Lights Out Classic:

	Total	1	25	300	2,300	12,650	53,130	176,176	476,104	982,335	1,596,279	1,935,294	1,684,446	1,004,934	383,670	82,614	7,350	8,388,608
		Buttons
		0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	Total
L i g h t s	0	1																1
	1												5					5
	2					8				10	14	18	20		2			72
	3		4	8	4	4	12	10	16	44	64	164	158	70	10	8		576
	4		12	16	24	24	68	100	164	159	500	854	668	373	160	32	12	3,166
	5		9	36	84	148	291	500	808	1,328	2,114	2,728	2,791	1,676	620	184	9	13,326
	6			30	136	324	672	1,482	2,706	4,668	7,360	9,658	9,004	5,558	2,000	548	110	44,256
	7			44	194	560	1,384	3,220	6,794	13,196	21,348	27,108	23,948	14,226	6,110	1,698	114	119,944
	8			88	376	1,147	2,884	6,806	15,348	30,486	49,032	60,090	54,180	33,334	13,392	2,932	436	270,531
	9			68	448	1,800	5,164	12,636	28,694	57,600	94,103	117,112	102,084	60,520	24,677	5,976	437	511,319
	10			10	312	1,920	6,976	19,464	46,096	91,996	153,820	189,106	161,908	98,400	37,776	8,104	864	816,752
	11				230	1,740	7,876	25,282	62,960	129,108	210,836	256,592	225,234	132,364	49,096	11,306	880	1,113,504
	12				276	1,812	7,940	27,162	72,848	155,728	249,624	299,298	261,332	153,752	57,872	12,044	1,164	1,300,852
	13				184	1,492	7,273	25,672	72,154	155,936	251,294	302,636	258,644	153,912	59,153	11,408	1,094	1,300,852
	14				32	796	5,464	21,560	61,568	131,404	215,184	259,788	223,984	132,652	49,472	10,912	688	1,113,504
	15					396	3,332	15,158	44,832	96,536	157,692	188,636	165,428	99,620	36,984	7,406	732	816,752
	16					311	2,044	8,834	27,440	61,002	97,396	117,958	104,628	62,006	23,928	5,496	276	511,319
	17					152	1,100	4,796	14,358	31,652	51,744	62,728	53,879	33,852	13,408	2,468	394	270,531
	18					16	408	2,286	6,716	14,206	22,626	27,134	24,396	14,880	5,858	1,370	48	119,944
	19						144	836	2,650	5,196	8,316	9,960	8,808	5,582	2,270	414	80	44,256
	20						76	278	716	1,564	2,504	2,920	2,648	1,720	656	244		13,326
	21						22	76	186	412	560	676	601	392	180	52	9	3,166
	22							16	50	80	132	118	88	42	36	12	2	576
	23							2		20	16	12	10	2	10			72
	24									4				1				5
	25																1	1

The average number of buttons needed to solve a position is 9.8998.

In Sloane's On-Line Encyclopedia of Integer Sequences these are included as sequences A079873 and A079874.

Lights Out 2000:

