Pentomino Cube


Martin Gardner (1957)。 Pentomino Cube は、C.J. Bouwkamp氏によって解析され(1997)、高島直昭氏と酒井香代子氏によって追解析されている(2004)。なお、酒井氏はBouwkamp氏の解析しなかった場合についても解析している。 わたしは、さらにそれを独自に解析した。 また、60単位表面の立方体ではなく、30単位表面の立方体2つに組む問題についても示す。30単位表面立方体に組む問題は、植松峰幸氏による発案。


Pentomino Cube : volume 60

60単位立方体

立方体表面の正方形に次のように名前を付ける。命名の方法は任意だが、便宜上高島氏のものと同一にした。

Development for 60 volume cube

各駒の回転を同一視した基本的な配置(Position)は次のとおり。

NamePositionNicePatterns
I 1, 5,20,31,42 24120
1, 2, 6,17,32 24
1, 2, 6,12,17 24
1, 2, 6,12,23 24
1, 2,12,23,34 12
5, 9,13,16,17 12
L 5, 6, 9,13,16 24480
1, 5,20,31,35 24
1, 2, 6,17,21 24
1, 2, 6,10,12 24
1, 2, 3,12,23 24
1, 2, 9,24,35 24
1, 2, 6,12,16 24
1, 2, 5, 6,17 24
1, 5,12,20,31 24
5, 6, 9,13,17 no24
5, 9,12,13,16 24
1, 2, 5,20,31 24
1, 2, 3, 7,18 24
1, 2, 6, 8,12 24
1, 2,12,19,23 24
1, 2, 9,12,23 24
1, 2, 6,12,13 24
1, 2, 6,13,17 no24
1, 5,20,27,31 24
1, 5, 9,13,17 24
Y 1, 8,12,15,16 24456
1, 5, 9,16,27 24
1, 2, 6,10,17 24
1, 2, 3, 6,12 24
1, 2, 3, 9,24 24
1, 2,12,16,23 24
1, 2, 5, 6,12 24
1, 2, 6, 9,17 24
1, 5,16,20,31 no (2-ways)24
5, 6, 9,13,17 no24
1, 5, 9,13,16 24
1, 5, 9,20,31 24
1, 2, 3, 6,17 24
1, 2, 3, 7, 9 24
1, 2, 8,12,23 24
1, 2, 5,12,23 24
1, 2, 6, 9,12 24
1, 2, 6,13,17 no24
1, 8,12,16,20 24
N 5, 6, 9,13,17 no24480
1, 5, 8,12,15 24
1, 2, 5,16,27 24
1, 2, 6,10,21 24
1, 2, 3,10,12 24
1, 2, 3,10,21 24
1, 2,12,16,27 24
1, 2, 5, 6,16 24
1, 5, 8,12,20 24
5, 9,12,16,20 no24
1, 5, 9,12,13 24
1, 8,12,19,30 24
1, 2, 3, 5,20 24
1, 2, 3, 5, 7 24
1, 2, 8,12,19 24
1, 5, 9,12,23 24
1, 2, 9,12,13 24
1, 2, 6,13,17 no24
1, 5,16,20,24 no24
1, 2, 9,13,17 24
V 5, 6, 9,10,13 24240
1, 2, 8,12,15 24
1, 2, 6,13,28 24
1, 2, 6,10,14 24
1, 2, 3, 7,12 24
1, 2, 9,12,24 24
1, 2,12,16,20 24
1, 2, 5, 6,20 24
1, 5,12,20,23 24
1, 5,12,16,20 no24
T 1, 2, 8,12,16 24240
1, 2, 6,10,13 24
1, 5, 9,13,20 24
1, 2, 3, 6, 7 24
1, 2, 3, 9,12 24
1, 8,12,15,23 24
1, 2, 5,12,20 24
1, 2, 6, 9,24 24
1, 5,16,20,24 no24
5, 9,12,16,20 no24
Z 1, 2, 3,12,16 24240
1, 2, 5, 6,10 24
5, 6, 9,13,20 12
1, 8,12,15,19 no24
1, 5,12,20,24 24
1, 2, 9,24,28 12
1,12,16,20,31 24
1, 2, 8, 9,12 24
1, 2, 3, 7,14 24
1, 5, 9,13,28 12
1, 2, 5,16,20 no24
1, 5,12,19,23 12
F 1, 2, 3, 9,13 24456
1, 2, 6, 9,10 24
1, 8,12,16,19 24
1, 2, 3, 5, 6 24
1, 2, 3, 5,12 24
1, 8,12,15,19 no24
1, 5, 9,12,20 24
1, 2, 9,13,24 24
1, 5,16,20,24 no24
1, 5, 9,16,20 no (2-ways)24
5, 9,12,16,20 no24
1, 2, 5, 8,12 24
1, 2, 3, 6,13 24
1, 5, 9,13,24 24
1, 2, 3, 7,10 24
1, 2, 3, 9,10 24
1, 5, 9,16,24 24
1, 2, 5,16,20 no24
1, 5, 8,12,23 24
W 1, 2, 3,10,14 24240
1, 5, 8, 9,12 24
1, 5, 8,12,19 24
1, 2, 3, 5,10 24
1, 2, 3, 5,16 24
1, 8,12,15,19 no24
1, 5, 9,12,24 24
1, 2, 9,13,28 24
1, 5,16,20,31 no24
1, 2, 5,16,20 no24
X 1, 5, 9,16,20 no2460
1, 8,12,16,23 12
1, 2, 3, 6, 9 24
U 1, 5, 6, 9,13 24216
1, 8,11,12,15 24
1, 2, 5,20,24 24
1, 2, 3, 7,11 24
1, 2, 3, 8,12 24
1, 2, 9,20,24 24
1, 2, 9,12,16 24
1, 2, 5, 6,13 24
1, 5,12,16,20 no (2-ways)24
P 1, 5, 8,12,16 24408
1, 2, 5, 9,16 24
1, 5, 9,20,24 24
1, 2, 3, 6,10 24
1, 2, 3, 4, 9 24
1, 2, 5, 9,24 24
1, 2, 5,12,16 24
1, 2, 5, 6, 9 24
1, 5,12,16,20 no (2-ways)24
1, 2, 5, 9,13 24
1, 5, 9,12,16 24
1, 2, 5, 9,20 24
1, 2, 3, 4, 5 24
1, 2, 3, 5, 9 24
1, 5,12,16,23 24
1, 2, 5, 9,12 24
1, 2, 6, 9,13 24

