Analysis and Copyright : 石野恵一郎 (ISHINO Keiichiro) (2003).
Pentomino 4個と Trominoと Tetrominoを重複しないように使って 3×3×3 に組む。
100,620通りの組み合わせのうち、解を持つものは 53,632通り。このうち、唯一解を持つ組み合わせは 10,934通り。(鏡像の組み合わせを除く)
このうち、すべて平面的な駒を使うのは 560通りのうち 190通りの可能な組み合わせがあり、唯一解を持つ組み合わせは 48通り。(鏡像の組み合わせを除く)
| Trominoes | |||||||
|---|---|---|---|---|---|---|---|
| 1 | ![]() |
2 | ![]() |
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| Tetrominoes | |||||||
| 2 | ![]() |
3 | ![]() |
4 | ![]() |
5 | ![]() |
| 6 | ![]() |
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8 | ![]() |
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| Pentominoes | |||||||
| 4 | ![]() |
5 | ![]() |
6 | ![]() |
7 | ![]() |
| 9 | ![]() |
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11 | ![]() |
12 | ![]() |
| 13 | ![]() |
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| 29 | ![]() |
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5/4 5/5 5/7 5/10 4/2 3/15/5 5/6 5/9 5/11 4/2 3/15/6 5/7 5/10 5/12 4/1 3/15/4 5/5 5/6 5/10 4/3 3/15/4 5/5 5/10 5/11 4/3 3/15/4 5/6 5/10 5/11 4/3 3/15/4 5/7 5/10 5/11 4/3 3/15/5 5/6 5/9 5/11 4/3 3/15/4 5/5 5/6 5/11 4/4 3/15/4 5/5 5/6 5/12 4/4 3/15/4 5/5 5/7 5/9 4/4 3/15/4 5/5 5/7 5/11 4/4 3/15/4 5/5 5/9 5/10 4/4 3/15/4 5/5 5/7 5/10 4/5 3/15/4 5/5 5/9 5/10 4/5 3/15/4 5/6 5/9 5/10 4/5 3/15/4 5/9 5/10 5/11 4/5 3/15/5 5/6 5/9 5/11 4/5 3/15/5 5/7 5/9 5/10 4/5 3/15/5 5/7 5/9 5/11 4/5 3/15/6 5/7 5/10 5/11 4/5 3/15/6 5/9 5/10 5/11 4/5 3/15/5 5/6 5/10 5/12 4/2 3/25/5 5/10 5/11 5/12 4/2 3/25/6 5/7 5/10 5/11 4/2 3/25/4 5/5 5/7 5/12 4/3 3/25/4 5/6 5/7 5/9 4/3 3/25/4 5/7 5/9 5/11 4/3 3/25/5 5/6 5/7 5/11 4/3 3/25/5 5/6 5/9 5/11 4/3 3/25/5 5/7 5/9 5/10 4/3 3/25/5 5/7 5/10 5/11 4/3 3/25/5 5/9 5/10 5/11 4/3 3/25/5 5/10 5/11 5/12 4/3 3/25/6 5/9 5/10 5/11 4/3 3/25/7 5/9 5/10 5/11 4/3 3/25/4 5/5 5/9 5/10 4/4 3/25/4 5/6 5/7 5/9 4/4 3/25/4 5/7 5/9 5/11 4/4 3/25/5 5/6 5/7 5/9 4/4 3/25/5 5/6 5/7 5/11 4/4 3/25/5 5/6 5/10 5/12 4/4 3/25/5 5/9 5/10 5/11 4/4 3/25/4 5/7 5/9 5/10 4/5 3/25/5 5/6 5/7 5/9 4/5 3/25/5 5/6 5/7 5/11 4/5 3/25/5 5/6 5/9 5/11 4/5 3/25/6 5/7 5/9 5/11 4/5 3/2平面的な駒のみの解の数の分布は以下のとおり。
| Sols | Combi | |
|---|---|---|
| 1 | 48 | |
| 2 | 36 | |
| 3 | 13 | |