	Total:	1	25	325	2,900	19,850	110,630	520,948	2,125,078	7,644,164	24,561,916	71,147,752	186,876,765	446,015,084	964,537,892	1,872,111,656	3,203,446,007	4,709,112,417	5,767,439,109	5,710,406,148	4,433,675,458	2,590,026,921	1,073,252,214	279,734,731	36,143,633	2,147,985	31,381,059,609
		Buttons
		0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	Total
L i g h t s	0	1																									1
	1																				1						1
	2															4		6	1	2		4					17
	3		4														4		24	40	22	14					108
	4		12		8	20		8			6	16	16	4	20	44	44	114	112	145	80	65	34	6			754
	5		9		12	20		20	52	8	18	80	68	100	104	190	343	534	788	733	500	324	121	44	10		4,078
	6			10	24	72	8	76	168	60	152	315	214	432	774	1,138	1,628	2,434	3,531	3,534	2,562	1,388	536	148	52	6	19,262
	7			48	40	116	144	176	482	380	540	1,164	1,292	1,946	2,998	5,038	7,716	10,434	13,228	13,536	10,346	6,000	2,248	564	100	12	78,548
	8			114	48	234	488	456	1,124	1,409	1,944	3,524	4,900	7,004	11,718	17,436	28,228	39,618	48,014	48,543	35,966	21,327	8,368	2,336	310	6	283,115
	9			108	84	324	900	816	2,368	4,016	5,428	9,996	15,208	22,832	38,404	58,644	90,540	128,105	157,245	156,336	117,216	66,410	27,414	7,294	1,347	32	911,067
	10			45	148	596	1,520	1,990	4,672	9,540	13,196	25,816	41,644	64,960	108,200	174,452	269,200	378,381	457,366	452,515	343,029	195,318	80,158	21,566	3,040	307	2,647,659
	11				430	798	2,424	4,376	8,762	18,730	30,642	57,984	103,668	168,772	285,800	462,654	722,094	1,010,028	1,217,638	1,194,076	913,032	523,780	213,832	58,444	7,928	540	7,006,432
	12				774	1,009	3,424	9,063	16,148	35,246	64,557	121,628	227,418	396,787	678,528	1,128,796	1,756,635	2,483,600	2,975,452	2,913,951	2,222,231	1,272,226	524,380	142,189	22,288	1,240	16,997,570
	13				806	1,144	4,715	14,240	25,756	61,891	127,211	238,422	462,526	843,700	1,488,189	2,516,196	3,953,583	5,592,359	6,699,803	6,539,085	5,012,389	2,878,844	1,188,473	315,846	44,324	3,816	38,013,318
	14				452	1,552	6,646	20,517	42,374	100,494	226,922	439,032	875,292	1,659,543	2,998,252	5,171,799	8,230,497	11,654,645	13,985,694	13,612,933	10,421,804	6,007,026	2,481,611	681,887	89,472	5,778	78,714,222
	15				74	2,772	8,178	26,812	65,792	157,820	367,270	757,414	1,552,534	3,043,358	5,623,236	9,849,244	15,855,202	22,558,596	27,088,808	26,365,886	20,171,838	11,654,334	4,822,692	1,317,382	188,722	11,288	151,489,252
	16					4,039	9,250	33,242	98,820	232,516	562,136	1,225,172	2,567,216	5,201,290	9,853,515	17,511,132	28,437,088	40,620,258	48,884,806	47,562,716	36,428,155	21,067,964	8,776,099	2,357,851	332,899	26,778	271,792,942
	17					4,007	9,379	39,076	132,076	319,820	809,726	1,869,377	4,013,686	8,297,036	16,111,679	29,074,278	47,645,269	68,303,779	82,362,365	80,267,739	61,477,831	35,607,231	14,840,695	4,030,972	542,269	36,064	455,794,354
	18					2,464	10,276	45,927	160,102	423,570	1,097,083	2,672,794	5,897,330	12,475,496	24,691,688	45,187,320	74,693,640	107,566,115	129,821,652	126,831,073	97,236,288	56,418,901	23,463,461	6,331,686	892,386	55,194	715,974,446
	19					628	13,176	49,058	180,330	529,988	1,417,220	3,572,174	8,180,256	17,632,934	35,588,720	65,921,498	109,785,130	158,805,134	192,097,052	187,883,510	144,346,648	83,752,064	34,940,110	9,331,840	1,301,718	94,940	1,055,424,128
	20					55	15,366	49,380	191,458	636,360	1,731,092	4,500,303	10,686,842	23,523,762	48,267,104	90,481,461	151,686,272	220,132,390	266,876,454	261,556,779	201,212,641	116,928,773	48,716,933	13,084,192	1,775,427	112,078	1,462,165,122
	21						13,743	45,286	194,388	708,254	1,999,248	5,368,450	13,170,390	29,622,710	61,663,098	116,885,639	197,135,261	287,115,618	348,694,364	342,562,116	263,972,834	153,572,851	63,862,215	17,044,116	2,334,812	146,573	1,906,111,966
	22						8,253	42,315	193,754	730,101	2,196,630	6,042,802	15,361,060	35,215,356	74,340,297	142,232,284	241,245,339	352,524,911	429,105,725	422,225,183	326,117,852	189,878,886	79,030,480	20,899,931	2,828,131	190,644	2,340,409,934
	23						2,444	42,636	179,600	706,722	2,281,688	6,474,744	16,852,748	39,590,570	84,587,276	163,205,088	278,228,094	407,820,078	497,625,326	490,611,686	379,523,484	221,239,968	91,947,126	24,301,148	3,227,898	196,916	2,708,645,240