表の Patterns は、可能な全配置パタンの数である。I Z X は回転対称なパタンを持っている。他は、そのようなパタンを持っていないので、立方体上では非対称である。

Bouwkamp氏は、立方体頂点の3単位を占有しない駒を Niceな駒と称して特別視した。Niceな駒だけで構成される解は Niceな解である。 Niceでない駒には、同じ配置で2通りの置き方のあるものが4つある(表の 2-ways)。

解の数は次のとおり

Niceな解 284,402
2-waysを同一視した場合26,358,584
2-waysを別々とした場合45,332,581

Pentomino Cube : volume 30

30単位立方体

Development for 30 volume cube

各駒の回転を同一視した基本的な配置(Position)は次のとおり。

NamePositionNicePatterns
I 1, 2, 4,11,18 2460
1, 2, 4,11,13 12
1, 2,13,20,27 24
L 1, 2,13,20,24 24240
1, 2, 4,11,15 24
1, 2, 4, 6,11 24
1, 2, 3,10,21 24
2, 3, 6, 9,10 no24
1, 2, 3,13,20 24
1, 2, 4, 7,13 24
1, 2, 4, 7,11 no24
1, 2, 6,10,14 24
2, 3, 6, 7,11 24
Y 1, 2, 6, 9,16 24216
1, 2, 4, 6,13 24
1, 2, 3, 4,11 24
1, 2, 9,13,20 no (2-ways)24
2, 3, 6, 9,10 no24
1, 2, 6,13,20 24
1, 2, 3, 4,13 24
1, 2, 4, 7,11 no24
1, 2, 6, 9,10 24
N 2, 3, 6, 9,10 no24240
1, 2, 3, 9,16 24
1, 2, 4, 6,17 24
1, 2, 3, 9,10 24
2, 3, 6, 7,10 no24
2, 3, 6, 7,13 24
1, 2, 3, 7,13 24
1, 2, 4, 7,11 no24
1, 2, 9,13,16 no24
1, 2, 3, 7,11 24
V 2, 3, 6, 7, 9 24120
1, 2, 4, 7,14 24
1, 2, 4, 6,10 24
1, 2, 3,10,13 24
1, 2, 3, 6,10 no24
T 1, 2, 4, 6, 9 24120
1, 2, 6,10,13 24
1, 2, 3, 4,10 24
1, 2, 9,13,16 no24
2, 3, 6, 7,10 no24
Z 1, 2, 4, 6, 8 12120
2, 3, 6, 9,13 no24
1, 2, 3,10,14 24
1, 2, 6,10,21 24
1, 2, 4, 7, 9 12
1, 2, 3, 9,13 no24
F 1, 2, 3, 4, 8 24216
2, 3, 6, 9,13 no24
1, 2, 3, 7,10 24
1, 2, 9,13,16 no24
1, 2, 6, 9,13 no (2-ways)24
2, 3, 6, 7,10 no24
1, 2, 3, 4, 9 24
1, 2, 6, 9,17 24
1, 2, 3, 9,13 no24
W 1, 2, 3, 7, 9 24120
2, 3, 6, 9,13 no24
1, 2, 3, 7,14 24
1, 2, 9,13,20 no24
1, 2, 3, 9,13 no24
X 1, 2, 6, 9,13 no2430
1, 2, 3, 4, 5 6
U 2, 3, 4, 6, 7 2496
1, 2, 3,13,17 24
1, 2, 4, 6, 7 24
1, 2, 3, 6,10 no (2-ways)24
P 1, 2, 3, 6, 9 24168
1, 2, 3, 6,17 24
1, 2, 3, 4, 6 24
1, 2, 3, 6,10 no (2-ways)24
1, 2, 3, 6, 7 24
1, 2, 3, 6,13 24
1, 2, 3, 4, 7 24

