Mythic squares/rectangles

[WraithX]

I have created an interesting extension to the original Mythic Puzzle, the Mythic 3D Puzzle. Here are some example results:

3,3,3;base-10;score = 105;
1,0,1 : 9,6,0 : 4,5,5
4,5,6 : 2,0,3 : 4,3,1
7,8,9 : 8,7,9 : 2,1,3

4,4,4;base-10;score = 184;
1,1,9,1 : 1,0,0,5 : 1,1,7,2 : 1,8,0,1
1,3,1,1 : 5,0,2,3 : 7,4,5,6 : 1,7,4,1
5,3,2,2 : 3,6,3,1 : 4,8,4,9 : 7,1,9,8
1,7,6,1 : 1,6,9,3 : 4,6,0,8 : 1,8,6,1

5,5,5;base-10;score = 308;
1,7,1,1,1 : 9,1,3,5,6 : 7,4,2,1,8 : 2,1,1,5,1 : 2,2,2,5,2
9,2,3,0,3 : 7,3,6,7,1 : 7,2,7,4,2 : 1,5,4,8,9 : 2,8,9,1,9
1,1,1,8,1 : 2,9,5,0,6 : 0,4,6,9,3 : 0,4,3,2,9 : 8,2,1,2,9
2,1,6,1,8 : 0,6,8,2,2 : 3,2,0,7,2 : 9,0,5,3,3 : 1,9,0,2,6
2,0,4,2,5 : 5,1,6,7,2 : 5,2,3,8,0 : 5,3,7,8,8 : 6,2,3,5,2

I have posted a web page that can score these grids here: https://www.mersenneforum.org/wraith...c_score3d.html

This will also score regular 2D grids, identifying them as x,y,1

My python program was easily adapted to the extra dimension and I have found the following early results (x,y,1 table based on Gerbicz and Till results):

 1|  1   2   3   4   5   6   7   8   9  10  11  12
--+-----------------------------------------------
 1|  1   2   3   4   5   6   7   8   9  10  12  14
 2|      4   6   8  10  21  32  37  46  54  57  65
 3|          9  26  38  48  66  78  98 104 109 118
 4|             43  65  88 104 116 125 132 141 148
 5|                 98 108 126 136 149 161 171 180
 6|                    128 141 156 171 182 195 206
 7|                        158 175 191 205 231 244
 8|                            194 204 234 248 266
 9|                                237 256 279 294
10|                                    284 295 333
11|                                        342 368
12|                                            397

 2|  1   2   3   4   5   6   7   8   9  10  11  12
--+-----------------------------------------------
 1|  2   4   6   8  10  21  32  37  46  54  55  57
 2|      8  32  54  76  99 101 103 105 107 108 113
 3|         68 102 104 107 115 127 131 135 143 152
 4|            106 118 129 143 146 155 167 174 188
 5|                132 143 155 166 178 193 203 209
 6|                    155 168 186 204 209 231 256
 7|                        193 205 224 239 259 282
 8|                            233 251 279 315 346
 9|                                291 325 336 397
10|                                    363 385 464
11|                                        464 549
12|                                            619

 3|  1   2   3   4   5   6   7   8   9   10   11   12
--+--------------------------------------------------
 1|  3   6   9  26  38  48  66  78  98  104  109  118
 2|     32  68 102 104 107 115 127 131  135  143  152
 3|        105 120 129 143 161 170 178  195  203  214
 4|            143 167 184 201 225 247  266  295  306
 5|                192 208 244 272 306  338  394  417
 6|                    239 282 322 362  458  517  586
 7|                        338 403 495  596  716  948
 8|                            493 596  867 1003 1017
 9|                                837 1005 1017 1042
10|                                    1022 1043 1067
11|                                         1064 1083
12|                                              1128

 4|  1   2   3   4   5   6   7    8    9   10   11   12
--+----------------------------------------------------
 1|  4   8  26  43  65  88 104  116  125  132  141  148
 2|     54 102 106 118 129 143  146  155  167  174  188
 3|        120 143 167 184 201  225  247  266  295  305
 4|            184 208 234 289  319  357  403  469  557
 5|                245 303 363  425  516  627  837 1000
 6|                    375 457  606  756 1001 1019 1034
 7|                        685 1000 1003 1026 1050 1081
 8|                            1012 1027 1063 1113 1156
 9|                                 1069 1097 1183 1227
10|                                      1191 1243 1294
11|                                           1277 1346
12|                                                1407

 5|  1   2   3   4   5   6    7    8    9   10   11   12
--+-----------------------------------------------------
 1|  5  10  38  65  98 108  126  136  149  161  171  180
 2|     76 104 118 132 143  155  166  178  193  203  209
 3|        129 167 192 208  244  272  306  338  394  417
 4|            208 245 303  363  425  516  627  837 1000
 5|                308 404  514  668  968 1004 1021 1047
 6|                    564  828 1013 1033 1053 1098 1134
 7|                        1009 1048 1075 1144 1195 1253
 8|                             1087 1158 1232 1273 1325
 9|                                  1244 1283 1336 1305
10|                                       1356 1285 1174
11|                                            1255 1137
12|                                                 1099

I tried adapting Gerbicz's program to 3D, which seems to have worked, but is slower than my python program. I've probably made some part of the algorithm very inefficient. Hopefully Gerbicz will bring his great talents to bear on this new 3D extension to the original puzzle! Good luck to everyone who wants to tackle this new extension!

[Till]

Originally Posted by science_man_88

change that to a 1 and you get higher unless 1184, is only once in the puzzle ( I'll double check for more I may have missed) 554 may be a deal breaker as well.

455 or 554 is the deal breaker. Check it on https://www.mersenneforum.org/wraithx/mythic_score.html

[Till]

Originally Posted by WraithX

(x,y,1 table based on Gerbicz and Till results)

axn produced the first 4x4 with score 43.

[Till]

Originally Posted by WraithX

I have created an interesting extension to the original Mythic Puzzle, the Mythic 3D Puzzle.


...


I tried adapting Gerbicz's program to 3D, which seems to have worked, but is slower than my python program. I've probably made some part of the algorithm very inefficient. Hopefully Gerbicz will bring his great talents to bear on this new 3D extension to the original puzzle! Good luck to everyone who wants to tackle this new extension!

The original challenge was interesting to me, but there are too many possible generations: Other bases, higher dimensions, other topologies, etc. So I won't take the extended challenge.


But I'ld like to mention that your python program seems to be quite efficient. I tried to find better 11x11 and 12x12 base 10 results but failed. Good stuff! Maybe you can find better mxn base 10 results for m, n <= 10 ?