Table 5 - Level-Type Counts & Examples Level-Type General-Count Notch-Cnt --Example Assembly (LL format)-- Example Description- ----------- -------------- --------- -------------------------------- -------------------- 0 0 0 0 20,378,085,189 2,343,017 55551131143224221131143224226666 8-SYMMETRIES 0 0 0 1 9,327,791,180 3,553,037 35351110513344221110613344223636 First occurrence 1 1 1 1 2,254,762,064 4,594,630 55555515513324221116113644666464 Coffin's Burr #305 2 2 2 2 2,146,842,081 1,275,780 35351111143352226616443602226464 1-HOLE NOTCHABLE 2 0 0 0 187,208,203 242,032 55555511113004006616113344226464 Notchable; fewest holes 2 2 0 0 25,445,702 74,908 50501131042204226633042204226666 Notchable; fewest holes 3 3 3 3 823,314,689 515,610 35350130113244221131113244226464 Notchable; fewest holes 3 0 0 0 149,310,783 222,660 55555511113004226616113344006464 Notchable; fewest holes 2 3 3 3 55,542,472 59,128 05050130113244221131113244226464 Notchable; fewest holes 3 3 0 0 16,791,186 56,621 05051131042204226633042204226666 Notchable; fewest holes 2 2 3 3 3,026,411 29,204 55550130113044551100113024220606 Notchable; fewest holes 2 3 0 0 1,865,671 13,777 55555511113004000016113344226464 Notchable; fewest holes 2 2 3 0 14,862 0 55351130000354221111110324623636 First occurrence 3 3 3 0 1,614 0 50505133042300221131042604600606 First occurrence 4 4 4 4 99,318,351 111,851 35350110513254221111013364663636 Notchable; fewest holes 4 0 0 0 72,998,623 91,701 55551105513554221106613664226666 Notchable; fewest holes 3 4 4 4 26,380,651 40,725 50500130113244221131113244226464 Notchable; fewest holes 2 4 4 4 6,652,268 16,402 50500130113504001131113644226464 Notchable; fewest holes 4 4 0 0 5,858,634 3,066 54540115003524221111003664666666 Notchable; fewest holes 3 4 0 0 2,507,288 1,796 55555511113004220016113344006464 Notchable; fewest holes 2 4 0 0 1,551,174 2,189 05050130143024221101143324223636 Notchable; fewest holes 3 3 4 4 1,425,476 14,503 50500115013504221111013364003636 Notchable; fewest holes 2 2 4 4 582,279 8,520 55555530013044551130113044220606 Notchable; fewest holes 2 3 4 4 399,507 4,369 50500130043004221136643664006666 Notchable; fewest holes 3 3 4 0 81,576 0 35350011113354220630643064266666 First occurrence 2 4 4 0 23,359 0 55551100513504221110113224626666 First occurrence 4 4 4 0 17,364 0 54550011113354221003613364063636 First occurrence 2 2 3 4 8,945 0 35055113042500501113043300226060 First occurrence 2 3 4 0 6,703 0 05551101013004001101403004226466 First occurrence 3 4 4 0 5,407 0 54550011113354221003613364066666 First occurrence 2 2 4 0 789 0 05355105043000221131043000020606 First occurrence 3 3 3 4 49 0 50505133042300221131042600600606 First occurrence 5 0 0 0 26,632,759 22,226 55551135510554221136610664226666 Notchable; fewest holes 5 5 5 5 15,086,540 19,591 50500130113224221131113224223636 Notchable; fewest holes 4 5 5 5 9,041,227 6,205 55550110013554551116013624226464 Notchable; fewest holes 4 4 5 5 3,626,396 1,786 54540130143204221131143204226060 Notchable; fewest holes 3 5 5 5 2,645,817 8,189 50500130113044221131113044223636 Notchable; fewest holes 4 5 0 0 2,315,098 2,934 54540115003544221111003664226666 Notchable; fewest holes 2 5 5 5 1,944,047 4,910 05550100513554221101013664666666 Notchable; fewest holes 2 4 5 5 823,645 1,249 05050130143024221131143024223636 Notchable; fewest holes 3 5 0 0 635,101 1,292 50500115003544221111003664666666 Notchable; fewest holes 5 5 0 0 490,006 655 54540100143324221131143024220606 Notchable; fewest holes 3 4 5 5 319,204 474 50500130003544001133003344226666 