	24						292	40,490	159,598	645,836	2,264,200	6,573,959	17,508,576	41,994,943	90,918,533	176,750,138	302,668,774	444,816,915	543,959,567	537,310,886	416,479,094	243,029,714	100,905,047	26,485,547	3,509,526	215,316	2,956,236,951
	25						4	31,620	131,004	564,958	2,115,964	6,341,426	17,209,052	42,114,204	92,299,777	180,630,509	310,663,367	457,592,640	560,790,172	555,038,278	430,918,398	251,803,438	104,345,622	27,261,921	3,547,033	219,248	3,043,618,635
	26							17,544	106,112	481,450	1,848,893	5,820,664	16,017,922	39,968,866	88,470,555	174,301,065	300,720,487	444,062,784	545,274,397	540,785,717	420,502,819	245,968,142	101,863,217	26,440,715	3,390,670	194,932	2,956,236,951
	27							5,188	87,748	384,696	1,532,966	5,029,222	14,193,328	35,798,484	80,177,458	158,670,226	274,663,438	406,270,532	500,063,818	496,925,898	387,139,176	226,523,842	93,799,366	24,156,058	3,050,420	173,376	2,708,645,240
	28							628	68,322	298,786	1,191,272	4,157,379	11,885,420	30,368,222	68,519,196	136,356,208	236,566,158	350,616,840	432,199,270	430,611,967	335,876,388	196,790,865	81,263,820	20,906,315	2,588,998	143,880	2,340,409,934
	29							8	45,622	214,665	894,844	3,219,874	9,491,789	24,319,255	55,327,746	110,492,665	192,046,305	285,188,738	352,025,779	351,533,265	274,683,630	161,062,692	66,469,880	16,914,443	2,070,914	109,852	1,906,111,966
	30								22,148	151,114	644,424	2,367,370	7,148,072	18,444,982	42,155,483	84,374,261	146,943,634	218,331,958	270,134,286	270,037,121	211,570,796	124,031,146	51,226,073	12,952,928	1,549,264	80,062	1,462,165,122
	31								5,782	103,824	441,034	1,638,816	5,089,264	13,238,674	30,275,934	60,731,028	105,740,370	157,317,094	194,772,770	195,358,084	153,172,712	90,030,488	36,971,822	9,385,414	1,098,100	52,918	1,055,424,128
	32								516	66,489	293,472	1,067,441	3,422,070	8,961,301	20,496,025	41,086,652	71,607,331	106,516,249	131,962,716	132,573,363	104,257,006	61,377,652	25,191,586	6,314,198	745,558	34,821	715,974,446
	33									37,171	180,394	670,668	2,157,150	5,739,743	13,044,215	26,128,462	45,487,778	67,687,246	83,957,480	84,366,557	66,526,450	39,194,462	16,140,565	4,000,449	454,996	20,568	455,794,354
	34									15,104	109,243	399,568	1,289,861	3,444,562	7,815,050	15,596,513	27,071,696	40,298,646	49,946,855	50,357,665	39,688,800	23,478,331	9,606,087	2,403,719	261,146	10,096	271,792,942
	35									3,000	61,358	231,590	720,526	1,944,790	4,396,794	8,707,620	15,085,036	22,389,212	27,800,334	28,018,030	22,166,296	13,113,716	5,377,820	1,315,748	151,834	5,548	151,489,252
	36									146	31,650	127,335	381,072	1,024,684	2,311,688	4,541,239	7,828,430	11,609,004	14,413,952	14,536,561	11,504,104	6,828,136	2,813,696	684,292	75,001	3,232	78,714,222
	37										14,501	65,384	188,027	503,840	1,137,543	2,204,034	3,777,874	5,583,326	6,951,794	7,017,370	5,545,759	3,297,186	1,356,165	336,287	33,064	1,164	38,013,318
	38										4,464	33,098	89,236	226,734	515,805	997,573	1,696,859	2,486,233	3,094,477	3,132,968	2,480,205	1,468,445	605,866	149,509	15,602	496	16,997,570
	39										528	14,400	42,034	95,578	214,566	417,212	705,080	1,025,276	1,268,746	1,283,318	1,021,864	601,192	250,058	60,716	5,664	200	7,006,432
	40											5,886	17,870	37,663	82,224	160,257	267,670	386,157	477,459	482,631	384,322	224,818	94,490	24,336	1,856	20	2,647,659
	41											2,060	7,412	13,149	28,632	56,587	93,546	130,787	162,116	165,434	133,454	76,956	31,325	8,945	636	28	911,067
	42											393	2,662	4,700	8,416	18,207	29,161	40,647	49,813	51,090	41,881	23,680	9,630	2,661	158	16	283,115
	43											12	810	1,430	2,072	5,252	8,648	11,522	13,764	13,744	11,768	6,230	2,392	856	48		78,548
	44												252	492	458	1,292	2,026	2,825	3,277	3,326	2,930	1,652	544	188			19,262
	45												52	157	100	268	432	560	673	625	688	342	133	40	8		4,078
	46													31	19	42	88	85	136	106	129	86	24	4	4		754
	47													8	2	10	12	4	8	24	32	8					108
	48														1				2	2	8	4					17
	49															1											1
	50																			1							1