| 4 | 23 | |
| 5 | 11 | |
| 6 | 10 | |
| 7 | 6 | |
| 8 | 8 | |
| 9 | 8 | |
| 10 | 3 | |
| 11 | 2 | |
| 12 | 1 | |
| 13 | 1 | |
| 14 | 1 | |
| 15 | 2 | |
| 16 | 1 | |
| 17 | 2 | |
| 18 | 2 | |
| 20 | 2 | |
| 22 | 2 | |
| 23 | 1 | |
| 24 | 1 | |
| 25 | 1 | |
| 26 | 1 | |
| 27 | 1 | |
| 30 | 2 | |
| 63 | 1 | 5/4 5/5 5/6 5/9 4/2 3/2 |
非平面的な駒を含む解の数の分布は以下のとおり。
| Sols | Combi | |
|---|---|---|
| 1 | 10,934 | |
| 2 | 7,629 | |
| 3 | 5,528 | |
| 4 | 4,010 | |
| 5 | 3,133 | |
| 6 | 2,591 | |
| 7 | 2,031 | |
| 8 | 1,720 | |
| 9 | 1,401 | |
| 10 | 1,249 | |
| 11 | 1,117 | |
| 12 | 1,030 | |
| 13 | 864 | |
| 14 | 707 | |
| 15 | 684 | |
| 16 | 574 | |
| 17 | 556 | |
| 18 | 448 | |
| 19 | 429 | |
| 20 | 391 | |
| 21 | 365 | |
| 22 | 354 | |
| 23 | 318 | |
| 24 | 284 | |
| 25 | 289 | |
| 26 | 261 | |
| 27 | 224 | |
| 28 | 197 | |
| 29 | 196 | |
| 30 | 162 | |
| 31 | 179 | |
| 32 | 167 | |
| 33 | 146 | |
| 34 | 136 | |
| 35 | 129 | |
| 36 | 121 | |
| 37 | 127 | |
| 38 | 124 | |
| 39 | 94 | |
| 40 | 101 | |
| 41 | 101 | |
| 42 | 89 | |
| 43 | 92 | |
| 44 | 77 | |
| 45 | 79 | |
| 46 | 57 | |
| 47 | 53 | |
| 48 | 64 | |
| 49 | 54 | |
| 50 | 74 | |
| 51 | 67 | |
| 52 | 56 | |
| 53 | 44 | |
| 54 | 60 | |
| 55 | 54 | |
| 56 | 56 | |
| 57 | 43 | |
| 58 | 41 | |
| 59 | 48 | |
| 60 | 44 | |
| 61 | 38 | |
| 62 | 41 | |
| 63 | 51 | |
| 64 | 29 | |
| 65 | 25 | |
| 66 | 38 | |
| 67 | 18 | |
| 68 | 31 | |
| 69 | 28 | |
| 70 | 26 | |
| 71 | 24 | |
| 72 | 30 | |
| 73 | 29 | |
| 74 | 21 | |
| 75 | 29 | |
| 76 | 19 | |
| 77 | 16 | |
| 78 | 17 | |
| 79 | 22 | |
| 80 | 21 | |
| 81 | 11 | |
| 82 | 24 | |
| 83 | 13 | |
| 84 | 20 | |
| 85 | 13 | |
| 86 | 21 | |
| 87 | 11 | |
| 88 | 19 | |
| 89 | 8 | |
| 90 | 10 | |
| 91 | 15 | |
| 92 | 14 | |
| 93 | 10 | |
| 94 | 8 | |
| 95 | 10 | |
| 96 | 10 | |
| 97 | 9 | |
| 98 | 7 | |
| 99 | 19 | |
| 100 | 15 | |
| 101 | 12 | |
| 102 | 13 | |
| 103 | 4 | |
| 104 | 14 | |
| 105 | 8 | |
| 106 | 16 | |
| 107 | 12 | |
| 108 | 9 | |
| 109 | 6 | |
| 110 | 8 | |
| 111 | 13 | |
| 112 | 7 | |
| 113 | 4 | |
| 114 | 7 | |
| 115 | 7 | |
| 116 | 4 | |
| 117 | 5 | |
| 118 | 4 | |
| 119 | 7 | |
| 120 | 4 | |
| 121 | 7 | |
| 122 | 5 | |
| 123 | 8 | |
