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From: stan@clt.DEC (Stanley Rabinowitz)
Newsgroups: net.math
Subject: Re: magic cube inquiry
Message-ID: <200@decwrl.DEC.COM>
Date: Mon, 30-Dec-85 21:00:13 EST
Article-I.D.: decwrl.200
Posted: Mon Dec 30 21:00:13 1985
Date-Received: Wed, 1-Jan-86 04:02:38 EST
Sender: daemon@decwrl.DEC.COM
Organization: Digital Equipment Corporation
Lines: 64


Col. G. L. Sicherman asked for a magic cube of order 6.
The following example comes from [1].  Each of the 108
orthogonal rows sums to 651 as well as the 4 space diagonals.
It consists of all the integers from 1 to 216.
Other magic cubes of order 6 are also given in [1] as well
as methods of construction.

		Reference:

[1] W.S. Andrews, Magic Squares and Cubes, Dover Publications, Inc.
	    New York: 1960. Page 197.

Example of a magic cube of order 6:

		  4 139 161  26 174 147
		 85 166 107 188  93  12
		 98 152 138   3 103 157
Level 1		179  17  84 165 184  22
		183  21  13 175  89 170
		102 156 148  94   8 143

		193  58  80 215  39  66
		112  31 134  53 120 201
		125  71  57 192 130  76
Level 2		 44 206 111  30  49 211
		 48 210 202  40 116  35
		129  75  67 121 197  62

		 18 153 136 163  23 158
		 99 180   1  82 104 185
		181  19  95 176 171   9
Level 3		100 154 149  14  90 144
		167   5 108 189 172  10
		 86 140 162  27  91 145

		207  72  55  28 212  77
		126  45 190 109 131  50
		 46 208 122  41  36 198
Level 4		127  73  68 203 117  63
		 32 194 135  54  37 199
		113  59  81 216 118  64

		155  20 150  15 169 142
		101 182  96 177  88   7
		  6  87 106 187  92 173
Level 5		141 168 160  25  11 146
		151  16 137  83 105 159
		 97 178   2 164 186  24

		 74 209  69 204  34  61
		128  47 123  42 115 196
		195 114 133  52 119  38
Level 6		 60  33  79 214 200  65
		 70 205  56 110 132  78
		124  43 191  29  51 213


	Stanley Rabinowitz
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