Holey 6 Piece Burr – Notchable

内部空間のある Holey 6 Piece Burr の解の分布を示す。

Notchable

Notchable だけを使った構成のうち、Notchable32 以外を含む構成を示す。 Notchable32 でない Notchable は次の 34駒。

275	290	307	326	343
375	394	411	426	443
462	479	494	511	533
550	567	597	631	652
669	686	703	716	733
750	767		1416	1418
1448	1932	1934	2835	2839

分解不可能なものを含めた組み合わせは 1,027,210通り(除鏡像514,538通り)ある。穴の数による内訳は以下のとおり。Notchable32を使わない解はない。長さ12は長さ10と同じ。

Length 6
Holes	Combi	Apart	Assm	Unique Solutions					Non-Unique Solutions
Holes	Combi	Apart	Assm	1 move	2	3	4	5	max 1 move	2	3	4	5	6	7	8	9
1	983	1,660	1,980	584					399
2	5,282	10,006	12,941	2,790	26	4			2,374	88
3	18,829	46,577	68,159	7,835	641	66	10	6	8,800	1,363	94	6	8
4	46,933	149,886	249,786	13,885	2,190	380	51	20	22,858	6,286	1,010	167	86
5	84,432	373,669	698,758	14,852	3,428	904	112	32	42,146	16,750	4,700	1,004	494		10
6	111,869	758,167	1,515,185	9,249	2,996	1,382	272	62	51,725	27,905	13,335	3,427	1,456	10	50
7	112,091	1,277,311	2,579,506	3,422	1,480	1,466	314	54	41,027	29,677	23,847	7,558	3,130	34	80		2
8	88,776	1,817,662	3,505,820	888	467	1,098	206	32	20,976	19,887	28,554	11,742	4,703	157	66
9	58,748	2,211,740	3,863,685	134	118	580	86	8	7,228	9,496	22,798	12,458	5,286	418	134		4
10	33,345	2,304,753	3,466,988	14	34	136	10		1,906	3,945	12,916	9,223	4,338	625	184	8	6
11	16,732	2,030,777	2,597,632			16			528	1,916	6,056	4,942	2,594	538	134	2	6
12	7,629	1,470,591	1,639,211						205	1,213	2,880	1,999	1,038	248	42		4
13	3,175	847,874	870,504						103	882	1,264	618	254	52	2
14	1,222	383,921	384,295						57	588	433	122	18	4
15	430	137,832	137,832						32	318	76	4
16	137	38,386	38,386						24	105	8
17	40	7,840	7,840						16	24
18	9	1,018	1,018						9
19	2	64	64						2
Total	590,664	13,869,734	21,639,590	53,653	11,380	6,032	1,061	214	200,415	120,443	117,971	53,270	23,405	2,086	702	10	22
MaxMoves				1.2	2.5	3.3	4.6	5.4	1.2.2	2.5	3.6	4.6	5.5	6.2.2	7.2	8.2	9.2
MaxApart									896	1,832	2,352	1,920	3,054	1,693	1,005	263	399
MaxAssm				34	40	448	228	144	992	1,832	2,352	2,448	3,072	1,824	1,056	416	576