| 124 | 5 | |
| 125 | 10 | |
| 126 | 6 | |
| 127 | 9 | |
| 128 | 10 | |
| 129 | 12 | |
| 130 | 9 | |
| 131 | 3 | |
| 132 | 4 | |
| 133 | 6 | |
| 134 | 5 | |
| 135 | 5 | |
| 136 | 5 | |
| 137 | 5 | |
| 138 | 7 | |
| 139 | 5 | |
| 140 | 3 | |
| 141 | 5 | |
| 142 | 2 | |
| 143 | 3 | |
| 144 | 6 | |
| 145 | 6 | |
| 146 | 5 | |
| 147 | 1 | |
| 148 | 2 | |
| 149 | 4 | |
| 150 | 5 | |
| 151 | 3 | |
| 152 | 5 | |
| 153 | 6 | |
| 154 | 5 | |
| 155 | 4 | |
| 156 | 2 | |
| 157 | 3 | |
| 158 | 2 | |
| 160 | 4 | |
| 162 | 1 | |
| 163 | 4 | |
| 165 | 2 | |
| 167 | 5 | |
| 168 | 3 | |
| 169 | 4 | |
| 170 | 1 | |
| 171 | 5 | |
| 172 | 3 | |
| 174 | 1 | |
| 175 | 3 | |
| 176 | 5 | |
| 177 | 2 | |
| 178 | 1 | |
| 180 | 1 | |
| 181 | 4 | |
| 183 | 4 | |
| 185 | 3 | |
| 186 | 7 | |
| 188 | 4 | |
| 189 | 1 | |
| 190 | 2 | |
| 191 | 3 | |
| 192 | 3 | |
| 193 | 1 | |
| 194 | 1 | |
| 196 | 3 | |
| 197 | 2 | |
| 198 | 2 | |
| 199 | 3 | |
| 200 | 4 | |
| 201 | 3 | |
| 202 | 1 | |
| 205 | 3 | |
| 206 | 3 | |
| 207 | 2 | |
| 209 | 1 | |
| 212 | 1 | |
| 215 | 1 | |
| 216 | 1 | |
| 217 | 2 | |
| 218 | 1 | |
| 219 | 1 | |
| 221 | 1 | |
| 223 | 1 | |
| 224 | 1 | |
| 226 | 1 | |
| 230 | 1 | |
| 232 | 1 | |
| 234 | 2 | |
| 235 | 1 | |
| 237 | 1 | |
| 238 | 1 | |
| 239 | 2 | |
| 240 | 1 | |
| 241 | 1 | |
| 244 | 1 | |
| 245 | 1 | |
| 247 | 1 | |
| 249 | 1 | |
| 254 | 1 | |
| 255 | 3 | |
| 256 | 1 | |
| 258 | 1 | |
| 263 | 1 | |
| 266 | 1 | |
| 267 | 1 | |
| 272 | 1 | |
| 274 | 1 | |
| 277 | 1 | |
| 282 | 1 | |
| 283 | 1 | |
| 285 | 1 | |
| 286 | 1 | |
| 288 | 2 | |
| 292 | 1 | |
| 293 | 1 | |
| 294 | 1 | |
| 295 | 1 | |
| 297 | 2 | |
| 300 | 1 | |
| 306 | 2 | |
| 307 | 1 | |
| 310 | 1 | |
| 312 | 1 | |
| 313 | 1 | |
| 316 | 1 | |
| 323 | 1 | |
| 328 | 2 | |
| 329 | 1 | |
| 333 | 1 | |
| 334 | 1 | |
| 345 | 1 | |
| 347 | 1 | |
| 348 | 2 | |
| 350 | 1 | |
| 354 | 1 | |
| 356 | 1 | |
| 357 | 2 | |
| 372 | 1 | |
| 373 | 1 | |
| 378 | 1 | |
| 391 | 2 | |
| 395 | 1 | |
| 401 | 1 | |
| 414 | 1 | |
| 423 | 1 | |
| 456 | 1 | |
| 477 | 1 | |
| 506 | 1 | |
| 519 | 1 | |
| 605 | 1 | |
| 618 | 1 | |
| 641 | 1 | |
| 687 | 1 | |
| 698 | 1 | |
| 844 | 1 | 5/4 5/6 5/16 5/22 4/2 3/2 |