The average number of button presses needed to solve a position is 17.113.

In Sloane's On-Line Encyclopedia of Integer Sequences the bottom row is is included as sequence A079875.

Lights Out Cube:

Buttons	Positions
0	1
1	54
2	1,431
3	24,804
4	316,251
5	3,162,510
6	25,827,165
7	177,100,560
8	1,040,446,486
9	5,317,168,916
10	23,913,642,226
11	95,457,369,144
12	339,930,538,185
13	1,080,757,481,134
14	3,053,070,032,511
15	7,576,816,216,796
16	16,233,040,500,987
17	29,396,466,092,822
18	44,029,343,202,869
19	53,442,675,203,992
20	51,578,158,468,634
21	38,836,356,522,788
22	22,350,616,115,974
23	9,607,958,387,296
24	3,013,785,631,536
25	680,837,208,384
26	113,169,453,024
27	14,576,836,608
28	1,391,192,064
29	89,579,520
30	2,985,984
Total	281,474,976,710,656
Avg Depth	19.170

In Sloane's On-Line Encyclopedia of Integer Sequences this is included as sequence A079876.

Lights Out Deluxe:

The + move:

	Total	1	36	630	7,140	58,905	376,992	1,947,792	8,347,680	30,260,340	94,143,280	254,186,856	600,805,296	1,251,677,700	2,310,789,600	3,796,297,200	5,567,902,560	7,307,872,110	8,597,496,600	9,075,135,300	8,597,496,600	7,307,872,110	5,567,902,560	3,796,297,200	2,310,789,600	1,251,677,700	600,805,296	254,186,856	94,143,280	30,260,340	8,347,680	1,947,792	376,992	58,905	7,140	630	36	1	68,719,476,736
		Buttons
		0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	Total
L i g h t s	0	1																																					1
	1														4	8			20		4																		36
	2					8				4		8		8	24	52	40	36	40	106	88	56	8	108	24	20													630
	3		4	8	4	8	4	8	8	32	40	24	60	88	200	248	728	728	856	792	1,176	568	496	360	380	136	72	64	28	16	4								7,140
	4		16	20	24	20	72	80	96	172	192	352	552	969	1,448	2,816	4,496	6,996	6,472	7,588	7,096	7,421	4,624	3,292	2,168	1,146	416	228	96	29	8								58,905
	5		16	48	100	152	248	344	544	800	1,376	1,992	3,564	6,064	11,232	18,128	29,648	40,872	48,008	46,040	47,936	41,232	31,736	20,552	13,344	7,160	3,536	1,472	640	168	40								376,992
	6			56	184	396	824	1,512	2,400	3,768	6,384	11,060	18,208	31,760	56,008	94,844	150,688	213,856	250,080	254,602	237,120	209,584	161,728	110,426	67,208	36,272	17,432	7,410	2,752	940	248	42							1,947,792
	7			64	336	840	1,932	4,240	8,216	14,648	25,824	45,232	78,816	138,656	241,004	411,704	645,036	902,152	1,077,972	1,116,608	1,033,332	892,176	686,400	468,384	282,504	153,160	73,068	30,488	10,788	3,232	744	112	12						8,347,680
	8			172	656	1,808	4,296	10,140	22,296	43,949	84,224	156,700	288,824	514,470	899,416	1,508,412	2,351,280	3,224,882	3,894,992	4,072,884	3,821,936	3,224,714	2,474,088	1,676,828	1,016,040	545,748	260,520	108,184	38,416	11,230	2,624	528	72	11					30,260,340
	9			200	1,064	3,752	9,652	23,072	53,160	116,088	235,764	465,288	880,972	1,623,968	2,858,904	4,781,096	7,317,196	10,002,856	12,015,312	12,760,024	11,963,164	10,084,416	7,641,540	5,199,320	3,131,412	1,683,760	795,732	329,688	118,056	36,520	9,176	1,856	272						94,143,280
	10			62	1,128	5,556	17,976	47,612	115,432	267,704	580,624	1,190,640	2,343,240	4,411,028	7,868,264	13,095,994	19,849,304	26,938,248	32,376,112	34,423,538	32,448,112	27,262,508	20,583,448	13,934,922	8,415,776	4,522,968	2,143,096	890,444	322,296	98,964	25,680	5,244	840	96					254,186,856
	11				808	6,512	26,748	82,928	223,056	548,712	1,257,160	2,696,224	5,483,240	10,501,896	18,913,332	31,346,160	47,212,208	63,640,216	76,315,100	81,114,536	76,685,680	64,491,176	48,621,696	32,843,880	19,853,492	10,650,184	5,072,280	2,121,744	774,456	241,512	63,736	14,016	2,260	304	44				600,805,296
	12				1,072	7,798	36,392	128,568	379,568	996,866	2,407,160	5,410,072	11,300,144	22,075,662	39,973,496	66,160,136	98,914,240	132,621,718	158,379,872	168,494,640	159,320,472	134,452,471	101,258,560	68,422,588	41,309,760	22,216,594	10,606,504	4,462,652	1,637,408	523,127	141,736	31,648	5,880	832	56	8			1,251,677,700
	13				1,168	9,224	47,436	181,064	577,668	1,616,288	4,109,624	9,596,216	20,683,988	41,101,112	74,739,544	123,452,248	183,708,480	244,874,008	291,729,336	309,786,760	293,332,788	247,832,800	187,082,796	126,327,112	76,365,044	41,167,912	19,703,064	8,335,088	3,086,888	990,912	273,384	63,336	12,200	1,920	192				2,310,789,600
	14				536	8,152	52,368	228,230	792,736	2,367,664	6,317,896	15,279,674	33,759,920	67,961,196	124,134,352	204,774,458	303,448,688	402,627,792	478,040,736	506,833,824	480,242,528	406,368,992	307,470,368	207,909,692	125,831,416	67,966,796	32,615,176	13,838,360	5,157,808	1,669,060	463,800	110,196	21,376	2,988	376	46			3,796,297,200
	15				60	5,192	48,036	250,856	972,868	3,126,320	8,745,800	21,869,296	49,276,904	100,322,168	183,923,888	302,966,280	447,061,740	591,088,352	699,173,576	740,573,256	701,606,396	594,901,256	450,937,560	305,809,440	185,264,524	100,241,592	48,198,092	20,496,592	7,654,820	2,491,504	696,068	162,920	31,580	5,024	564	32	4		5,567,902,560