回転対称な駒は、I Z X である。

解の数は次のとおり。

Niceな解 3,090
2-waysを同一視した場合179,336
2-waysを別々とした場合332,406

これらから、立方体2つを組むことのできる組合せは以下の462通り。

PiecesNiceSols2-ways PiecesNiceSols2-waysNice-Combination
ILYPUV4336912 TNFWZX0187231
ILYPUT3162489 VNFWZX0101108
ILYPVT8222370 UNFWZX091145
ILYUVT0122250 PNFWZX2300388
ILPUVT5215546 YNFWZX0283364
IYPUVT3145390 LNFWZX2217242 nice
LYPUVT104391,065 INFWZX02731
ILYPUN144791,383 VTFWZX03840
ILYPVN21592944 UTFWZX06197
ILYUVN6304608 PTFWZX0185244
ILPUVN85071,279 YTFWZX0113150
IYPUVN74021,153 LTFWZX0111125
LYPUVN281,0792,728 ITFWZX01014
ILYPTN4332537 UVFWZX03658
ILYUTN1190374 PVFWZX0137172
ILPUTN8181400 YVFWZX06385
IYPUTN8176509 LVFWZX06363
LYPUTN228201,996 IVFWZX01111
ILYVTN1227255 PUFWZX2117225 nice
ILPVTN3243336 YUFWZX061123
IYPVTN5217367 LUFWZX05586
LYPVTN251,0021,504 IUFWZX01526
ILUVTN2128221 YPFWZX3204323 nice
IYUVTN3118244 LPFWZX0134172
LYUVTN5489935 IPFWZX02740
IPUVTN3173447 LYFWZX0138186
LPUVTN65281,277 IYFWZX03139
YPUVTN104841,126 ILFWZX02224
ILYPUF153181,055 VTNWZX05757
ILYPVF20402745 UTNWZX26395 nice
ILYUVF5206483 PTNWZX1148180 nice
ILPUVF7309758 YTNWZX0109128
IYPUVF8234675 LTNWZX0111111
LYPUVF268162,168 ITNWZX01212
ILYPTF9232447 UVNWZX04165
ILYUTF1143337 PVNWZX2137161 nice
ILPUTF2156438 YVNWZX07490
IYPUTF4153491 LVNWZX06868
LYPUTF217401,927 IVNWZX01212
ILYVTF2176230 PUNWZX0120222
ILPVTF5200310 YUNWZX066124
IYPVTF7188329 LUNWZX066104
LYPVTF297741,285 IUNWZX01222
ILUVTF283178 YPNWZX1210312 nice
IYUVTF179179 LPNWZX1192230 nice (unique)
LYUVTF7389784 IPNWZX03343
IPUVTF2129374 LYNWZX0143180
LPUVTF184371,150 IYNWZX04156
YPUVTF84181,112 ILNWZX03131
ILYPNF205881,068 UVTWZX02135
ILYUNF2342742 PVTWZX16175 nice
ILPUNF9308766 YVTWZX04352
IYPUNF113581,197 LVTWZX03636
LYPUNF561,5164,089 IVTWZX099
ILYVNF7389492 PUTWZX155104 nice
ILPVNF10390585 YUTWZX14279 nice
IYPVNF16425819 LUTWZX04166
LYPVNF451,7942,987 IUTWZX01018
ILUVNF0197377 YPTWZX1108163
IYUVNF1222539 LPTWZX0102127
LYUVNF148871,830 IPTWZX01725
IPUVNF7274707 LYTWZX07492
LPUVNF219632,362 IYTWZX01725
YPUVNF248452,248 ILTWZX01111
ILYTNF3244371 PUVWZX04279
ILPTNF8336539 YUVWZX02948
IYPTNF7216439 LUVWZX03860
LYPTNF381,5362,610 IUVWZX1711 nice
ILUTNF3213405 YPVWZX071103
IYUTNF0138335 LPVWZX07395
LYUTNF197521,590 IPVWZX01317
IPUTNF0121349 LYVWZX05766
