164 4096212825651210241161409615121204813218 1412561641128121123456789101112131415161 7181920212223242526271234681012141618202 2232425579111317192115 MAGIC SQUARELEX ICON:Illustrated 1276355226959451948471166239226138745096 4148128574026243349811783463372356422554 1681380301873325844214767066657513677102 979152741556735372546177531204360 MAGIC SQUARE LEXICON : Illustrated By Harvey D. Heinz & John R. Hendricks Published November 2000 By HDH Second print run July 2005 Copyright 2000 by Harvey D.

4 Heinz Published in small quantities by HDH as demand indicates ISBN 0-9687985-0-0 Binding courtesy of Pacific Bindery Services Ltd. For Erna & Celia Two ladies with patience and forbearance, while their men are playing with numbers . To commemorate the year 2000 Prime MAGIC SQUARE A 67 241 577 571 547 769 127 13 223 139 421 673 619 307 331 199 Plus prime MAGIC SQUARE B 1933 1759 1423 1429 1453 1231 1873 1987 1777 1861 1579 1327 1381 1693 1669 1801 Equals MAGIC SQUARE C 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 Designed by John E.

5 Everett (July, 2000) By permission, Carlos Rivera, Contents Tables and Illustrations iii Preface 1 xi Preface 2 xiii MAGIC SQUARE LEXICON 1 to 174 References 175 The Authors 1 81 MAGIC SQUARE Bibliography A1-1 to A1-15 John Hendricks Bibliography A2-1 to A2-3 12b1234567891011121314151617181920212223 24 Tables and Illustrations 1 - Two types of almost MAGIC 2 2 - The Alphamagic SQUARE of 3 3 - An order-4 and an order-5 anti- MAGIC 4 4 - Number of anti- MAGIC 4 5 - Two order-5 anti- MAGIC 5 6 - The 8 aspects of a MAGIC 6 7 - One of four order-3 MAGIC cubes, all associated.

6 7 8 - Three associated MAGIC 8 9 - An order-9 associated, pandiagonal, 32 ply MAGIC 9 10 - One of 4 basic MAGIC 11 - An order-4 Basic MAGIC SQUARE ..12 12 - A basic order-6 MAGIC 13 - Basic tesseract MT# 9 shown in the standard 14 - A disguised version of MT# 9 (previous 15 - The 58 basic tesseracts of order-3 in indexed 16 - An order-8 bent-diagonal MAGIC SQUARE ..17 17 - An order-9 bimagic SQUARE with unusual 18 - An order-5 and an order-6 bordered 19 -The continuous nature of a pandiagonal MAGIC 20 -Two order-3 MAGIC squares and their 21 - An order-6 MAGIC SQUARE and its 22 - An order-5 pandiagonal and its complement.)

7 Pair 23 - An order-4 complete cube of binary 24 - 12 order-3 MAGIC squares form an order-12 composition ..27 25 - Two order-4 MAGIC squares formed from the iii Tables and Illustrations 26 - 2 order-5 MAGIC SQUARE that don t obey the rule for 27 - A hypercube of order-3 (a cube) showing the 28 - Crosmagic Quadrant pattern for order-9 and 29 - Diamagic Quadrant pattern for order-9 and 30 - Diametrically equidistant pairs in even and odd 31 - A MAGIC SQUARE in ternary, decimal 0-8 and decimal 1 to 32 - Digital-root MAGIC squares with digital roots of 3, 6 and 9..36 33 - Divide MAGIC SQUARE from a multiply MAGIC 34 - An order-4 domino MAGIC 35 - An order-7 MAGIC SQUARE using a complete set of 36 - Six doubly-even MAGIC squares in one.

8 39 37 - The 12 Dudeney groups..40 38 - An order-7 MAGIC SQUARE with embedded orders 3 and 4..41 39 - Table Summary of MAGIC squares 40 - Table Summary of MAGIC stars count..43 41 - Index # 6 of the 36 essentially different pandiagonals..44 42 - An order-4, doubly-even, within a singly-even order-6..45 43 - An order-3 MAGIC SQUARE with 2 expansion 44 - Franklin s order-8 MAGIC 45 - Some Franklin order-8 46 - Two MAGIC Generalized 47 - Exponential geometric MAGIC SQUARE ..53 48 - Ratio geometric MAGIC SQUARE ..53 49 - Order-4 Latin, Greek and Graeco-Latin 50 - A bipartite anti- MAGIC iv Tables and Illustrations 51 - A bipartite super- MAGIC 52 - An order-4 supermagic graph and MAGIC 53 - An order-5 star and two isomorphic tree-planting 54 - Orders 3 and 4 55 - Horizontal and vertical steps in an order-3 MAGIC 56 - This non-normal order-4 MAGIC SQUARE does not use integers.

9 59 57 - The first 3 order-4 MAGIC 58 - Star A shows the name of the cells, Star B is solution # 1..60 59 - The first six order-6 MAGIC stars in tabular 60 - An order-5 with inlaid diamond and even corner numbers..62 61 - Comparison of order-4 Inlaid and Bordered MAGIC 62 - The primary intermediate SQUARE for 63 - Pandiagonal order-5 and solution 64 - An order-9 iso-like MAGIC 65 - The order-9 diamagic SQUARE for the above star..67 66 - An order-8 MAGIC star isomorphic to an order-5 67 - Four aspects of the IXOHOXI MAGIC 68 - An order-8 with two half-board re-entrant Knight 69 - The two re-entrant knight tour paths for the above 70 - Variations of a numerical Latin 71 - Bergholt s general form for order-4.

10 74 72 - A solution set and the resulting MAGIC 73 - An order-7 Lozenge MAGIC SQUARE ..76 74 - Lringmagic Quadrant pattern for order-9 and 75 - An order-6 multiply MAGIC SQUARE is 22 ply and 32 ply..77 v Tables and Illustrations 76 - Two MAGIC 77 - An order-3 basic normal MAGIC 78 - Number of lower hyperplanes within a given 79 - An order-4 semi-pandiagonal and its MAGIC line 80 - A 3 x 9 MAGIC rectangle with correct 81 - An order-5 pandiagonal SQUARE with special 82 - An order-9 pandiagonal MAGIC SQUARE that is also 83 - An order-12 pattern b normal MAGIC 84 - An order-11 pattern b normal MAGIC 85 - A summary of some MAGIC star 86 - Order-10 MAGIC stars, Type S and Type 87 - The 3-D order-3 MAGIC star.