	16					3,992	41,072	246,092	1,062,232	3,680,576	10,836,848	28,006,212	64,452,296	132,494,428	243,667,312	400,547,340	589,355,320	776,208,274	915,862,936	968,380,868	917,758,136	778,996,320	592,037,312	402,293,572	244,235,280	132,274,201	63,696,888	27,115,496	10,139,592	3,294,026	920,168	216,728	41,304	6,413	824	52			7,307,872,110
	17					3,480	35,316	225,488	1,050,192	3,891,592	12,041,224	32,180,632	75,494,848	156,619,448	288,805,544	474,272,944	695,964,772	913,846,488	1,075,681,608	1,135,877,296	1,076,478,804	914,696,448	696,479,540	474,307,944	288,516,668	156,377,024	75,331,976	32,057,672	11,979,700	3,889,728	1,079,360	253,032	49,528	7,504	712	80	8		8,597,496,600
	18					1,728	25,424	187,562	948,960	3,726,940	12,075,712	33,256,902	79,283,824	165,920,548	306,601,272	503,325,824	736,717,408	965,386,812	1,133,937,120	1,196,342,266	1,133,269,816	964,098,724	735,034,136	501,744,636	305,597,560	165,741,656	79,799,392	33,935,958	12,633,312	4,084,928	1,133,480	263,998	50,416	7,952	968	66			9,075,135,300
	19					280	14,000	133,736	764,500	3,221,360	10,904,708	30,843,112	74,787,092	157,631,832	291,871,044	478,826,656	699,903,608	914,956,320	1,073,396,488	1,131,046,320	1,071,628,228	912,087,192	696,535,412	476,002,248	290,409,576	157,549,368	75,748,796	32,120,032	11,919,716	3,833,456	1,058,064	247,784	47,660	6,992	904	112	4		8,597,496,600
	20					7	7,616	86,636	552,864	2,496,522	8,827,328	25,676,220	63,223,000	134,190,611	249,110,536	408,576,708	596,312,944	778,178,006	911,704,736	960,058,160	909,490,232	774,516,059	592,115,288	405,141,896	247,396,568	134,208,636	64,387,824	27,202,128	10,053,552	3,222,274	884,408	204,172	39,824	6,498	792	56	8	1	7,307,872,110
	21						4,964	55,400	369,192	1,755,248	6,443,440	19,191,176	47,859,268	102,287,816	190,344,332	312,233,960	455,100,200	593,488,776	694,230,752	730,822,592	692,092,952	589,837,624	451,144,604	309,084,072	188,737,496	102,367,672	49,000,336	20,616,544	7,575,664	2,411,456	659,228	152,856	29,288	4,816	760	72	4		5,567,902,560
	22						2,240	30,734	226,848	1,131,192	4,258,136	12,898,798	32,494,128	69,722,220	130,031,288	213,270,242	310,812,816	404,726,944	473,221,728	497,765,984	471,661,216	401,958,588	307,826,632	210,935,984	128,900,568	69,837,384	33,363,648	13,954,244	5,093,232	1,609,440	436,648	101,896	20,560	3,416	384	54	8		3,796,297,200
	23						368	13,760	121,604	652,136	2,542,220	7,797,120	19,735,648	42,497,896	79,306,776	130,030,544	189,317,064	246,335,064	287,835,568	302,711,208	286,857,980	244,662,008	187,508,708	128,626,320	78,634,540	42,557,096	20,268,056	8,432,664	3,053,372	957,672	259,284	60,264	12,112	2,224	300	24			2,310,789,600
	24						8	5,812	58,512	334,841	1,352,784	4,215,980	10,722,040	23,097,946	43,049,424	70,573,260	102,560,472	133,432,430	155,700,584	163,758,148	155,171,056	132,544,154	101,617,400	69,858,676	42,690,560	23,097,394	10,978,264	4,547,184	1,627,824	505,974	136,648	32,536	6,592	1,017	152	28			1,251,677,700
	25							2,792	27,800	158,920	647,148	2,034,088	5,183,356	11,141,064	20,765,076	33,929,352	49,276,508	63,917,304	74,633,424	78,400,624	74,400,988	63,560,984	48,863,368	33,595,216	20,589,612	11,132,336	5,279,532	2,175,272	771,408	236,272	63,740	15,200	3,272	576	64				600,805,296
	26							990	11,456	70,044	282,968	872,186	2,218,240	4,777,072	8,839,112	14,392,408	20,843,808	26,963,172	31,439,424	33,083,128	31,366,920	26,876,872	20,719,600	14,281,212	8,776,536	4,758,684	2,243,168	915,346	322,496	97,984	26,272	6,226	1,280	204	48				254,186,856
	27							136	3,676	25,848	108,780	335,128	843,040	1,796,888	3,303,792	5,359,168	7,696,068	9,960,280	11,563,304	12,180,088	11,565,048	9,949,752	7,691,428	5,339,168	3,286,976	1,787,464	841,444	340,280	118,000	35,336	9,348	2,288	472	80					94,143,280
	28								1,248	8,488	35,720	112,848	282,384	589,578	1,080,328	1,724,152	2,473,520	3,176,648	3,695,832	3,868,600	3,711,784	3,184,471	2,488,424	1,731,644	1,073,888	581,448	275,784	111,228	37,776	10,813	2,856	704	136	38					30,260,340
	29								468	2,720	10,320	32,896	82,332	169,808	302,212	481,656	679,624	868,584	1,004,984	1,058,824	1,010,524	883,064	685,624	485,664	301,364	164,056	77,648	31,304	10,088	2,968	748	152	48						8,347,680
	30								72	684	3,032	8,408	20,232	41,692	72,824	114,500	158,824	200,284	228,680	242,762	232,520	204,480	161,584	115,342	71,776	40,384	19,096	7,310	2,488	636	128	46	8						1,947,792
	31								8	160	716	1,960	4,304	8,144	14,828	21,960	30,856	37,424	43,924	44,856	45,316	38,560	32,868	22,360	14,776	7,976	3,824	1,496	516	120	32	8							376,992
	32									46	112	352	696	1,428	2,408	3,512	4,256	6,004	6,048	7,672	6,360	6,692	4,896	3,840	2,376	1,301	536	244	72	34	16	4							58,905
	33									8	16	48	120	192	368	368	676	504	924	656	832	680	632	440	372	144	96	32	20	8	4								7,140
	34											12	16	44	8	62	40	72	48	50	48	68	48	62	16	28		8											630
	35																4	8	4		12		8																36
	36																													1									1