Notchable; fewest holes 2 2 5 5 259,762 1,838 50500133043304221133043304006666 Notchable; fewest holes 3 3 5 5 248,050 1,809 50500100113044221130113044226666 Notchable; fewest holes 2 5 0 0 128,904 225 05050100043020221131443000666666 Notchable; fewest holes 2 4 4 5 109,099 0 55551100513504221110113224226666 First occurrence 4 4 4 5 85,311 0 35551100513504221110113224223666 NELSON 4-HOLE 2 3 5 5 51,417 702 05050110003204221110043204226666 Notchable; fewest holes 4 4 5 0 32,779 0 55550011113354220603643364266666 NELSON 3 3 4 5 6,879 0 35051100143020521130043200223606 First occurrence 3 4 4 5 6,341 0 55550011113354221603643304066666 First occurrence 4 5 5 0 3,516 0 54550011113524221003613364063636 First occurrence 3 4 5 0 3,338 0 50541101013554551116003064226066 First occurrence 3 5 5 0 2,718 0 35051101013004001101403004226466 First occurrence 5 5 5 0 2,265 0 35051103103554521103102224223666 First occurrence 2 3 4 5 1,467 0 55550000003004221100613604226666 First occurrence 2 2 4 5 919 0 50500133003004001130003304226666 First occurrence 2 5 5 0 713 0 05055135042502501133040000220606 First occurrence 3 3 5 0 457 0 54551131142222000630643062266666 MARINEAU'S 10/12 2 2 5 0 430 0 50500130003054251101003004226060 First occurrence 2 4 5 0 370 0 50500000013204221110043024226660 First occurrence 2 2 3 5 20 0 54505130400004221136100004006060 First occurrence 2 3 5 0 14 0 50500100003004221110403064266460 First occurrence 3 3 3 5 2 0 54550011143000006103143000223606 First occurrence 6 0 0 0 1,407,765 1,752 55550130042000551131442660226666 Notchable; fewest holes 6 6 6 6 929,995 539 54541105413520221106413620226464 Notchable; fewest holes 4 6 6 6 374,315 293 35351103510254221103610264223636 Notchable; fewest holes Level-Type General-Count Notch-Cnt --Example Assembly (LL format)-- Example Description- ----------- -------------- --------- -------------------------------- -------------------- 5 6 6 6 300,045 119 35350130143050221131143060663636 Notchable; fewest holes 2 6 6 6 229,701 375 05050100513324221101013324226464 Notchable; fewest holes 3 6 6 6 182,120 206 50500105013324221101013324226464 Notchable; fewest holes 4 6 0 0 124,432 670 35350103540254221103600264223636 Notchable; fewest holes 5 6 0 0 81,012 123 05050130540054001136640664226666 Notchable; fewest holes 2 2 6 6 76,257 126 50550115013004001116013644226464 Notchable; fewest holes 4 4 6 6 56,351 11 00005505013544551130113024226666 Notchable; fewest holes 3 6 0 0 49,470 117 50500100003024221131003664666666 Notchable; fewest holes 6 6 0 0 37,483 0 35050030043020021130143320220666 L44AA CASE 4 5 6 6 34,528 9 55500105513504221101013304006464 Notchable; fewest holes 5 5 6 6 30,186 0 05051135513544226030013644663636 First occurrence 2 6 0 0 27,795 267 05050100003024221101043664666666 Notchable; fewest holes 3 5 6 6 27,177 5 54540133140020221131140004206060 Notchable; fewest holes 2 5 6 6 25,967 1 55500130142000001131142004226060 Notchable; fewest holes 3 3 6 6 14,199 17 50500105003504221136603664006666 Notchable; fewest holes 2 4 6 6 11,300 4 05050100143000221131143060666606 Notchable; fewest holes 3 4 6 6 7,408 0 54551101013004501106613604226060 First occurrence 2 3 6 6 4,037 11 05050130103004001131100224226606 Notchable; fewest holes 5 5 5 6 3,386 0 35051103103554551103102224223666 First occurrence 4 5 5 6 1,947 0 05051110013024521133013204223636 First occurrence 2 5 5 6 1,699 0 35051110013024521130013204223636 First occurrence 3 5 5 6 1,108 0 54540533013004051130003304226464 First occurrence 2 2 5 6 902 0 05055105003004001116003064226666 