Holey 6 Piece Burr – Millable

内部空間のある Holey 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。 Millable は次の 19駒。

分解不可能なものを含めた組み合わせは 3,443,382通り(除鏡像1,723,177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	1,546	2,386	3,360	1,054					486	6
2	8,208	14,926	25,458	4,604	345	66			2,896	255	35		7
3	32,739	71,920	151,056	13,430	2,574	784	40	18	12,283	2,718	690	94	108
4	95,160	263,813	674,133	26,118	7,861	3,308	220	74	36,411	13,674	5,725	1,013	754		2
5	196,021	762,980	2,301,837	31,060	12,754	6,708	764	210	72,567	38,920	24,742	5,260	3,016	6	14
6	288,937	1,793,387	6,063,367	21,253	11,844	8,129	1,874	334	91,987	66,889	61,187	16,849	8,502	53	34		2
7	312,280	3,479,550	12,172,155	8,168	6,092	7,186	2,558	366	70,435	70,714	93,287	35,610	17,394	348	118	4
8	254,785	5,587,945	18,002,350	1,838	1,589	4,972	1,602	254	30,947	45,789	91,407	49,320	25,314	1,287	446	16	4
9	159,513	7,398,640	19,296,398	204	260	1,696	372	58	7,202	18,432	58,533	43,734	25,436	2,678	878	22	8
10	79,305	7,918,909	15,431,975	8	26	244	10		845	5,213	25,477	26,393	17,003	3,224	830	18	14
11	33,428	6,628,552	9,694,312			10	2		122	1,430	8,862	12,084	8,248	2,224	428	6	12
12	12,566	4,148,605	4,860,441						41	721	3,571	4,378	2,977	771	103	4
13	4,280	1,872,164	1,941,104						24	606	1,688	1,174	636	126	22	4
14	1,338	605,088	606,108						16	478	626	170	32	12	4
15	376	143,424	143,424						4	280	92
16	97	24,100	24,100						7	90
17	20	2,560	2,560						4	16
18	4	128	128						4
Total	1,480,603	40,719,077	91,394,266	107,737	43,345	33,103	7,442	1,314	326,281	266,231	375,922	196,079	109,427	10,729	2,879	74	40
MaxMoves				1.3	2.5.1.2	3.4.2	4.6	5.4.2	1.3	2.5.2	3.6	4.6	5.5	6.2.2	7.2	8.2	9.2
MaxApart									256	1,536	1,920	2,833	2,895	2,352	3,044	766	336
MaxAssm				34	94	768	304	288	384	1,536	2,464	3,072	3,072	2,464	3,072	864	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	9
1	1,546	2,386	3,360	1,054					486	6
2	8,203	14,914	25,446	4,606	345	66			2,896	255	35
3	32,609	71,526	150,218	13,454	2,578	804	16		12,287	2,728	684	46	12
4	94,251	259,422	659,227	26,237	7,821	3,427	134	8	36,604	13,653	5,541	607	217		2
5	192,604	734,658	2,172,691	31,306	12,484	7,062	572	66	74,036	38,256	23,362	3,928	1,514	4	14
6	280,500	1,670,277	5,510,307	21,624	11,241	8,927	1,315	210	96,723	63,917	56,256	14,340	5,883	38	26
7	299,232	3,093,406	10,979,629	8,534	5,534	8,588	1,796	318	78,777	64,658	84,617	31,510	14,632	238	30
8	243,388	4,694,246	16,736,846	1,946	1,398	6,306	1,342	254	39,409	39,667	84,496	43,649	23,851	990	74	6
9	154,169	5,868,272	18,635,194	230	150	2,114	372	38	11,811	15,204	56,788	39,046	25,626	2,616	142	32
10	77,773	6,029,877	15,233,757	8	8	284	14		2,162	3,853	25,098	24,040	17,794	4,286	178	48
11	33,130	5,036,092	9,659,928			14	2		294	914	8,072	10,852	8,636	4,132	184	28	2
12	12,536	3,318,075	4,858,585						47	589	2,326	3,984	3,088	2,371	121	10
13	4,280	1,648,238	1,941,104						24	540	776	1,236	794	844	60	6
14	1,338	584,214	606,108						16	398	345	255	182	128	14
15	376	143,050	143,424						4	222	112	8	26	4
16	97	24,100	24,100						7	74	16
17	20	2,560	2,560						4	16
18	4	128	128						4
Total	1,436,056	33,195,441	87,342,612	108,999	41,559	37,592	5,563	894	355,591	244,950	348,524	173,501	102,255	15,651	845	130	2
MaxMoves				1.3	2.5.2	3.6	4.6	5.4.1.2	1.3	2.5.2	3.6	4.6	5.5	6.2.2	7.2	8.2	9
MaxApart									256	1,536	1,232	1,344	2,271	2,153	2,868	734	168
MaxAssm				34	94	768	696	448	416	1,536	1,536	3,072	3,072	3,072	3,072	864	198