LPUTNF288251,974 IYVWZX01519
YPUTNF317722,002 ILVWZX099
ILVTNF7232258 YPUWZX076159
IYVTNF1168230 LPUWZX079159
LYVTNF14775999 IPUWZX01125
IPVTNF1162249 LYUWZX04685
LPVTNF218891,278 IYUWZX0612
YPVTNF208421,337 ILUWZX0714
IUVTNF260131 LYPWZX0130196
LUVTNF5393716 IYPWZX01728
YUVTNF6383753 ILPWZX02027
PUVTNF7402941 ILYWZX02232
ILYPUW1216759 VTNFZX0120141
ILYPVW6288541 UTNFZX1146261 nice
ILYUVW0139343 PTNFZX5255377
ILPUVW2126277 YTNFZX1207282 nice
IYPUVW0196661 LTNFZX1158177
LYPUVW135111,364 ITNFZX02123
ILYPTW3159296 UVNFZX265105 nice
ILYUTW086202 PVNFZX1206260
ILPUTW293239 YVNFZX0143166
IYPUTW086270 LVNFZX1120129
LYPUTW43971,039 IVNFZX01214
ILYVTW1101131 PUNFZX3203382 nice
ILPVTW2129176 YUNFZX2156279 nice
IYPVTW0108185 LUNFZX1134228
LYPVTW3432699 IUNFZX02037
ILUVTW056103 YPNFZX7350564
IYUVTW048111 LPNFZX1311419
LYUVTW3222442 IPNFZX24158 nice
IPUVTW049121 LYNFZX0273404
LPUVTW6210439 IYNFZX04368
YPUVTW4202441 ILNFZX03436
ILYPNW4387722 UVTFZX13049 nice
ILYUNW1176439 PVTFZX16686 nice (unique)
ILPUNW10211487 YVTFZX28298 nice
IYPUNW3222648 LVTFZX08084
LYPUNW318822,342 IVTFZX01113
ILYVNW2214288 PUTFZX188164 nice
ILPVNW4258343 YUTFZX284166 nice
IYPVNW3277462 LUTFZX097169
LYPVNW171,0511,665 IUTFZX01225
ILUVNW0116201 YPTFZX2184330
IYUVNW1124275 LPTFZX2173256 nice
LYUVNW3462948 IPTFZX02136
IPUVNW1133308 LYTFZX1144218 nice (unique)
LPUVNW205151,042 IYTFZX01631
YPUVNW24801,148 ILTFZX01214
ILYTNW0123158 PUVFZX075169
ILPTNW1164211 YUVFZX057113
IYPTNW0128235 LUVFZX05788
LYPTNW88321,226 IUVFZX0610
ILUTNW172119 YPVFZX0140235
IYUTNW075164 LPVFZX1136182
LYUTNW2309600 IPVFZX01216
IPUTNW063166 LYVFZX0104130
LPUTNW10431888 IYVFZX02231
YPUTNW7406965 ILVFZX01212
ILVTNW08585 YPUFZX3151376
IYVTNW086110 LPUFZX1121246
LYVTNW3381436 IPUFZX11739 nice
IPVTNW098131 LYUFZX186169
LPVTNW6477621 IYUFZX22356 nice
YPVTNW2428637 ILUFZX01019
IUVTNW04073 LYPFZX0208335
LUVTNW1219363 IYPFZX03580
YUVTNW5212383 ILPFZX12433 nice
PUVTNW1198376 ILYFZX13243 nice (unique)
ILYPFW12316682 UVTNZX02847
ILYUFW0152437 PVTNZX1100119
ILPUFW1167480 YVTNZX198116 nice (unique)
IYPUFW2176619 LVTNZX07575
LYPUFW117302,111 IVTNZX199 nice
ILYVFW2164244 PUTNZX182156 nice
ILPVFW3229348 YUTNZX0101195
IYPVFW5238466 LUTNZX289141 nice
LYPVFW128611,550 IUTNZX0915