The average number of buttons needed to solve a position is obviously 18.

Lights Out Deluxe:

The × move:

	Total	1	36	630	7,140	58,905	376,992	1,947,792	8,347,680	30,260,340	94,143,280	254,186,856	600,805,296	1,251,677,700	2,310,789,600	3,796,297,200	5,567,902,560	7,307,872,110	8,597,496,600	9,075,135,300	8,597,496,600	7,307,872,110	5,567,902,560	3,796,297,200	2,310,789,600	1,251,677,700	600,805,296	254,186,856	94,143,280	30,260,340	8,347,680	1,947,792	376,992	58,905	7,140	630	36	1	68,719,476,736
		Buttons
		0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	Total
L i g h t s	0	1																																					1
	1										8	16	12																										36
	2		4	4		4	12	18	28	30	60	24	48	58	8	8				16	64	112	96	36															630
	3		16	12	24	44	56	84	172	244	256	356	248	164	116	80	192	328	452	648	756	744	760	784	444	112	48												7,140
	4			58	48	162	156	464	652	948	1,444	1,278	1,368	1,255	1,300	1,834	2,280	3,397	4,888	6,526	7,244	7,694	6,620	4,000	2,984	1,585	424	248	32	16									58,905
	5		16	60	260	252	936	1,312	2,368	3,880	4,460	6,060	6,536	7,908	10,656	13,816	19,880	27,364	35,232	42,484	49,264	45,968	38,736	29,892	15,972	8,556	4,084	736	304										376,992
	6			154	392	1,188	2,056	4,318	7,280	11,556	17,680	22,800	32,452	42,008	59,956	84,642	118,956	157,464	197,488	234,808	236,956	231,754	194,508	133,006	89,276	42,390	16,008	7,448	816	432									1,947,792
	7			56	960	1,820	5,612	9,984	20,336	34,552	54,384	87,336	125,192	190,400	273,636	399,276	544,392	728,240	901,296	999,736	1,061,048	949,220	767,460	569,152	326,824	182,336	81,556	22,020	9,976	592	288								8,347,680
	8			208	656	4,781	8,760	26,256	46,996	93,595	162,744	270,438	441,096	678,264	1,044,188	1,490,040	2,120,016	2,742,644	3,329,636	3,784,828	3,714,916	3,430,529	2,754,184	1,878,454	1,220,032	608,095	268,456	112,744	19,152	8,568	48	16							30,260,340
	9				1,540	4,908	21,696	43,796	117,276	216,384	434,200	758,528	1,285,976	2,122,164	3,225,052	4,899,840	6,708,244	8,843,772	10,711,672	11,577,332	11,817,572	10,397,040	8,272,564	5,973,184	3,492,036	1,937,452	864,784	284,112	116,436	10,608	5,112								94,143,280
	10			78	656	9,442	25,560	96,642	203,688	505,644	964,132	1,872,032	3,325,176	5,520,984	8,990,156	13,182,480	18,861,196	24,378,980	29,042,840	32,201,090	31,170,200	28,031,696	22,218,508	15,250,148	9,764,884	5,007,730	2,301,700	948,786	217,816	88,940	3,920	1,752							254,186,856
	11				1,468	6,184	48,812	122,760	412,608	881,920	2,052,080	3,968,464	7,419,492	13,030,616	20,797,408	32,314,172	44,841,460	58,767,784	70,349,024	75,201,188	74,937,096	65,271,968	51,344,296	36,568,200	21,809,508	12,139,968	5,552,116	2,020,800	786,584	113,280	45,456	440	144						600,805,296
	12				236	11,275	40,704	220,306	544,744	1,645,762	3,511,872	7,704,118	14,732,544	26,177,551	44,301,504	66,746,806	96,099,748	124,271,779	146,803,556	160,147,848	153,783,084	136,021,252	106,828,612	73,361,906	46,467,664	24,306,289	11,414,912	4,726,064	1,281,420	474,980	36,424	14,720	16	4					1,251,677,700
	13				788	4,448	64,100	209,440	897,120	2,213,836	5,986,168	12,684,472	25,903,596	48,021,456	80,017,816	126,649,212	178,076,852	232,699,728	276,474,252	293,450,764	287,610,444	248,680,144	193,861,240	136,624,928	82,164,016	45,485,516	21,082,172	8,077,512	3,054,480	578,976	206,292	7,088	2,744						2,310,789,600
	14					7,790	38,288	300,822	924,520	3,303,920	8,039,136	19,591,574	40,381,528	76,205,792	133,254,376	206,318,618	298,734,408	387,281,016	455,579,204	490,845,874	468,311,248	408,601,900	317,762,768	217,796,862	136,429,864	72,179,082	34,205,412	14,175,434	4,288,288	1,491,844	183,040	64,072	400	120					3,796,297,200
	15				112	2,016	51,564	218,148	1,214,076	3,529,020	10,919,332	25,593,496	56,438,064	110,235,764	191,307,948	308,272,744	439,491,988	574,688,236	679,415,212	717,733,100	694,228,652	595,697,828	460,009,488	320,331,904	193,224,688	106,139,760	49,711,588	19,765,480	7,361,100	1,713,288	557,068	37,360	13,536						5,567,902,560
	16					3,398	20,900	259,062	976,784	4,237,310	11,691,256	31,567,032	70,024,136	139,744,249	252,536,936	401,286,476	585,798,756	762,798,774	895,601,248	955,992,140	907,195,536	781,684,842	602,176,496	410,887,564	254,097,248	135,453,416	64,455,788	26,848,582	8,864,964	2,986,965	515,536	160,816	4,352	1,548					7,307,872,110