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	1,546	2,386	3,360	1,054					486	6
2	8,203	14,914	25,446	4,606	345	66			2,896	255	35
3	32,609	71,524	150,218	13,454	2,578	804	16		12,289	2,728	684	46	10
4	94,251	259,386	659,227	26,239	7,821	3,427	134	8	36,626	13,655	5,543	607	189		2
5	192,564	734,030	2,163,109	31,322	12,486	7,062	572	62	74,132	38,304	23,346	3,928	1,332	4	14
6	280,191	1,664,603	5,417,063	21,664	11,249	8,933	1,315	168	96,925	64,238	56,066	14,367	5,202	38	26
7	298,382	3,063,382	10,698,777	8,566	5,542	8,642	1,770	234	78,985	65,596	84,047	31,756	13,044	184	14	2
8	242,358	4,590,693	16,410,008	1,946	1,398	6,420	1,292	204	39,513	41,331	83,500	44,382	21,739	609	6	16		2
9	153,671	5,622,680	18,497,726	230	150	2,178	340	46	11,859	17,258	55,506	40,208	24,288	1,538	20	46		4
10	77,677	5,621,135	15,215,217	8	8	292	12		2,206	5,440	24,024	25,035	17,857	2,667	74	52		2
11	33,120	4,556,780	9,658,904			14	2		326	1,446	7,630	11,462	9,258	2,826	126	24	2	4
12	12,536	2,932,133	4,858,585						69	690	2,134	4,147	3,609	1,788	93	6
13	4,280	1,448,664	1,941,104						28	550	616	1,236	1,062	716	66	6
14	1,338	527,786	606,108						16	398	206	261	259	180	18
15	376	136,652	143,424						4	222	42	14	58	32	4
16	97	23,876	24,100						7	74	4		8	4
17	20	2,560	2,560						4	16
18	4	128	128						4
Total	1,433,223	31,273,312	86,475,064	109,089	41,577	37,838	5,453	722	356,375	252,207	343,383	177,449	97,915	10,586	463	152	2	12
MaxMoves				1.3	2.5.2	3.6	4.6	5.2	1.3	2.5.2	3.6	4.6.2	5.5	6.2.2	7.2	8.2	9	10
MaxApart									256	1,536	1,226	1,228	2,101	2,042	2,789	734	162	82
MaxAssm				34	94	768	696	768	416	1,536	1,392	3,072	3,072	3,072	3,072	864	198	112

Name	Pieces	Holes	Length	Moves	Sol	Designer
Favorite Level 5.4 Millable Burr	102 765×2 927 974 1023	5	6	5.4	1 / 3	David V. Winkler
Favorite Level 5.4 Millable Burr	102 507×2 823 927 1023	5	6	5.4	1 / 3	David V. Winkler
Millable Unique 5.4.2 Moves 4 Holes	159 187 375 669 991 1023	4	6	5.4.2	1 / 16
Millable Unique 5.4.2 Moves 4 Holes	159 187 411 750 959 1023	4	6	5.4.2	1 / 16
Millable 2 Moves 1 Hole #1	119 191 791 823 910 991	1	6+	2	2 / 2
Millable 2 Moves 1 Hole #1	119 223 791 910 959 974	1	6+	2	2 / 2
Millable 2 Moves 1 Hole #2	87 791 823 910 959 1006	1	6+	2	2 / 2
Millable 2 Moves 1 Hole #2	117 791 887 910 974 991	1	6+	2	2 / 2
Millable 2 Moves 1 Hole #3	87 191 791 823 910 1023	1	6+	2	2 / 2
Millable 2 Moves 1 Hole #3	117 223 791 910 974 1023	1	6+	2	2 / 2
Millable 5.4 Moves 2 Holes #1	102 159 191 927 974 1023	2	6	5.4	2 / 2
Millable 5.4 Moves 2 Holes #1	102 159 223 823 927 1023	2	6	5.4	2 / 2
Millable 5.4 Moves 2 Holes #2	102 159×2 191 991 1023	2	6	5.4	2 / 2
Millable 5.4 Moves 2 Holes #2	102 159×2 223 959 1023	2	6	5.4	2 / 2
Millable 7 Moves 4 Holes	87 187 870 927 959 1023	4	6+	7.2 max	7 / 16
Millable 7 Moves 4 Holes	117 187 870 927 991 1023	4	6+	7.2 max	7 / 16
Millable 9 Moves 6 Holes	87 153 511 1006 1023×2	6	6	9.2 max	16 / 26
Millable 9 Moves 6 Holes	117 153 767 887 1023×2	6	6	9.2 max	16 / 26
Millable 10 Moves 8 Holes	153 191 631 1023×3	8	10+	10 max	36 / 56
Millable 10 Moves 8 Holes	153 223 494 1023×3	8	10+	10 max	36 / 56

Aug 30, 2002 by k16@chiba.email.ne.jp