# The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.

Author Message
Alfie
Bovine Member

 Posted: Sat Feb 12, 2000 7:26 am    Post subject: 1 Arrange the numbers 1-169 into a 13x13 square where every row and column and both diagonals add to the same number. I can do it in less than five minutes and without a calculator. (And have done so.)
Amb
Amb the Hitched.

 Posted: Sat Feb 12, 2000 9:04 am    Post subject: 2 Well I can do a 17 by 17? (An odd numbered square is very easy to create) code:``` 155 174 193 212 231 250 269 288 1 20 39 58 77 96 115 134 153 173 192 211 230 249 268 287 17 19 38 57 76 95 114 133 152 154 191 210 229 248 267 286 16 18 37 56 75 94 113 132 151 170 172 209 228 247 266 285 15 34 36 55 74 93 112 131 150 169 171 190 227 246 265 284 14 33 35 54 73 92 111 130 149 168 187 189 208 245 264 283 13 32 51 53 72 91 110 129 148 167 186 188 207 226 263 282 12 31 50 52 71 90 109 128 147 166 185 204 206 225 244 281 11 30 49 68 70 89 108 127 146 165 184 203 205 224 243 262 10 29 48 67 69 88 107 126 145 164 183 202 221 223 242 261 280 28 47 66 85 87 106 125 144 163 182 201 220 222 241 260 279 9 46 65 84 86 105 124 143 162 181 200 219 238 240 259 278 8 27 64 83 102 104 123 142 161 180 199 218 237 239 258 277 7 26 45 82 101 103 122 141 160 179 198 217 236 255 257 276 6 25 44 63 100 119 121 140 159 178 197 216 235 254 256 275 5 24 43 62 81 118 120 139 158 177 196 215 234 253 272 274 4 23 42 61 80 99 136 138 157 176 195 214 233 252 271 273 3 22 41 60 79 98 117 137 156 175 194 213 232 251 270 289 2 21 40 59 78 97 116 135 ```
Amb
Amb the Hitched.

 Posted: Sat Feb 12, 2000 9:15 am    Post subject: 3 The trick is to start with the number one in the middle square of the top row. The numbering follows upward diagonally. If the number reaches an edge then it simply wraps to the other side, and still up one. eg a 5 by 5 code:``` ..1.. ..... ..... ....3 ...2. ``` If the numbers be written ever collide trying to take a used square, then the number simply drops down one square and continues code:``` ..18. .57.. 46... ....3 ...2. ``` And finally becomes: code:``` 17 24 .1 .8 15 23 .5 .7 14 16 .4 .6 13 20 22 10 12 19 21 .3 11 18 25 .2 .9 ``` Now you go and do 13 X 13! [This message has been edited by amb (edited 02-14-2000).]
Alfie
Bovine Member

 Posted: Sat Feb 12, 2000 7:58 pm    Post subject: 4 Just what I thought, way to easy for this group. Anyone want to try a 6x6? Bwahahahahaha.
mithrandir
Daedalian Member

 Posted: Sat Feb 12, 2000 8:18 pm    Post subject: 5 code:``` 22 21 24 25 6 7 20 23 27 26 5 4 3 0 17 16 35 34 1 2 19 18 33 32 31 30 8 9 12 15 28 29 10 11 14 13 ``` [This message has been edited by mithrandir (edited 02-12-2000).]
Ghost Post
Icarian Member

 Posted: Sun Feb 13, 2000 2:22 pm    Post subject: 6 There's a definite pattern in that one. 2-by-2 blocks, the blocks arranged similar to the the numbers in the 3-by-3 square. And a pattern within the 2-by-2 blocks. Does it extend to 8-by-8? 10-by-10?
Alfie
Bovine Member

 Posted: Mon Feb 14, 2000 5:20 am    Post subject: 7 How did you get that? I didn't know of an even order pattern.
Amb
Amb the Hitched.

 Posted: Mon Feb 14, 2000 6:14 am    Post subject: 8 What about a three dimensional magic "Square" (or now a magic cube). Is that even possible? eg code:``` 11 and 11 11 11 Works for a 2 by 2 cube, but the numbers are not sequential. ``` I would be fascinated to know
araya
Daedalian Member

 Posted: Tue Feb 15, 2000 12:59 am    Post subject: 9 I know a general method for creating a nxn magic square where n is odd, or where n is divisible by 4 (different methods). Magic cube: Richard Myers discovered a general method for finding an order-8 magic cube, when he was 16 years old.
Amb
Amb the Hitched.