ILUVFW0112223 YPTNZX3179286
IYUVFW0103270 LPTNZX0161213
LYUVFW2433962 IPTNZX01723
IPUVFW176169 LYTNZX0154187
LPUVFW8415907 IYTNZX11421 nice
YPUVFW04121,000 ILTNZX21919
ILYTFW0129225 PUVNZX180173
ILPTFW0118186 YUVNZX070139
IYPTFW2139346 LUVNZX073117
LYPTFW77871,466 IUVNZX01424
ILUTFW162124 YPVNZX1179260 nice (unique)
IYUTFW195277 LPVNZX2159203 nice
LYUTFW5375872 IPVNZX13545 nice
IPUTFW265184 LYVNZX1111136 nice
LPUTFW7414904 IYVNZX03541
YPUTFW64301,144 ILVNZX03232
ILVTFW06977 YPUNZX1158373
IYVTFW199158 LPUNZX2136278 nice
LYVTFW1402557 IPUNZX02457
IPVTFW5101147 LYUNZX0102197
LPVTFW4441636 IYUNZX03067
YPVTFW3423738 ILUNZX02648
IUVTFW13775 LYPNZX3257393 nice
LUVTFW0187347 IYPNZX04284
YUVTFW2178382 ILPNZX25274 nice
PUVTFW3217493 ILYNZX03142
ILYNFW3287444 PUVTZX144100 nice
ILPNFW9292418 YUVTZX03465
IYPNFW5283614 LUVTZX03655
LYPNFW191,7803,012 IUVTZX024
ILUNFW1118228 YPVTZX077119
IYUNFW0153393 LPVTZX07392
LYUNFW96491,411 IPVTZX0911
IPUNFW2178517 LYVTZX05971
LPUNFW198451,984 IYVTZX01217
YPUNFW149102,386 ILVTZX099
ILVNFW4144160 YPUTZX371173 nice
IYVNFW1171247 LPUTZX165128 nice (unique)
LYVNFW27821,031 IPUTZX21124 nice
IPVNFW4245377 LYUTZX257108 nice
LPVNFW229781,442 IYUTZX01028
YPVNFW201,0041,680 ILUTZX0612
IUVNFW1117228 LYPTZX2123192 nice
LUVNFW3485885 IYPTZX02042
YUVNFW0432896 ILPTZX01521
PUVNFW9456968 ILYTZX01420
ILTNFW0158177 YPUVZX056121
IYTNFW1129198 LPUVZX04587
LYTNFW77721,156 IPUVZX0610
IPTNFW1128209 LYUVZX04690
LPTNFW89481,426 IYUVZX0722
YPTNFW79211,774 ILUVZX035
IUTNFW063135 LYPVZX0105160
LUTNFW4437820 IYPVZX02341
YUTNFW24471,045 ILPVZX01012
PUTNFW65221,167 ILYVZX01417
IVTNFW06680 LYPUZX091218
LVTNFW0424501 IYPUZX11749
YVTNFW2432636 ILPUZX1818 nice
PVTNFW4531765 ILYUZX01430
UVTNFW3239428 ILYPZX12648 nice
ILYPUZ7160458 VTNFWX0112128
ILYPVZ12213338 UTNFWX0148258
ILYUVZ2106214 PTNFWX1291432 nice
ILPUVZ12136310 YTNFWX0248337
IYPUVZ4122362 LTNFWX1236266 nice
LYPUVZ174681,116 ITNFWX03036
ILYPTZ7121207 UVNFWX072133
ILYUTZ265135 PVNFWX0204284
ILPUTZ275189 YVNFWX0144189
IYPUTZ161166 LVNFWX0134145
LYPUTZ22363825 IVNFWX02729
ILYVTZ28798 PUNFWX1185364 nice
ILPVTZ3111147 YUNFWX0147285
IYPVTZ379119 LUNFWX0147257
LYPVTZ14404583 IUNFWX03060
ILUVTZ24783 YPNFWX3418685 nice
IYUVTZ13161 LPNFWX1379523 nice (unique)
LYUVTZ4198347 IPNFWX05282