Length 8
Holes	Combi	Apart	Assm	Unique Solutions					Non-Unique Solutions
Holes	Combi	Apart	Assm	1 move	2	3	4	5	max 1 move	2	3	4	5	6	7	8
1	983	1,660	1,980	584					399
2	5,282	10,006	12,941	2,790	26	4			2,374	88
3	18,815	46,549	68,089	7,837	641	66	8		8,800	1,363	96	4
4	46,844	149,629	249,018	13,897	2,190	388	28		22,864	6,314	1,022	135	6
5	84,084	371,499	693,520	14,910	3,380	924	88	10	42,342	16,796	4,686	792	144	2	10
6	111,121	747,789	1,497,521	9,313	2,900	1,442	226	24	52,619	27,805	13,153	2,931	637	21	50
7	110,853	1,242,259	2,533,638	3,498	1,356	1,534	210	22	42,950	29,407	23,198	6,734	1,800	64	80
8	87,366	1,727,106	3,427,449	927	415	1,174	162	8	23,467	19,730	27,611	10,317	3,375	148	32
9	57,712	2,032,974	3,797,997	162	90	666	66	6	9,152	9,436	22,556	10,848	4,452	270	4	4
10	32,896	2,040,812	3,436,834	24	22	202	6		2,842	3,764	13,235	8,121	4,188	466	16	10
11	16,590	1,752,454	2,587,320			26			811	1,640	6,051	4,608	2,866	564	22	2
12	7,592	1,277,005	1,637,035			2			253	991	2,457	1,977	1,435	463	10	4
13	3,171	772,204	870,440						103	754	914	642	504	232	20	2
14	1,222	371,838	384,295						57	511	290	166	125	59	14
15	430	137,568	137,832						32	280	74	20	16	8
16	137	38,386	38,386						24	96	17
17	40	7,840	7,840						16	24
18	9	1,018	1,018						9
19	2	64	64						2
Total	585,149	12,728,660	21,383,217	53,942	11,020	6,428	794	70	209,116	118,999	115,360	47,295	19,548	2,297	258	22
MaxMoves				1.2	2.5	3.2.2	4.6	5.4	1.2.2	2.5	3.6	4.6	5.5	6.2.2	7.2	8.2
MaxApart									896	1,832	1,222	1,536	2,344	2,043	2,835	694
MaxAssm				34	40	688	456	228	992	1,832	1,224	2,448	2,448	3,072	3,072	864

Length 10
Holes	Combi	Apart	Assm	Unique Solutions					Non-Unique Solutions
Holes	Combi	Apart	Assm	1 move	2	3	4	5	max 1 move	2	3	4	5	6	7	8	9	10
1	983	1,660	1,980	584					399
2	5,282	10,006	12,941	2,790	26	4			2,374	88
3	18,815	46,549	68,089	7,837	641	66	8		8,800	1,363	96	4
4	46,844	149,629	249,018	13,897	2,190	388	28		22,864	6,314	1,022	135	6
5	84,084	371,489	693,520	14,910	3,380	924	88	10	42,344	16,798	4,688	788	142	2	10
6	111,121	747,669	1,497,521	9,313	2,900	1,442	226	24	52,627	27,829	13,165	2,903	621	21	50
7	110,831	1,241,027	2,531,848	3,498	1,356	1,536	210	18	42,992	29,541	23,188	6,624	1,724	64	80
8	87,308	1,721,216	3,420,383	927	415	1,184	148	10	23,533	19,992	27,619	10,133	3,179	136	32
9	57,654	2,014,356	3,791,169	162	90	682	64	6	9,244	9,796	22,502	10,712	4,200	190	2	2		2
10	32,866	1,998,536	3,434,098	24	22	208	2		2,952	4,049	13,047	8,169	4,084	293	8	8
11	16,582	1,683,256	2,587,108			28			867	1,828	5,839	4,680	2,988	334	12	4		2
12	7,590	1,197,623	1,637,003			2			266	1,059	2,283	2,017	1,680	275	8
13	3,171	711,684	870,440						107	766	718	684	748	134	12	2
14	1,222	344,032	384,295						57	492	152	203	265	43	10
15	430	131,278	137,832						32	256	20	30	84	8
16	137	37,806	38,386						24	88	3		22
17	40	7,818	7,840						16	20			4
18	9	1,018	1,018						9
19	2	64	64						2
Total	584,971	12,416,716	21,364,553	53,942	11,020	6,464	774	68	209,509	120,279	114,342	47,082	19,747	1,500	224	16	0	4
MaxMoves				1.2	2.5	3.2.2	4.6	5.1.2	1.2.2	2.5	3.6	4.6	5.5	6.2	7.2	8.2		10
MaxApart									896	1,832	962	1,536	2,344	2,011	2,664	694		77
MaxAssm				34	40	688	456	480	992	1,832	1,056	2,448	3,072	2,448	3,072	864		112