 Posted: Tue Feb 15, 2000 8:17 pm    Post subject: 10 Would you mind telling me the method for n where n mod 4 = 0. That would be interesting. (I have already explained the n mod 2 = 1 method in my higher posts) Thanks Araya
araya
Daedalian Member

 Posted: Wed Feb 16, 2000 12:19 am    Post subject: 11 Sure, amb, I'll explain both methods since mine is different from yours for odd order squares, Place 1 in upper right corner. Move one cell to the left and 2 cells down and place 2. Continue moving in this way. If you land outside the square, wrap around to the opposite side (move up or right n cells as necessary). If you are going to land in an occupied square, instead move two cells to the left. Magic squares made in this way are also "pandiagonal" meaning if you tiled a plane with it, any nxn square in the plane is also magic. code:``` 13 25 07 19 01 17 04 11 23 10 21 08 20 02 14 05 12 24 06 18 09 16 03 15 22 ``` Method for n mod 4 = 0 squares: Divide the square into 4 subsquares, and draw the two main diagonals in all of these. Now, starting in the top left cell, insert numbers sequentially starting with 1 by moving left to right, only inserting a number if it is not crossed by a diagonal. code:``` xx 02 03 xx xx 06 07 xx 09 xx xx 12 13 xx xx 16 17 xx xx 20 21 xx xx 24 xx 26 27 xx xx 30 31 xx xx 34 35 xx xx 38 39 xx 41 xx xx 44 45 xx xx 48 49 xx xx 52 53 xx xx 56 xx 58 59 xx xx 62 63 xx Now, starting in the lower right, count up from 1 and fill in the empty cells. ``` source: Ancient Puzzles by Dominic Olivastro
Amb
Amb the Hitched.

 Posted: Wed Feb 16, 2000 1:30 am    Post subject: 12 Thanks araya, I love magic squares, but until today have never known a pattern for even squares but this pushes me closer and higher in what I know. Thanks
Alfie
Bovine Member

 Posted: Wed Feb 16, 2000 1:44 am    Post subject: 13 Thanks. These make great puzzles for my pre-cal class at school.
Amy
Daedalian Member

 Posted: Thu Feb 17, 2000 3:29 pm    Post subject: 14 Wow, that would make it an "Educator Idea"! I haven't seen one of those before...
mathgrant
A very tilted cell member

 Posted: Sun Apr 08, 2001 10:29 pm    Post subject: 15 I like this. I can't help but bump it.Last edited by mathgrant on Sun Jul 11, 2004 5:43 am; edited 1 time in total
CzarJ
Hot babe

 Posted: Mon Apr 09, 2001 10:35 pm    Post subject: 16 Well, somebody had to say it... Magic Hypercube? ------------------ Basket-Weaving For Donuts, Where You Weave Baskets And Get Donuts.
Courk
Daedalian Member

 Posted: Tue Apr 10, 2001 1:29 am    Post subject: 17 I love threads where I learn something! Thankyou!!!
CrystyB
Misunderstood Guy

 Posted: Wed Apr 11, 2001 7:15 am    Post subject: 18 What is the length of the side, CzarJ? You made me develop a Pascal program for finding it, but you still need to provide the input data...
CzarJ
Hot babe

 Posted: Thu Apr 12, 2001 3:33 am    Post subject: 19 I don't know... I just want a Magic Hypercube... It'll be cool ------------------ Basket-Weaving For Donuts, Where You Weave Baskets And Get Donuts.
Ghost Post
Icarian Member

 Posted: Fri May 25, 2001 12:58 am    Post subject: 20 I realize this is probably a stupid question, and no I'm not a math teacher . What's a hypercube?
CzarJ
Hot babe

 Posted: Fri May 25, 2001 1:14 am    Post subject: 21 It's a cube in 4 dimensions, basically. I could try to give a more mathematical explanation, but it probably wouldn't work out that well... ------------------ Basket-Weaving For Donuts, Where You Weave Baskets And Get Donuts.
 Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year by All usersAlfieAmbAmyarayaCourkCrystyBCzarJGhost Postmathgrantmithrandir Oldest FirstNewest First
 All times are GMT Page 1 of 1

 Jump to: Select a forum Puzzles and Games----------------Grey Labyrinth PuzzlesVisitor Submitted PuzzlesVisitor GamesMafia Games Miscellaneous----------------Off-TopicVisitor Submitted NewsScience, Art, and CulturePoll Tournaments Administration----------------Grey Labyrinth NewsFeature Requests / Site Problems
You cannot post new topics in this forum
You can reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum