Caged 6 Piece Burr – Millable

Caged Burr 枠内に組む Caged 6 Piece Burr の解の分布を示す。

Millable

Notchable と Millable を使った構成のうち、Millable を含む構成を示す。枠は、Type-3 のもののみを解析。

Type-3

XXXXXX | X....X | X....X | X....X | X....X | XXXXXX
X....X | ...... | ...... | ...... | ...... | X....X
X....X | ...... | ...... | ...... | ...... | X....X
X....X | ...... | ...... | ...... | ...... | X....X
X....X | ...... | ...... | ...... | ...... | X....X
XXXXXX | X....X | X....X | X....X | X....X | XXXXXX

分解不可能なものを含めた組み合わせは 3,444,549通り(除鏡像1,723,814通り)ある。穴の数による内訳は以下のとおり。

Length 6 (Type-3)
Holes	Combi	Apart	Assm	Unique Solutions															Non-Unique Solutions
Holes	Combi	Apart	Assm	1 move	2	3	4	5	6	7	8	9	10	11	12	13	14	15	max 1 move	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	27	28	29	30
0	4	8	8																4
1	54	82	144	34															20
2	357	655	1,466	217															136	4
3	926	3,064	6,710	314															576	36
4	1,503	10,706	33,080	110	8														1,107	278
5	3,153	34,344	127,779	30	130	8													1,821	1,126	36	2
6	8,569	88,073	439,516	78	634	20	4												3,472	4,055	258	30	18
7	21,570	194,118	1,442,422	92	1,594	72		60		18	4	12							6,269	12,266	895	146	114	18	6	4
8	39,995	389,302	3,804,755	24	2,902	202		348	6	170	12	72	30	14					7,938	24,718	2,025	554	668	130	82	52	28	18			2
9	55,143	662,922	7,773,270	6	3,200	244	6	608	26	336	72	138	146	52	30	2			6,547	33,644	3,808	1,448	2,488	612	714	254	266	230	106	66	30	46	4	10	2	2
10	50,126	943,487	10,432,319	8	1,534	72	8	438	14	152	118	100	154	62	34	4	2	2	2,678	25,677	4,752	1,878	4,450	1,671	1,861	790	838	932	586	528	232	291	75	94	41	22	16	10							2
11	29,132	1,118,986	8,734,868		226	24	4	124	14	8	22	12	44	8	10	4	2		324	8,860	3,002	1,056	3,294	1,906	1,852	1,162	1,224	1,426	1,118	1,078	534	654	328	332	210	104	92	40	12	8	2	2	2		4		4
12	12,259	1,099,164	4,832,669		8			6			2								25	1,674	774	276	894	915	858	652	779	893	761	834	479	628	450	499	324	189	194	66	26	16	17	4	4	4	2	4	2
13	4,266	842,266	1,940,612																	294	110	52	176	276	202	198	322	324	272	254	240	308	270	304	186	182	168	42	38	14	30			4
14	1,338	438,084	606,440																	82	12	6	72	85	37	66	68	64	108	55	135	102	100	114	66	62	44	18	16	6	20
15	376	134,918	143,424																	62	8		20	20	22	16	22	10	16	8	58	34	26	22	18	2	8	4
16	97	24,086	24,112																	33	20				8	8	6	2	8	8					2	2
17	20	2,560	2,560																	16	4
18	4	128	128																	4
Total	228,892	5,986,953	40,346,282	913	10,236	642	22	1,584	60	684	230	334	374	136	74	10	4	2	30,917	112,829	15,704	5,448	12,194	5,633	5,642	3,202	3,553	3,899	2,975	2,831	1,710	2,063	1,253	1,375	849	565	522	180	92	44	69	6	6	8	8	4	6
MaxMoves				1.17.2 .4	2.11.2 .3.2.2	3.9.1 .2.2	4.10.4 .4.2.2	5.17.4 .2.2.2	6.8.3 .2	7.15.3 .3.2	8.6.3 .6.2	9.16.3 .3.2	10.7.3 .5.2	11.7.3 .4.2.2	12.10.3 .4.2.2	13.2.2 .2.2	14.2.3	15.2.3 .2	1.18.2 .4.2.2	2.17.3 .4.2.2	3.13.2 .2.2.2	4.11.2 .2	5.17.4 .2.2.2	6.14.3 .3.2.2	7.15.3 .3.3.2	8.15.1 .2.2	9.16.3 .3.2	10.16.2 .4.2.2	11.12.3 .4.2	12.16.2 .4.2.2	13.14.3 .3.2.2	14.16.3 .3.2.2	15.10.3 .4.2	16.16.3 .3.2	17.16.3 .3.2	18.16.3 .2.2	19.15.3 .4.2.2	20.6.2 .2	21.9.2 .4.2.2	22.11.2 .3.2	23.3.1 .2	24.3.1 .5.2.2	25.2.2 .2	27.3.2 .3	28.3.3 .4	29.2	30.2
MaxApart																			248	252	370	342	349	460	512	510	640	689	640	640	978	1,793	1,784	1,399	2,104	1,961	1,403	1,108	1,076	753	1,482	112	57	118	113	169	67
MaxAssm				112	448	176	64	1,536	768	384	1,376	1,376	1,392	336	1,376	106	688	896	1,392	2,464	1,392	2,464	3,072	3,072	3,072	2,448	1,376	2,464	1,728	2,464	2,464	3,072	3,072	3,072	3,072	3,072	3,072	3,072	1,728	1,536	1,920	240	192	200	212	448	150