IPUVTZ041106 LYNFWX1306484
LPUVTZ5194420 IYNFWX15281 nice
YPUVTZ3196444 ILNFWX04554
ILYPNZ17303481 UVTFWX03056
ILYUNZ3142282 PVTFWX098134
ILPUNZ11147335 YVTFWX180101 nice
IYPUNZ10162462 LVTFWX08189
LYPUNZ337151,718 IVTFWX01820
ILYVNZ4168190 PUTFWX190204 nice
ILPVNZ15212279 YUTFWX094189
IYPVNZ7190307 LUTFWX095174
LYPVNZ328861,305 IUTFWX01737
ILUVNZ193160 YPTFWX2222399 nice
IYUVNZ191198 LPTFWX2204303 nice
LYUVNZ9432788 IPTFWX03256
IPUVNZ694215 LYTFWX0185283
LPUVNZ17425871 IYTFWX03152
YPUVNZ8407995 ILTFWX02024
ILYTNZ2114138 PUVFWX071150
ILPTNZ3103144 YUVFWX058138
IYPTNZ292146 LUVFWX04874
LYPTNZ237971,146 IUVFWX0712
ILUTNZ165106 YPVFWX1164311 nice (unique)
IYUTNZ055103 LPVFWX0134180
LYUTNZ13312596 IPVFWX12029 nice
IPUTNZ24188 LYVFWX0107139
LPUTNZ12385783 IYVFWX23866 nice
YPUTNZ16383854 ILVFWX01618
ILVTNZ38080 YPUFWX3171494 nice
IYVTNZ16979 LPUFWX0121254
LYVTNZ5356405 IPUFWX01851
IPVTNZ26579 LYUFWX094195
LPVTNZ10447566 IYUFWX031106
YPVTNZ8427592 ILUFWX01528
IUVTNZ01933 LYPFWX0245432
LUVTNZ5193312 IYPFWX150140 nice
YUVTNZ3189329 ILPFWX03045
PUVTNZ6170297 ILYFWX04474
ILYPFZ8216424 UVTNWX02743
ILYUFZ3110273 PVTNWX07894
ILPUFZ7139363 YVTNWX088107
IYPUFZ4132382 LVTNWX08383
LYPUFZ336431,727 IVTNWX01515
ILYVFZ1136186 PUTNWX185150 nice (unique)
ILPVFZ14202279 YUTNWX194191 nice
IYPVFZ4159282 LUTNWX094158
LYPVFZ257731,292 IUTNWX01731
ILUVFZ482152 YPTNWX0219342
IYUVFZ360148 LPTNWX2205269 nice
LYUVFZ10396792 IPTNWX02640
IPUVFZ151120 LYTNWX0168214
LPUVFZ12382853 IYTNWX01424
YPUVFZ194211,049 ILTNWX01919
ILYTFZ090138 PUVNWX072140
ILPTFZ985134 YUVNWX067127
IYPTFZ8104214 LUVNWX06299
LYPTFZ177541,337 IUVNWX01831
ILUTFZ14485 YPVNWX1159229 nice (unique)
IYUTFZ252128 LPVNWX0140177
LYUTFZ9379828 IPVNWX04255
IPUTFZ241120 LYVNWX0110134
LPUTFZ14363824 IYVNWX02126
YPUTFZ114371,116 ILVNWX01717
ILVTFZ15766 YPUNWX0150335
IYVTFZ172104 LPUNWX0133244
LYVTFZ7411543 IPUNWX02866
IPVTFZ974107 LYUNWX089172
LPVTFZ9434617 IYUNWX02147
YPVTFZ20449747 ILUNWX01830
IUVTFZ02450 LYPNWX0258400
LUVTFZ2173326 IYPNWX04179
YUVTFZ6194401 ILPNWX03547
PUVTFZ5199458 ILYNWX16287 nice
ILYNFZ6207289 PUVTWX153105 nice
ILPNFZ9199317 YUVTWX03361
IYPNFZ8193405 LUVTWX03048
LYPNFZ311,5632,615 IUVTWX024
ILUNFZ290187 YPVTWX271113 nice
IYUNFZ3106276 LPVTWX07189