	17					296	26,760	140,368	1,041,556	3,603,476	12,721,360	33,039,848	78,434,264	161,236,220	291,118,600	477,765,180	691,552,664	906,361,112	1,068,757,340	1,125,180,872	1,075,610,108	916,289,656	700,606,424	482,299,456	291,212,064	158,738,388	75,161,116	30,836,964	11,506,472	3,139,156	966,864	114,360	35,544	88	24				8,597,496,600
	18					848	7,484	142,454	659,092	3,464,152	10,994,912	32,617,554	78,158,904	164,420,092	307,262,336	501,149,710	738,290,968	967,105,972	1,134,252,804	1,201,762,768	1,133,977,044	965,707,446	736,754,860	499,563,288	305,836,644	164,113,922	78,600,028	33,303,232	11,834,652	3,982,792	893,728	254,902	17,024	5,688					9,075,135,300
	19						9,056	58,700	577,316	2,371,504	9,570,812	27,610,520	70,317,584	152,462,276	285,707,120	478,344,488	702,694,936	924,224,212	1,088,224,668	1,141,325,728	1,079,884,504	912,402,996	690,655,888	470,440,424	283,843,484	154,188,060	74,096,964	31,379,004	11,977,376	3,730,664	1,135,020	205,632	56,032	1,232	400				8,597,496,600
	20					49	1,792	53,660	290,496	1,843,576	6,703,192	21,889,354	56,551,916	125,280,950	242,098,308	404,833,292	602,662,808	793,932,379	930,625,224	979,217,924	918,103,108	772,962,798	583,840,648	393,493,016	238,990,780	129,273,019	62,704,556	27,259,660	10,363,756	3,589,491	987,256	272,958	36,096	10,048					7,307,872,110
	21						2,324	16,608	219,684	1,022,232	4,711,988	15,024,048	40,912,600	93,404,212	181,417,020	309,812,472	461,783,640	609,589,960	716,949,952	748,852,760	701,291,340	587,435,092	440,098,460	296,977,684	179,318,168	97,625,764	47,875,636	21,057,452	8,384,672	2,912,552	921,404	223,080	56,208	4,228	1,320				5,567,902,560
	22						112	14,998	90,112	667,810	2,695,288	9,586,784	26,578,188	61,640,182	123,091,164	210,616,244	316,811,996	419,896,456	491,742,224	514,188,514	478,681,732	398,581,550	298,128,612	199,721,138	120,857,356	66,092,696	32,706,440	14,739,844	5,995,224	2,203,966	710,504	204,270	43,392	10,228	136	40			3,796,297,200
	23						252	3,716	61,300	309,656	1,555,792	5,365,504	15,427,880	36,824,848	73,768,672	128,400,432	193,921,524	257,143,236	302,141,532	314,321,896	291,645,808	241,975,296	179,658,628	120,271,204	72,738,300	39,927,840	20,070,076	9,208,748	3,866,448	1,478,016	505,020	150,636	39,164	6,492	1,684				2,310,789,600
	24							3,012	20,456	176,953	743,700	2,776,160	8,084,012	19,370,025	39,717,720	69,337,394	105,351,048	140,488,402	164,620,324	171,194,124	158,341,756	130,446,402	96,571,072	64,372,442	38,886,004	21,519,541	10,926,412	5,143,486	2,232,316	891,583	322,860	104,330	28,744	6,626	616	180			1,251,677,700
	25							428	13,012	69,752	364,408	1,281,448	3,757,736	9,199,420	18,785,396	33,172,656	50,748,168	67,668,680	79,649,168	82,667,988	76,074,520	62,553,636	45,956,804	30,477,096	18,418,172	10,228,860	5,277,064	2,536,976	1,145,820	479,296	186,240	66,104	19,972	5,404	1,072				600,805,296
	26							436	3,272	34,764	149,240	548,176	1,592,512	3,815,316	7,890,188	13,943,560	21,405,564	28,786,870	33,885,892	35,202,076	32,350,016	26,411,362	19,283,748	12,705,034	7,665,284	4,270,306	2,238,888	1,108,970	517,320	230,236	95,408	35,764	12,304	3,346	796	208			254,186,856
	27								1,960	11,168	62,328	214,004	591,932	1,422,100	2,881,616	5,099,460	7,899,772	10,662,908	12,627,988	13,166,200	12,069,336	9,766,360	7,079,516	4,626,520	2,768,908	1,557,280	829,316	424,644	211,072	98,900	43,488	17,552	6,472	1,980	444	44	12		94,143,280
	28								488	4,812	21,336	74,972	202,472	456,834	914,820	1,613,706	2,499,304	3,419,863	4,101,776	4,276,300	3,918,104	3,155,529	2,247,884	1,450,096	861,664	487,425	266,056	142,890	75,468	37,827	18,004	7,988	3,124	1,162	380	56			30,260,340
	29								288	1,144	7,272	23,276	59,288	129,828	247,132	430,708	676,800	937,272	1,141,316	1,201,600	1,096,572	878,176	611,740	386,216	228,160	128,240	73,468	42,060	23,052	12,732	6,400	2,888	1,268	504	184	76	20		8,347,680
	30									516	1,912	5,784	15,472	30,228	55,664	97,522	152,696	216,706	268,220	288,734	263,752	205,090	141,208	85,728	49,528	28,518	16,620	10,500	6,528	3,636	1,808	832	360	162	56	12			1,947,792
	31									160	464	1,216	2,720	5,688	10,868	17,492	27,872	41,868	52,492	58,004	54,428	40,268	26,308	15,476	8,428	4,948	3,112	2,056	1,484	860	420	204	84	40	24	8			376,992
	32									64	64	152	336	788	1,696	2,524	3,968	6,096	8,572	9,802	9,036	6,815	3,900	2,146	1,104	562	460	342	212	134	72	28	12	5	4	6	4	1	58,905
	33											32	16	56	224	292	416	576	1,044	1,456	1,172	880	488	200	108	40	36	60	36	8									7,140
	34													4		24	48	32	64	168	164	58	36	16	4	4		2	4	2									630
	35																	4		4	20	8																	36
	36																					1																	1