Length 8 (Type-3)
Holes	Combi	Apart	Assm	Unique Solutions						Non-Unique Solutions
Holes	Combi	Apart	Assm	1 move	2	3	4	5	7	max 1 move	2	3	4	5	6	7	8	9	11	13
0	4	8	8							4
1	42	68	86	24						18
2	205	413	818	121						80	4
3	572	1,938	4,382	198						342	32
4	1,052	6,710	20,858	114	12					737	189
5	2,165	20,886	87,751	32	96	6				1,137	858	36
6	5,642	56,145	306,032	32	450	16				2,005	2,890	249
7	13,630	126,158	999,572	20	1,144	46				3,365	8,238	785	32
8	25,552	251,173	2,619,653	4	1,876	98				4,285	17,401	1,696	192
9	35,201	432,618	5,285,928	4	1,712	132	6	4	8	3,533	26,294	2,882	600		26
10	34,891	616,871	7,455,353	6	646	72	8	8	32	1,775	27,106	3,785	1,224	16	191	22
11	23,540	716,998	6,892,774		142	20	4		24	388	16,974	3,560	1,630	78	584	120	10	4	2
12	11,245	664,347	4,321,313					6		27	6,409	2,129	1,408	112	926	174	36	8	10
13	4,202	480,902	1,913,588							2	1,556	792	764	106	764	114	78	8	18
14	1,338	260,322	606,440								343	226	243	75	298	36	95	8	12	2
15	376	96,534	143,424								96	68	56	16	70	8	56	2		4
16	97	21,758	24,112								43	30	12			2	10
17	20	2,560	2,560								16	4
18	4	128	128								4
Total	159,778	3,756,537	30,684,780	555	6,078	390	18	18	64	17,698	108,453	16,242	6,161	403	2,859	476	285	30	42	6
MaxMoves				1.8.3 .5	2.12.2 .2	3.3.2 .4.2	4.1.3 .6	5.8.2 .2.2	7.6.2	1.11.3 .5	2.12.4 .6.2.2	3.11.3 .4.2	4.4.3	5.11.4 .5	6.12.4 .5.2.2	7.6.2	8.10.4 .4.2	9.12.4 .3.2	11.5.2	13.2
MaxApart										200	448	1,097	1,170	1,160	1,110	266	1,054	298	138	434
MaxAssm				72	356	134	26	96	192	1,392	3,072	3,072	2,464	1,536	3,072	768	1,920	576	384	960

Length 10 (Type-3)
Holes	Combi	Apart	Assm	Unique Solutions				Non-Unique Solutions
Holes	Combi	Apart	Assm	1 move	2	3	4	max 1 move	2	3	4	5
0	4	4	8	4
1	34	48	70	20				14
2	158	285	620	85				71	2
3	466	1,402	3,528	160				286	20
4	870	5,022	15,622	100	4			644	122
5	1,774	15,682	69,577	24	64	4		1,046	614	22
6	4,494	43,443	237,566	30	282	16		1,869	2,104	193
7	10,970	98,856	790,756	18	790	52		3,205	6,188	693	24
8	20,931	199,143	2,114,662	8	1,454	92	2	4,297	13,404	1,512	162
9	29,743	347,594	4,446,840		1,612	126	10	3,933	20,934	2,590	538
10	30,486	503,685	6,572,555		832	66	6	2,254	22,746	3,438	1,140	4
11	21,360	595,152	6,300,048		218	20	4	616	15,592	3,314	1,578	18
12	10,629	560,543	4,041,153		24			69	6,939	2,116	1,445	36
13	4,046	410,336	1,805,316					2	2,162	922	912	48
14	1,318	225,172	596,200						539	361	379	39
15	376	85,852	143,424						134	124	106	12
16	97	20,220	24,112						51	34	12
17	20	2,560	2,560						16	4
18	4	128	128						4
Total	137,780	3,115,127	27,164,745	449	5,280	376	22	18,306	91,571	15,323	6,296	157
MaxMoves				1.8.4	2.8	3.3.2.4.2	4.1.2	1.8.5.2.2	2.8	3.7.1.2.2	4.4.3	5.6.3
MaxApart								200	480	962	1,092	1,078
MaxAssm				80	480	134	120	1,392	3,072	3,072	2,464	1,536

Jan 4, 2004 by k16@chiba.email.ne.jp