Name	Pieces	Holes	Length	Moves	Sol	Designer
Notchable Unique 2.5 Moves 4 Holes	153 343 703 959 991 1006	4	6+	2.5	1 / 1
Notchable Unique 2.5 Moves 4 Holes	153 479 686 887 959 991	4	6+	2.5	1 / 1
Notchable Unique 3 Moves 2 Holes #1	119 187 791 887 1023 1932	2	6+	3	1 / 1
Notchable Unique 3 Moves 2 Holes #1	119 187 910 1006 1023 2835	2	6+	3	1 / 1
Notchable Unique 3 Moves 2 Holes #2	119 187 275 910 1023×2	2	6+	3	1 / 2
Notchable Unique 3 Moves 2 Holes #2	119 187 652 791 1023×2	2	6+	3	1 / 2
Notchable Unique 4.6 Moves Length 6	443 767 870 887 927×2	6	6	4.6	1 / 4
Notchable Unique 4.6 Moves Length 6	511 733 870 927×2 1006	6	6	4.6	1 / 4
Notchable Unique 4.6 Moves Length 8	343 411 669 887 1023×2	6	8+	4.6	1 / 4
Notchable Unique 4.6 Moves Length 8	411 669 686 1006 1023×2	6	8+	4.6	1 / 4
jvk's favorite notchable burr	102 255 669 927 974 1023	3	6	5.4	1 / 4	Jürg von Känel
jvk's favorite notchable burr	102 255 411 823 927 1023	3	6	5.4	1 / 4	Jürg von Känel
Notchable Unique 5 Moves 3 Holes #2	119 153 255 411 959 1023	3	6	5.4	1 / 8
Notchable Unique 5 Moves 3 Holes #2	119 153 255 669 991 1023	3	6	5.4	1 / 8
Notchable Unique 5 Moves 3 Holes #3	187 255 326 927 974 1023	3	6	5.2	1 / 5
Notchable Unique 5 Moves 3 Holes #3	187 255 550 823 927 1023	3	6	5.2	1 / 5
Notchable Unique Most Holes	255×2 511×2 887 1023	12	8+	3	1 / 24
Notchable Unique Most Holes	255×2 767×2 1006 1023	12	8+	3	1 / 24
Favorite Level 5.4 Notchable Burr	119 187 411 927 959 1023	5	6	5.4	1 / 24	David V. Winkler
Favorite Level 5.4 Notchable Burr	119 187 669 927 991 1023	5	6	5.4	1 / 24	David V. Winkler
Complex Level 5.4 Notchable Burr	479×2 669 703 767 991	8	6	5.4	1 / 144	David V. Winkler
Complex Level 5.4 Notchable Burr	411 479 511 703×2 959	8	6	5.4	1 / 144	David V. Winkler
L46AA Notchable	153 479 494 1023×3	9	10+	10 max	36 / 56	Bill Cutler
	153 479 494 1023×3		8	6 max	36 / 56
	153 631 703 1023×3		8	6 max	36 / 56
	153 631 703 1023×3		6	5 max	44 / 56
L5 Notchable Most Assemblies	187 255 411 767×2 1023	8	10+	5	1 / 480	Bill Cutler
L5 Notchable Most Assemblies	187 255 511×2 669 1023	8	10+	5	1 / 480	Bill Cutler
Notchable Unique 5 Moves Length 8 Most Assemblies	255×2 411 479 511 959	8	8	5	1 / 228
Notchable Unique 5 Moves Length 8 Most Assemblies	255×2 669 703 767 991	8	8	5	1 / 228
Notchable Unique Most Assemblies	187 255 479 511 703 991	8	8+	3	1 / 688
Notchable Unique Most Assemblies	187 255 479 703 767 959	8	8+	3	1 / 688
Notchable Most Assemblies & Most Solutions	479 511 767 959 991 1023	14	6	5 max	3,054 / 3,072
Notchable Most Assemblies & Most Solutions	511 703 767 959 991 1023	14	6	5 max	3,054 / 3,072
Notchable 9 Moves 7 Holes	153 343 511 1006 1023×2	7	6	9.2 max	16 / 26
Notchable 9 Moves 7 Holes	153 686 767 887 1023×2	7	6	9.2 max	16 / 26
Notchable 10 Moves 11 Holes	411 479 494 1023×3	11	10+	10 max	77 / 112
Notchable 10 Moves 11 Holes	631 669 703 1023×3	11	10+	10 max	77 / 112
Notchable Impossible Most Assemblies 9 Holes	187 479 511×2 703 767	9	6+	0	0 / 1,224
	187 479 511 703 767×2	9	6+	0	0 / 1,224
	255 443 479 511 703 767	9	6+	0	0 / 1,224
	255 479 511 703 733 767	9	6+	0	0 / 1,224

Jul 28, 2002 by k16@chiba.email.ne.jp