LYUNFZ166291,347 IPVTWX21214 nice
IPUNFZ3121337 LYVTWX16886 nice
LPUNFZ256961,706 IYVTWX01726
YPUNFZ268462,224 ILVTWX088
ILVNFZ1121147 YPUTWX065164
IYVNFZ2138203 LPUTWX067127
LYVNFZ15724950 IPUTWX0820
IPVNFZ5173261 LYUTWX063134
LPVNFZ168941,337 IYUTWX01952
YPVNFZ209391,576 ILUTWX01018
IUVNFZ165134 LYPTWX1135232 nice (unique)
LUVNFZ6421799 IYPTWX02864
YUVNFZ2423872 ILPTWX01624
PUVNFZ9389893 ILYTWX03050
ILTNFZ194111 YPUVWX04798
IYTNFZ2111162 LPUVWX04180
LYTNFZ8663955 IPUVWX058
IPTNFZ0106155 LYUVWX059131
LPTNFZ168141,194 IYUVWX01540
YPTNFZ118061,526 ILUVWX0917
IUTNFZ14082 LYPVWX0113202
LUTNFZ5355671 IYPVWX04072
YUTNFZ84531,028 ILPVWX11826 nice
PUTNFZ7419987 ILYVWX01827
IVTNFZ04957 LYPUWX086238
LVTNFZ7384452 IYPUWX031104
YVTNFZ6465663 ILPUWX01337
PVTNFZ5468693 ILYUWX02463
UVTNFZ3217383 ILYPWX04190
ILYPWZ3164288 UVTNFX080127
ILYUWZ281184 PVTNFX3180235 nice
ILPUWZ6104251 YVTNFX0173234
IYPUWZ599264 LVTNFX0147162
LYPUWZ16391957 IVTNFX02127
ILYVWZ088114 PUTNFX2170349
ILPVWZ6130178 YUTNFX2213471 nice
IYPVWZ2135217 LUTNFX4178319 nice
LYPVWZ15472706 IUTNFX02045
ILUVWZ059107 YPTNFX13397721
IYUVWZ153111 LPTNFX2395573 nice
LYUVWZ2233425 IPTNFX34467 nice
IPUVWZ255126 LYTNFX2347524 nice
LPUVWZ1245509 IYTNFX03461
YPUVWZ7246565 ILTNFX13135 nice
ILYTWZ06788 PUVNFX5126238
ILPTWZ16888 YUVNFX2120269 nice
IYPTWZ071135 LUVNFX0100165
LYPTWZ6473718 IUVNFX02343
ILUTWZ02646 YPVNFX11310528
IYUTWZ13587 LPVNFX3268357 nice
LYUTWZ3225441 IPVNFX05780
IPUTWZ03785 LYVNFX1202262
LPUTWZ2182374 IYVNFX07293
YPUTWZ7233533 ILVNFX03333
ILVTWZ03434 YPUNFX5297790
IYVTWZ14963 LPUNFX5242506 nice
LYVTWZ3252288 IPUNFX147125 nice
IPVTWZ25270 LYUNFX0223463
LPVTWZ5246311 IYUNFX074167
YPVTWZ5244352 ILUNFX04067
IUVTWZ01937 LYPNFX13474821
LUVTWZ090155 IYPNFX387181
YUVTWZ083149 ILPNFX26386
PUVTWZ3101189 ILYNFX271103 nice
ILYNWZ1126154 PUVTFX281161 nice
ILPNWZ1156203 YUVTFX260134 nice
IYPNWZ1150255 LUVTFX267111 nice
LYPNWZ209151,308 IUVTFX0612
ILUNWZ264111 YPVTFX1155291 nice
IYUNWZ072156 LPVTFX1126179
LYUNWZ5327627 IPVTFX21521 nice
IPUNWZ098244 LYVTFX0120175
LPUNWZ3366832 IYVTFX12839 nice
YPUNWZ144691,069 ILVTFX01515
ILVNWZ07777 YPUTFX2151458
IYVNWZ191116 LPUTFX3123251 nice
LYVNWZ4401463 IPUTFX11234 nice
IPVNWZ1115157 LYUTFX1143317 nice (unique)
LPVNWZ9489651 IYUTFX02363