First occurrence 2 4 4 6 780 0 35351101013004051116003064226066 First occurrence 4 6 6 0 509 0 55545111113340251100003240226664 First occurrence 4 4 4 6 488 0 35351101013004051116003064226466 First occurrence 5 5 6 0 463 0 35055111013044001116003064226066 First occurrence 4 4 5 6 459 0 35351101013044001116003064226066 First occurrence 4 5 6 0 393 0 04005115403504521116003204226664 First occurrence 3 4 6 0 382 0 04005115003504521116003244226664 First occurrence 2 4 5 6 346 0 05055100003004051116003064226666 First occurrence 4 4 6 0 291 0 55350011110324220613640364263636 First occurrence 3 5 6 0 183 0 50500500013204221110043024226660 First occurrence 3 4 5 6 116 0 54541110413024021100013204226060 First occurrence 3 3 4 6 60 0 50500135043504001131042222003666 First occurrence 2 3 5 6 49 0 50500000113004051100643604226666 First occurrence 3 3 5 6 37 0 50500100113004051100643604223666 First occurrence 3 3 6 0 36 0 55351130140350221100040300620636 First occurrence 5 6 6 0 36 0 50505100143024221100003064266460 First occurrence 2 6 6 0 10 0 50500111503054251110003004226060 First occurrence 2 4 6 0 8 0 00500500513054251100113324226060 First occurrence 2 3 6 0 4 0 35350011113044000100043064220606 First occurrence 2 3 4 6 1 0 50500130140054251130000004226060 First occurrence 7 7 7 7 208,430 107 54541135410520221136410620226464 Notchable; fewest holes 7 0 0 0 201,721 522 05050100013224221131013644666464 Notchable; fewest holes 5 7 7 7 94,299 0 35350011113244226603643364223636 NELSON 6 7 7 7 42,751 3 54540105103542001106103642226464 Notchable; fewest holes 4 7 7 7 36,501 1 50500130003524221131000004000666 Notchable; fewest holes 5 6 7 7 12,254 6 54540135140024221131140000200606 Notchable; fewest holes 4 7 0 0 11,912 20 54540133140224221131140000006060 Notchable; fewest holes 7 7 0 0 11,854 0 35050030043020051130143320220666 L44AA CASE 5 7 0 0 10,624 0 35550530013044551130613344220636 First occurrence 3 7 7 7 9,343 14 05050130443250221100043000006666 Notchable; fewest holes 2 7 0 0 7,598 0 05551101013004001101403044223666 First occurrence 3 7 0 0 6,510 8 05055533510044221130113044006606 Notchable; fewest holes 6 7 0 0 6,094 0 35350011113254220603643364203636 First occurrence 2 7 7 7 4,862 1 05050130003044001131000224226606 Notchable; fewest holes 5 5 7 7 4,794 0 35550011113544220603043224223636 First occurrence 6 6 7 7 4,042 0 04000530503054256111103004226060 First occurrence 3 5 7 7 3,061 1 50500130140000021131143200220666 Notchable; fewest holes 4 5 7 7 3,016 0 55550011113544220603043224223636 First occurrence 4 4 7 7 2,634 0 54500035400520221130410620226460 First occurrence 2 5 7 7 1,963 0 50501110013044221133013004066606 First occurrence 4 6 7 7 1,536 0 55550130510004501136110044226060 First occurrence 3 3 7 7 1,288 0 50501110013004221133013044006606 First occurrence 2 2 7 7 1,138 1 50500130003524221101003004006606 Notchable; fewest holes 3 6 7 7 1,017 1 50500100003504001131003224226606 Notchable; fewest holes 3 4 7 7 935 0 55351100410344001101100344226636 First occurrence Level-Type General-Count Notch-Cnt --Example Assembly (LL format)-- Example Description- ----------- -------------- --------- -------------------------------- -------------------- 2 3 7 7 480 0 50501110013004221133013004006606 First occurrence 2 4 7 7 463 0 05051130140002021133443200223606 First occurrence 2 6 7 7 287 0 05050130000004221131003644620606 First occurrence 4 4 5 7 263 0 35355135040004001131642222000606 First occurrence 4 5 7 0 238 0 05550030112004001130043004226060 First occurrence 5 7 7 0 182 0 35551101013004221101403004006466 First occurrence 4 6 7 0 122 0 35350011113354000110643004226666 First occurrence 4 7 7 0 112 0 35550103003004001110003004226466 First occurrence 3 5 5 7 78 0 50500100003024221131003204226606 First occurrence 5 6 7 0 75 0 04005115413504521106113204226464 First occurrence 3 5 7 0 72 0 35050103013004001106403004226466 First occurrence 4 5 5 7 72 0 55541130143040001133642222006664 First occurrence 3 4 5 7 64 0 35051103100544551103040004223666 First occurrence 5 5 7 0 54 0 05055105003004221131003004620606 First occurrence 3 5 6 7 26 0 54501100143204251100003024226460 First occurrence 4 4 7 0 22 0 35550103003004001101403004226466 First occurrence 4 4 6 7 22 0 00500530513354251130110024226060 First occurrence 3 3 4 7 22 0 55540101103340221130003340006664 First occurrence 2 5 5 7 21 0 50500110113004501100613604226664 First occurrence 2 3 4 7 8 0 05050130000004221131003604620606 First occurrence 3 4 6 7 8 0 35350011113044000100643004226660 First occurrence 2 2 5 7 6 0 50500110013004501100643604226664 First occurrence 5 5 6 7 5 0 50500110113304001100613604226664 First occurrence 3 4 7 0 3 0 35050103003004001101403004226466 First occurrence 4 6 6 7 2 0 00005105013504521106443304226660 First occurrence 2 5 6 7 2 0 55505130140004501131040600226060 First occurrence 2 3 5 7 1 0 50500100113004001100643604226664 First occurrence 4 5 6 7 1 0 05055130043054001131142222006606 First occurrence 6 8 8 8 12,995 0 55550130510004501631110024226060 First occurrence 8 0 0 0 11,562 17 05050100013244221131013204226660 Notchable; fewest holes 8 8 8 8 10,409 2 50500105143500201101143624226060 Notchable; fewest holes 2 8 8 8 3,601 0 54551101013204221100613264006606 First occurrence 5 8 8 8 3,209 3 35350130100054021131103264220606 Notchable; fewest holes 4 8 8 8 2,632 1 50500130003524221131000044000666 Notchable; fewest holes 3 8 0 0 2,199 2 05550000513004021106113604226060 Notchable; fewest holes 7 8 8 8 1,929 0 35350011113254226003413644603636 First occurrence 7 8 0 0 1,921 0 35350011113354220603643264203636 First occurrence 4 8 0 0 1,360 0 35350011113254220603643304266666 First occurrence 3 8 8 8 1,276 1 50500130003524221101003044006606 Notchable; fewest holes 6 8 0 0 1,248 3 05550110503004001111603264223636 Notchable; fewest holes 5 8 0 0 1,170 0 35355003442222551103442600223666 First occurrence 8 8 0 0 794 0 50500003103304501103103304226466 First occurrence 6 6 8 8 751 0 50501101143524521106143000226060 First occurrence 3 6 8 8 539 0 50501133140002021130643200220636 First occurrence 4 5 8 8 447 0 55351101510344051110000364226636 First occurrence 2 8 0 0 387 0 05050030140000221130140224226636 First occurrence 4 4 8 8 373 0 50545035102040001130103040226664 First occurrence 2 2 8 8 312 0 50550130443004001110443204226060 First occurrence 6 7 8 8 309 0 00005035113544521116143344226660 First occurrence 5 6 8 8 303 1 50500105143000201101143624226060 Notchable; fewest holes 5 5 8 8 302 0 50501130142222501130643300006636 First occurrence 3 3 8 8 120 0 00005135003504521131002004223666 First occurrence 7 7 8 8 93 0 50545105003040001113003342226664 First occurrence 5 7 8 8 87 0 50500110013304001106113604226464 First occurrence 3 5 8 8 72 2 05550110513004001116013604226060 Notchable; fewest holes 2 3 8 8 70 0 50550100513054001111013004226466 First occurrence 4 6 8 8 66 0 05051131103224521130100004223606 First occurrence 4 7 8 8 61 0 55540110503004221110603664006060 First occurrence 3 4 8 8 61 0 35555103410044221103400044003666 First occurrence 2 5 8 8 56 0 55500003113004001113143304220606 First occurrence 