6x6x6 Perfect Magic Cube
Though we do not have systematic algorithm to derive 4n+2 type
magic cubes, there exist beautiful example of 6x6x6 magic cube
shown below. It is found by a japanese mania Mr. Abe (1948)
according to the reference (Oomori, 1991). It is quite intrigueing
that the magic cube is perfect magic cube in spite that there must
not exist any perfect magic square for order 4n+2!
------- Floor 1 -------
1 144 14 198 118 176
140 172 190 122 18 9
180 5 126 10 194 136
28 135 59 153 109 167
131 163 145 113 63 36
171 32 117 55 149 127
---
------- Floor 2 -------
141 173 192 121 17 7
178 6 125 12 193 137
2 142 12 197 120 177
132 164 147 112 62 34
169 33 116 57 148 128
29 133 58 152 111 168
---
------- Floor 3 -------
161 67 88 47 186 102
66 107 51 187 83 157
103 156 182 87 52 71
206 22 79 38 213 93
21 98 42 214 74 202
94 201 209 78 43 26
--
------- Floor 4 -------
64 108 50 189 82 158
104 154 181 86 54 72
162 68 90 46 185 100
19 99 41 216 73 203
95 199 208 77 45 27
207 23 81 37 212 91
---
------- Floor 5 -------
105 155 183 85 53 70
160 69 89 48 184 101
65 106 49 188 84 159
96 200 210 76 44 25
205 24 80 39 211 92
20 97 40 215 75 204
---
------- Floor 6 -------
179 4 124 11 195 138
3 143 15 196 119 175
139 174 191 123 16 8
170 31 115 56 150 129
30 134 60 151 110 166
130 165 146 114 61 35
Mathemusement
:
Magic Squares and Magic Cubes