YPVNWZ3527771 ILUTFX01629
IUVNWZ15799 LYPTFX6236453 nice
LUVNWZ1247409 IYPTFX13988 nice (unique)
YUVNWZ1216384 ILPTFX13041 nice (unique)
PUVNWZ2218417 ILYTFX13046 nice
ILTNWZ06969 YPUVFX1110314
IYTNWZ06381 LPUVFX189177
LYTNWZ4344403 IPUVFX0721
IPTNWZ25368 LYUVFX288162 nice
LPTNWZ2510620 IYUVFX02045
YPTNWZ5482742 ILUVFX01323
IUTNWZ02237 LYPVFX2203330
LUTNWZ1178288 IYPVFX13973 nice (unique)
YUTNWZ0208425 ILPVFX02537
PUTNWZ2209451 ILYVFX04364
IVTNWZ03030 LYPUFX11209547
LVTNWZ1213213 IYPUFX037127
YVTNWZ0239299 ILPUFX02671
PVTNWZ2242327 ILYUFX040100
UVTNWZ1125210 ILYPFX466138 nice
ILYFWZ1133214 PUVTNX278133 nice
ILPFWZ6160237 YUVTNX25282 nice
IYPFWZ2167302 LUVTNX05992
LYPFWZ78971,543 IUVTNX01426
ILUFWZ163127 YPVTNX2130167 nice
IYUFWZ069166 LPVTNX3140173
LYUFWZ4383805 IPVTNX13951 nice
IPUFWZ372184 LYVTNX0123142
LPUFWZ9392941 IYVTNX13644 nice
YPUFWZ104801,174 ILVTNX02727
ILVFWZ18087 YPUTNX5123262 nice
IYVFWZ084122 LPUTNX6148301
LYVFWZ3420538 IPUTNX13486 nice
IPVFWZ182123 LYUTNX1143257 nice (unique)
LPVFWZ10509742 IYUTNX03166
YPVFWZ1566911 ILUTNX13047 nice (unique)
IUVFWZ03570 LYPTNX4262400
LUVFWZ4247453 IYPTNX03572
YUVFWZ2219428 ILPTNX14259 nice
PUVFWZ3246542 ILYTNX04353
ILTFWZ06273 YPUVNX1117278
IYTFWZ058104 LPUVNX3108202
LYTFWZ1522715 IPUVNX01430
IPTFWZ36099 LYUVNX090168
LPTFWZ3501740 IYUVNX02757
YPTFWZ35971,003 ILUVNX02035
IUTFWZ01951 LYPVNX6233326
LUTFWZ1217401 IYPVNX26099 nice
YUTFWZ2209458 ILPVNX04156
PUTFWZ3259584 ILYVNX35766 nice
IVTFWZ03039 LYPUNX1209476
LVTFWZ1226260 IYPUNX049136
YVTFWZ2222315 ILPUNX04094
PVTFWZ2282425 ILYUNX149102 nice
UVTFWZ1133243 ILYPNX389145 nice
ILNFWZ0125153 YPUVTX273179
IYNFWZ1157264 LPUVTX393189 nice
LYNFWZ68611,193 IPUVTX02054
IPNFWZ1149230 LYUVTX14273 nice (unique)
LPNFWZ101,0451,474 IYUVTX01220
YPNFWZ71,0921,909 ILUVTX01834
IUNFWZ055118 LYPVTX6115156
LUNFWZ2398717 IYPVTX02738
YUNFWZ9421898 ILPVTX33652 nice
PUNFWZ65151,177 ILYVTX02327
IVNFWZ17080 LYPUTX293210 nice
LVNFWZ1431496 IYPUTX02358
YVNFWZ2487646 ILPUTX23184 nice
PVNFWZ9640954 ILYUTX12654 nice
UVNFWZ3294533 ILYPTX13562 nice
ITNFWZ06172 LYPUVX299252
LTNFWZ2530632 IYPUVX12977 nice
YTNFWZ3591848 ILPUVX01222
PTNFWZ97571,111 ILYUVX01946
UTNFWZ1287559 ILYPVX04577
VTNFWZ2293345 ILYPUX138114 nice

Jan 30, 2005 by k16@chiba.email.ne.jp