Small rectangular sliding block puzzles of size nX2 for n=3,4,5,6 Author: Hugo Pfoertner http://www.pfoertner.org/ Version history: Nov 23 2003 Initial version The 3*2 puzzle: (OEIS A090034) ________ | 1 | 2 | |___|___| | 3 | 4 | |___|___| | 5 | | |___|___| Neighbor relations (6 is initial position of empty square) Position | Number of targets | | Positions of | | targets 1 2 3 2 2 2 4 1 3 3 1 5 4 4 3 2 6 3 5 2 3 6 6 2 4 5 Init blank square: Row 3, Column 2 Move Total Configs Configs reachable in n-th move 1 3 2 2 6 3 3 11 5 4 17 6 5 24 7 6 34 10 7 46 12 8 58 12 9 74 16 10 97 23 11 122 25 12 150 28 13 189 39 14 233 44 15 273 40 16 302 29 17 323 21 18 341 18 19 353 12 20 359 6 21 360 1 Most distant position: ________ | 2 | 1 | |___|___| | 4 | 3 | |___|___| | | 5 | |___|___| reached by moves: 360 2 1 4 3 6 5 356 2 1 4 3 5 6 345 2 1 4 6 5 3 325 2 1 6 4 5 3 305 6 1 2 4 5 3 282 1 6 2 4 5 3 243 1 4 2 6 5 3 197 1 4 2 3 5 6 158 1 4 2 3 6 5 129 1 4 6 3 2 5 101 1 4 3 6 2 5 78 1 6 3 4 2 5 62 6 1 3 4 2 5 49 3 1 6 4 2 5 37 3 1 2 4 6 5 27 3 1 2 4 5 6 19 3 1 2 6 5 4 12 3 1 6 2 5 4 7 6 1 3 2 5 4 4 1 6 3 2 5 4 2 1 2 3 6 5 4 1 1 2 3 4 5 6 The 4*2 puzzle (OEIS A090035) _______ | 1 | 2 | |___|___| | 3 | 4 | |___|___| | 5 | 6 | |___|___| | 7 | | |___|___| Neighbor relations (8 is initial position of empty square) Position | Number of targets | | Positions of | | targets 1 2 3 2 2 2 4 1 3 3 1 5 4 4 3 2 6 3 5 3 3 7 6 6 3 4 8 5 7 2 5 8 8 2 6 7 Init blank square: Row 4 Column 2 Move Total Configs Configs reachable in n-th move 1 3 2 2 6 3 3 12 6 4 22 10 5 36 14 6 55 19 7 83 28 8 125 42 9 186 61 10 271 85 11 390 119 12 551 161 13 766 215 14 1059 293 15 1455 396 16 1961 506 17 2593 632 18 3381 788 19 4366 985 20 5560 1194 21 6974 1414 22 8638 1664 23 10522 1884 24 12521 1999 25 14479 1958 26 16249 1770 27 17712 1463 28 18788 1076 29 19455 667 30 19816 361 31 20006 190 32 20094 88 33 20133 39 34 20152 19 35 20159 7 36 20160 1 Most distant position: _______ | | 7 | |___|___| | 6 | 5 | |___|___| | 3 | 4 | |___|___| | 1 | 2 | |___|___| reached by moves: 20160 8 7 6 5 3 4 1 2 20154 7 8 6 5 3 4 1 2 20136 7 5 6 8 3 4 1 2 20097 7 5 8 6 3 4 1 2 20009 7 5 3 6 8 4 1 2 19823 7 5 3 6 4 8 1 2 19467 7 5 3 6 4 2 1 8 18814 7 5 3 6 4 2 8 1 17742 7 5 3 6 8 2 4 1 16275 7 5 3 6 2 8 4 1 14502 7 5 3 8 2 6 4 1 12538 7 5 8 3 2 6 4 1 10536 7 5 2 3 8 6 4 1 8649 7 5 2 3 6 8 4 1 6984 7 5 2 3 6 1 4 8 5567 7 5 2 3 6 1 8 4 4373 7 5 2 3 8 1 6 4 3386 7 5 8 3 2 1 6 4 2596 8 5 7 3 2 1 6 4 1963 5 8 7 3 2 1 6 4 1457 5 3 7 8 2 1 6 4 1061 5 3 7 1 2 8 6 4 767 5 3 7 1 8 2 6 4 552 5 3 8 1 7 2 6 4 391 8 3 5 1 7 2 6 4 272 3 8 5 1 7 2 6 4 187 3 1 5 8 7 2 6 4 126 3 1 5 2 7 8 6 4 84 3 1 5 2 7 4 6 8 56 3 1 5 2 7 4 8 6 37 3 1 5 2 8 4 7 6 23 3 1 8 2 5 