2 4 8 8 35 0 55500033113004001133043004220606 First occurrence 2 6 8 8 17 0 55500033113004001130643304220606 First occurrence 6 8 8 0 4 0 50505130140024221130000064266460 First occurrence 4 4 5 8 3 0 00005115443500521136413600226460 First occurrence 6 6 8 0 2 0 50505130140024221130000064266060 First occurrence 3 5 8 0 2 0 00045115013504521106443604226660 First occurrence 2 7 8 8 2 0 50500110003304001106103604226464 First occurrence 3 3 4 8 2 0 50500135043504001131142222006636 First occurrence Level-Type General-Count Notch-Cnt --Example Assembly (LL format)-- Example Description- ----------- -------------- --------- -------------------------------- -------------------- 3 4 5 8 2 0 05050130543054001131142222006664 First occurrence 4 5 6 8 1 0 00005135140500521131043200223666 First occurrence 9 0 0 0 3,484 16 50500100013224221131013224226464 Notchable; fewest holes 5 9 9 9 603 0 00005115403544521116603344223636 First occurrence 7 9 0 0 496 0 35051133103554221130000604620606 First occurrence 4 9 9 9 380 0 55350000140344021100140344226636 First occurrence 9 9 9 9 309 0 35050013543554220011113224623636 First occurrence 7 9 9 9 211 0 35350011113244226603043644603636 First occurrence 8 9 9 9 161 0 55351100412344221101100304000636 First occurrence 5 9 0 0 158 0 05050130000504521131003664220606 First occurrence 2 9 0 0 152 0 05055130040052001131640020220606 First occurrence 8 8 9 9 126 0 00005035113524521111643044226606 First occurrence 5 5 9 9 105 0 00005005013504521110403044223666 First occurrence 6 9 9 9 88 0 04005005113554521111443264220606 First occurrence 3 9 0 0 79 0 50550000113024001100043324220606 First occurrence 6 7 9 9 68 0 04005035113554521116143304226060 First occurrence 4 9 0 0 65 0 50500100003524221131003004006466 First occurrence 4 6 9 9 64 0 05051131143200221133140002220606 First occurrence 4 8 9 9 61 0 00005015113524521100613044226606 First occurrence 4 4 9 9 58 0 55350000140302001100140304226636 First occurrence 6 6 9 9 36 0 50501131143200221133140002226060 First occurrence 3 9 9 9 35 0 35055113440222001113640004223606 First occurrence 6 9 0 0 21 0 35551100143004001100003264220606 First occurrence 5 7 9 0 12 0 35550103013004221106403004006466 First occurrence 7 8 9 9 6 0 00005015113524521130613044226606 First occurrence 4 5 9 9 3 0 05350000140302501100140304226636 First occurrence 5 5 9 0 3 0 35550103003004221101403004006466 First occurrence 5 7 9 9 3 0 55500130510004001133040604226060 First occurrence 7 7 9 9 3 0 54550100143004001110003264220606 First occurrence 9 9 0 0 2 0 50501100013524221131003004006466 First occurrence 4 6 10 10 145 1 05550110503004001116603664226666 L46AA Notchable 4 4 10 10 101 1 54540130140000201131140024226060 Notchable; fewest holes 10 0 0 0 57 0 35350030043044251130143344220666 HORDERN/PJM 5 9 10 10 34 0 55355131140304001130642222000636 First occurrence 4 10 0 0 10 0 00005105013544521131003204226466 First occurrence 5 10 0 0 10 0 05050100013254221101043004003666 First occurrence 10 10 10 10 6 0 05550033010024001131040024220606 First occurrence 4 5 10 10 5 0 55355131140304001130642222000606 First occurrence 4 10 10 10 2 0 50501135103244221100003224006060 First occurrence 4 9 10 10 1 0 55545133143040001136042222006060 First occurrence 7 10 0 0 1 0 05051100013254221101043004003666 First occurrence 6 10 10 10 1 0 50505133140002551131042000220606 First occurrence 12 0 0 0 1 0 35550030542024221131642000220606 LOVE'S DOZEN ----------- -------------- --------- -------------------------------- -------------------- Totals 35,657,131,235 13,354,991