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|
Length of the longest directed, closed, non-intersecting rook path on an n X n
chess board avoiding right turns on squares of one color and avoiding left
turns on the other color.
| max length | count paths
|
|---|
| n=1 | 0 |
| | 2 | 0 |
| | 3 | 8 | 1
| | 4 | 12 | 1
| | 5 | 16 | 4
| | 6 | 20 | 13
| | 7 | 40 | 2
| | 8 | 48 | 14
| | 9 | 62 | 177
| | 10 | 76 | >2121
| | 11 | 98 | 616
| | 12 | 116 | 3
| | 13 | 136 |
| | 14 | 156 |
| | 15 | 188 |
| | 16 | 208 |
| |
Length of the longest directed, closed, non-intersecting rook path on an n X k
chess board avoiding right turns on squares of one color and avoiding left
turns on the other color.
| n=3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| | k=3 | 8 | 8 | 12 | 12 | 18 | 18 | 22 | 22 | 28 | 28 | 32 | 32 | 38 | 38 | 42 | 42 | 48 | 48 | len
|
| 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 6 | 6 | 3 | 3 | 15 | 15 | 6 | 6 | cnt
| | 4 |
| 12 | 14 | 16 | 20 | 24 | 26 | 28 | 32 | 36 | 38 | 40 | 44 | 48 | 50 | 52 | 56 | 60 | len
|
|
| 1 | 1 | 3 | 2 | 1 | 3 | 11 | 3 | 1 | 4 | 26 | 4 | 1 | 6 | 47 | 5 | 1 | cnt
| | 5 |
|
| 16 | 18 | 26 | 28 | 30 | 32 | 44 | 46 | 52 | 54 | 62 | 64 | 70 | 72 | 80 | 82 | len
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| 4 | 5 | 1 | 1 | 10 | 17 | 1 | 2 | 2 | 4 | 4 | 7 | 14 | 28 | 12 | 24 | cnt
| | 6 |
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| 20 | 30 | 36 | 40 | 44 | 50 | 56 | 60 | 64 | 70 | 76 | 80 | 84 | 90 | 96 | len
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| 13 | 5 | 4 | 8 | 36 | 55 | 29 | 106 | 697 | 481 | 178 | 980 | 8712 | 3921 | 1126 | cnt
| | 7 |
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| 40 | 42 | 50 | 52 | 62 | 64 | 72 | 74 | 88 | 90 | 100 | 102 | 114 | 116 | len
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| 2 | 18 | 18 | 259 | 66 | 315 | 629 | 6171 | 6 | 29 | 12 | 58 | 18 | 91 | cnt
| | 8 |
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| 48 | 54 | 60 | 68 | 76 | 82 | 88 | 96 | 104 | 110 | 116 | 124 | 132 | len
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| 14 | 40 | 232 | 57 | 35 | 90 | 726 | 700 | 299 | 1400 | 13220 | 8421 | 2728 | cnt
| | 9 |
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| 62 | 68 | 80 | 84 | 94 | 98 | 110 | 114 | 124 | 128 | 144 | 148 | len
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| 177 | 610 | 356 | 1384 | 860 | 32010 | 9787 | >9283 | >9715 | >10000 | 217 | 646 | cnt
| | 10 |
|
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| 76 | 86 | 96 | 104 | 112 | 122 | 132 | 140 | 148 | 158 | 168 | len
|
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| >2121 | 6 | 6 | 12 | 72 | 90 | 54 | 216 | 1641 | 1246 | 558 | cnt
| | 11 |
|
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| 98 | 104 | 116 | 122 | 136 | 142 | 154 | 160 | 174 | 180 | len
|
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| 616 | 1188 | 633 | >9177 | >8102 | >9430 | >9588 | >9998 | >9872 | >10000 | cnt
| | 12 |
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| 116 | 124 | 136 | 146 | 160 | 168 | 180 | 190 | 204 | len
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| 3 | 306 | 23 | 354 | 21 | 540 | 483 | >4218 | 210 | cnt
| | 13 |
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| 136 | 146 | 162 | 170 | 182 | 192 | 208 | 216 | len
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| | | | | | | | | cnt
| | 14 |
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| 156 | 170 | 184 | 196 | 208 | 222 | 236 | len
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| | | | | | | | cnt
| | 15 |
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| 188 | 198 | | | | | len
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| | | | | | | cnt
| | 16 |
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| 208 | | | | | len
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| | | | | | cnt
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| n=3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| |
| 3x3 - 1 solution
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| 4x4 - 1 solution
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| 7x7 - 2 solutions
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| 15x15 | 16x16
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