4 7 6 13 8 1 3 2 5 4 7 6 7 1 8 3 2 5 4 7 6 4 1 2 3 8 5 4 7 6 2 1 2 3 4 5 8 7 6 1 1 2 3 4 5 6 7 8 The 5*2 puzzle (OEIS A090036): ___________________ | 1 | 2 | 3 | 4 | 5 | |___|___|___|___|___| | 6 | 7 | 8 | 9 | | |___|___|___|___|___| Neighbor relations (10 is initial position of empty square) Position | Number of targets | | Positions of | | targets 1 2 6 2 2 3 7 1 3 3 3 8 2 4 4 3 9 3 5 5 2 10 4 6 2 1 7 7 3 2 6 8 8 3 3 7 9 9 3 4 8 10 10 2 5 9 Init blank square: Row 2 Column 5 Move Total Configs Configs reachable in n-th move 1 3 2 2 6 3 3 12 6 4 23 11 5 42 19 6 72 30 7 116 44 8 184 68 9 296 112 10 472 176 11 743 271 12 1154 411 13 1756 602 14 2607 851 15 3839 1232 16 5622 1783 17 8152 2530 18 11719 3567 19 16715 4996 20 23553 6838 21 32832 9279 22 45295 12463 23 61892 16597 24 83740 21848 25 111967 28227 26 147649 35682 27 192113 44464 28 246710 54597 29 312676 65966 30 391109 78433 31 482834 91725 32 587730 104896 33 704696 116966 34 831031 126335 35 963029 131998 36 1096136 133107 37 1224856 128720 38 1344188 119332 39 1450523 106335 40 1542068 91545 41 1617810 75742 42 1677929 60119 43 1723769 45840 44 1757191 33422 45 1780414 23223 46 1795554 15140 47 1804648 9094 48 1809721 5073 49 1812326 2605 50 1813550 1224 51 1814078 528 52 1814303 225 53 1814378 75 54 1814398 20 55 1814400 2 Most distant position 1 ___________________ | | 9 | 3 | 7 | 1 | |___|___|___|___|___| | 5 | 4 | 8 | 2 | 6 | |___|___|___|___|___| reached by moves: 1814399 10 9 3 7 1 5 4 8 2 6 1814382 9 10 3 7 1 5 4 8 2 6 1814309 9 3 10 7 1 5 4 8 2 6 1814097 9 3 7 10 1 5 4 8 2 6 1813590 9 3 7 2 1 5 4 8 10 6 1812417 9 3 7 2 1 5 4 10 8 6 1809907 9 3 7 2 1 5 10 4 8 6 1804984 9 3 7 2 1 10 5 4 8 6 1796098 10 3 7 2 1 9 5 4 8 6 1781291 3 10 7 2 1 9 5 4 8 6 1758483 3 7 10 2 1 9 5 4 8 6 1725642 3 7 2 10 1 9 5 4 8 6 1680497 3 7 2 1 10 9 5 4 8 6 1621156 3 7 2 1 6 9 5 4 8 10 1546236 3 7 2 1 6 9 5 4 10 8 1455539 3 7 2 1 6 9 5 10 4 8 1349966 3 7 2 1 6 9 10 5 4 8 1231401 3 7 2 1 6 10 9 5 4 8 1102932 10 7 2 1 6 3 9 5 4 8 969964 7 10 2 1 6 3 9 5 4 8 837656 7 2 10 1 6 3 9 5 4 8 711015 7 2 1 10 6 3 9 5 4 8 593477 7 2 1 6 10 3 9 5 4 8 487973 7 2 1 6 8 3 9 5 4 10 395483 7 2 1 6 8 3 9 5 10 4 316423 7 2 1 6 8 3 9 10 5 4 249802 7 2 10 6 8 3 9 1 5 4 194648 7 2 6 10 8 3 9 1 5 4 149715 7 2 6 8 10 3 9 1 5 4 113627 7 2 6 8 4 3 9 1 5 10 85014 7 2 6 8 4 3 9 1 10 5 62869 7 2 6 8 4 3 9 10 1 5 46009 7 2 6 8 4 3 10 9 1 5 33380 7 10 6 8 4 3 2 9 1 5 23961 7 6 10 8 4 3 2 9 1 5 17026 7 6 9 8 4 3 2 10 1 5 11929 7 6 9 8 4 3 2 1 10 5 8302 7 6 9 10 4 3 2 1 8 5 5726 7 6 10 9 4 3 2 1 8 5 3910 7 6 1 9 4 3 2 10 8 5 2656 7 6 1 9 4 3 10 2 8 5 1790 7 6 1 9 4 10 3 2 8 5 1174 10 6 1 9 4 7 3 2 8 5 757 6 10 1 9 4 7 3 2 8 5 482 6 1 10 9 4 7 3 2 8 5 303 6 1 2 9 4 7 3 10 8 5 188 6 1 2 9 4 7 10 3 8 5 119 6 1 2 9 4 10 7 3 8 5 74 10 1 2 9 4 6 7 3 8 5 43 1 10 2 9 4 6 7 3 8 5 24 1 2 10 9 4 6 7 3 8 5 13 1 2 3 9 4 6 7 10 8 5 7 1 2 3 9 4 6 7 8 10 5 4 1 2 3 10 4 6 7 8 9 5 2 1 2 3 4 10 6 7 8 9 5 1 1 2 3 4 5 6 7 8 9 10 Most distant position 2 ___________________ | | 5 | 3 | 2 | 1 | |___|___|___|___|___| | 9 | 4 | 8 | 7 | 6 | |___|___|___|___|___| reached by moves: 1814400 10 5 3 2 1 9 4 8 7 6 1814388 5 10 3 2 1 9 4 8 7 6 1814326 5 3 10 2 1 9 4 8 7 6 1814151 5 3 2 10 1 9 4 8 7 6 1813695 5 3 2 1 10 9 4 8 7 6 1812658 5 3 2 1 6 9 4 8 7 10 1810374 5 3 2 1 6 9 4 8 10 7 1805824 5 3 2 1 6 9 4 10 8 7 1797534 5 3 2 1 6 9 10 4 8 7 1783551 5 10 2 1 6 9 3 4 8 7 1761738 5 2 10 1 6 9 3 4 8 7 1730180 5 2 1 10 6 9 3 4 8 7 1686605 5 2 1 6 10 9 3 4 8 7 1629076 5 2 1 6 7 9 3 4 8 10 1556161 5 2 1 6 7 9 3 4 10 8 1467359 5 2 1 6 7 9 3 10 4 8 1363384 5 2 10 6 7 9 3 1 4 8 1246083 5 10 2 6 7 9 3 1 4 8 1118286 10 5 2 6 7 9 3 1 4 8 985337 9 5 2 6 7 10 3 1 4 8 852554 9 5 2 6 7 3 10 1 4 8 724918 9 5 2 6 7 3 1 10 4 8 605947 9 5 10 6 7 3 1 2 4 8 498974 9 5 6 10 7 3 1 2 4 8 404952 9 5 6 7 10 3 1 2 4 8 324317 9 5 6 7 8 3 1 2 4 10 256402 9 5 6 7 8 3 1 2 10 4 200047 9 5 6 7 8 3 1 10 2 4 154077 9 5 10 7 8 3 1 6 2 4 117110 9 10 5 7 8 3 1 6 2 4 87722 10 9 5 7 8 3 1 6 2 4 64922 3 9 5 7 8 10 1 6 2 4 47558 3 9 5 7 8 1 10 6 2 4 34519 3 9 5 7 8 1 6 10 2 4 24787 3 9 5 7 8 1 6 2 10 4 17636 3 9 5 10 8 1 6 2 7 4 12356 3 9 10 5 8 1 6 2 7 4 8609 3 10 9 5 8 1 6 2 7 4 5947 10 3 9 5 8 1 6 2 7 4 4063 1 3 9 5 8 10 6 2 7 4 2761 1 3 9 5 8 6 10 2 7 4 1870 1 3 9 5 8 6 2 10 7 4 1225 1 3 9 5 8 6 2 7 10 4 789 1 3 9 10 8 6 2 7 5 4 502 1 3 9 8 10 6 2 7 5 4 315 1 3 9 8 4 6 2 7 5 10 195 1 3 9 8 4 6 2 7 10 5 125 1 3 9 10 4 6 2 7 8 5 78 1 3 10 9 4 6 2 7 8 5 45 1 10 3 9 4 6 2 7 8 5 25 1 2 3 9 4 6 10 7 8 5 13 1 2 3 9 4 6 7 10 8 5 7 1 2 3 9 4 6 7 8 10 5 4 1 2 3 10 4 6 7 8 9 5 2 1 2 3 4 10 6 7 8 9 5 1 1 2 3 4 5 6 7 8 9 10 The 6*2 puzzle (OEIS A090167): _______ | 1 | 2 | |___|___| | 3 | 4 | |___|___| | 5 | 6 | |___|___| | 7 | 8 | |___|___| | 9 | 10| |___|___| | 11| | |___|___| Neighbor relations (12 is initial position of empty square) Position | Number of targets | | Positions of | | targets 1 2 3 2 2 2 4 1 3 3 1 5 4 4 3 2 6 3 5 3 3 7 6 6 3 4 8 5 7 3 5 9 8 8 3 6 10 7 9 3 7 11 10 10 3 8 12 9 11 2 9 12 12 2 10 11 Init blank square: Row 6 Column 2 Move Total Configs Configs reachable in n-th move 1 3 2 2 6 3 3 12 6 4 23 11 5 43 20 6 79 36 7 139 60 8 234 95 9 389 155 10 647 258 11 1073 426 12 1761 688 13 2867 1106 14 4590 1723 15 7205 2615 16 11106 3901 17 16991 5885 18 25842 8851 19 39047 13205 20 58555 19508 21 87148 28593 22 128327 41179 23 187226 58899 24 270808 83582 25 388917 118109 26 664053 165136 27 782649 228596