The average number of buttons needed to solve a position is obviously 18.

Mini Lights Out:

	Total	1	16	120	560	1,820	4,368	8,008	11,440	12,870	11,440	8,008	4,368	1,820	560	120	16	1	65,536
		Buttons
		0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	Total
L i g h t s	0	1																	1
	1						16												16
	2							80				40							120
	3								400				160						560
	4					140				1,440				240					1,820
	5		16				1,152				3,040				160				4,368
	6			80				4,016				3,872				40			8,008
	7				400				8,000				3,040						11,440
	8					1,440				9,990				1,440					12,870
	9						3,040				8,000				400				11,440
	10			40				3,872				4,016				80			8,008
	11				160				3,040				1,152				16		4,368
	12					240				1,440				140					1,820
	13						160				400								560
	14							40				80							120
	15												16						16
	16																	1	1

The average number of buttons needed to solve a position is obviously 8.

Gamze Lights Out

The + move

	Total	1	25	300	2,300	12,650	53,130	177,100	480,700	1,081,575	2,042,975	3,268,760	4,457,400	5,200,300	5,200,300	4,457,400	3,268,760	2,042,975	1,081,575	480,700	177,100	53,130	12,650	2,300	300	25	1	33,554,432
		Buttons
		0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	Total
L i g h t s	0	1																										1
	1												4	4		4	4	8	1									25
	2		4			4	4		8	18	12	28	24	18	44	64	36	4	12	20								300
	3		8	12		20	24	24	16	92	160	152	234	352	400	256	200	192	108	36	14							2,300
	4			38	32	36	124	176	192	254	744	1,080	1,448	1,879	1,856	1,760	1,372	782	564	226	52	35						12,650
	5		13	28	152	100	365	704	1,058	1,716	2,763	4,644	6,024	7,688	8,561	6,772	5,562	4,044	1,636	816	436	32	16					53,130
	6			60	216	518	680	1,924	4,036	5,904	9,636	15,492	22,020	25,776	25,264	24,836	18,872	10,958	6,768	2,904	876	360						177,100
	7			44	350	1,068	1,994	4,224	9,538	17,420	26,690	44,792	60,270	65,220	72,728	67,340	47,638	31,748	17,854	8,312	2,844	424	202					480,700
	8			82	276	1,852	4,232	8,922	18,828	39,128	68,880	94,130	130,888	164,776	161,620	140,562	110,692	72,111	39,896	16,948	5,604	2,020	92	36				1,081,575
	9				512	1,568	7,590	15,840	33,644	73,072	125,435	189,172	254,668	309,316	312,838	257,536	206,348	140,616	68,084	31,284	12,204	2,428	820					2,042,975
	10			36	228	2,234	7,848	25,700	55,228	105,074	202,120	319,900	421,048	478,750	485,156	446,316	327,524	199,106	117,144	51,200	17,612	5,772	556	208				3,268,760
	11				290	1,608	8,756	28,852	75,332	149,332	265,664	442,032	582,546	648,704	681,648	606,660	435,290	275,548	151,032	70,744	25,412	6,088	1,820	32	10			4,457,400
	12				92	1,653	6,548	28,088	81,048	178,852	321,180	487,726	683,756	821,860	796,280	669,374	508,632	329,404	173,332	74,890	27,288	8,531	1,364	402				5,200,300
	13				124	776	6,187	21,812	70,066	177,244	322,916	499,904	696,652	826,704	804,706	666,108	504,668	326,268	166,100	72,344	27,168	8,136	2,119	224	74			5,200,300
	14					750	3,896	17,440	53,264	134,742	282,292	457,620	600,836	684,162	693,864	608,236	431,808	253,374	137,868	63,708	23,764	7,316	2,008	452				4,457,400
	15				28	224	2,702	11,488	36,728	91,848	198,212	339,700	450,558	510,028	522,316	448,632	308,366	182,976	97,020	43,628	16,782	5,628	1,502	312	82			3,268,760
	16					152	1,212	6,524	23,004	56,855	115,496	199,994	291,472	347,624	330,556	263,242	190,540	119,927	58,352	24,206	9,128	3,384	1,040	226	32	9		2,042,975
	17					40	600	3,232	11,432	30,920	59,268	102,228	156,544	186,896	176,302	143,252	101,784	60,408	29,131	12,036	4,836	1,764	634	232	36			1,081,575
	18					42	216	1,464	4,688	12,688	27,772	46,976	66,112	79,352	81,616	70,076	46,136	23,322	11,464	5,200	2,240	868	304	108	44	12		480,700
	19						124	500	1,758	4,424	10,160	17,176	23,456	29,632	31,872	25,908	16,634	8,684	3,940	1,752	656	252	124	40	8			177,100
	20					5	20	146	680	1,446	2,724	4,798	6,988	9,169	9,896	7,614	4,932	2,926	1,104	394	152	64	40	24	8			53,130
	21						8	40	124	428	664	1,036	1,604	1,976	2,285	2,320	1,386	504	147	44	32	28	9	4	6	4	1	12,650
	22								20	98	160	176	224	350	432	488	288	44	12	8								2,300
	23								8	20	26	4	16	64	60	36	40	20	6									300
	24												8			8	8	1										25
	25										1																	1

The average number of buttons needed to solve a position is obviously 12.5.

Gamze Lights Out

The × move

	Total	1	25	300	2,300	12,217	46,305	127,692	260,300	396,675	454,219	389,932	248,124	114,275	36,475	7,452	828	32	2,097,152
		Buttons
		0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	Total
L i g h t s	0	1																	1
	1					4	5												9
	2					12	20	8											40
	3		8	16	18	12	28	28	2	20	20								152
	4		12	24	60	74	60	80	72	52	112	104	40						690
	5		5	28	80	140	188	300	484	512	505	496	272	80					3,090
	6			32	148	304	468	756	1,420	2,304	2,464	1,876	952	260	48	32			11,064
	7			80	302	816	1,372	2,084	3,502	5,768	7,180	5,608	2,732	944	308	32			30,728
	8			84	428	1,410	3,056	5,180	8,176	12,025	14,848	12,868	7,040	2,500	656	112	24		68,407
	9			32	332	1,584	4,461	9,336	15,964	23,256	27,506	23,768	13,784	5,216	1,456	368	8		127,071
	10			4	272	1,648	5,688	13,836	25,920	37,988	43,624	37,576	22,800	9,612	2,832	460	56	4	202,320
	11				348	1,992	7,404	18,744	35,680	52,224	58,668	50,712	32,564	14,464	4,196	864	76		277,936
	12				240	1,816	7,704	21,192	42,088	62,664	69,360	58,692	38,416	18,200	5,536	1,032	120	8	327,068
	13				64	992	5,834	18,896	41,320	63,952	71,196	59,616	38,872	18,848	6,166	1,160	152		327,068
	14				8	660	4,128	14,368	33,016	53,576	62,056	52,272	34,000	16,896	5,656	1,152	136	12	277,936
	15					536	3,084	10,360	22,984	37,240	44,888	39,512	25,704	12,600	4,332	944	136		202,320
	16					193	1,648	6,552	15,040	23,072	27,488	25,152	16,408	7,874	2,928	660	48	8	127,071
	17					24	568	3,360	8,724	13,028	14,311	13,128	9,108	4,312	1,404	376	64		68,407
	18						384	1,632	3,720	6,000	6,756	5,788	3,792	1,784	680	192			30,728
	19						200	680	1,486	2,164	2,392	2,044	1,266	564	212	48	8		11,064
	20						4	252	556	594	620	572	328	96	48	20			3,090
	21						1	36	108	196	168	108	40	16	17				690
	22							4	28	36	44	28	4	8					152
	23							8	6		12	12	2						40
	24								4	4				1					9
	25										1								1

The average number of buttons needed to solve a position is 8.9307.

Merlin Magic Square

Original version:

	Total	1	9	36	84	126	126	84	36	9	1	512
		Buttons
		0	1	2	3	4	5	6	7	8	9	Total
L i g h t s	0									1		1
	1					8	1					9
	2			12	4	8	4	8				36
	3				2	24	24	24	2	8		84
	4		4	8	24	54	24	8	4			126
	5		1	8	24	24	20	24	24		1	126
	6		4	8	24	8	24	12	4			84
	7				2		24	8	2			36
	8	1			4		4					9
	9						1					1

The average number of buttons needed to solve a position is obviously 4.5.

Merlin Magic Square

Reissued version:

	Total	1	9	36	84	126	126	84	36	9	1	512
		Buttons
		0	1	2	3	4	5	6	7	8	9	Total
L i g h t s	0									1		1
	1				4		1	4				9
	2			4	4	12	16					36
	3			12	14	12	20	20	6			84
	4			8	28	34	12	20	20	4		126
	5		5		20	44	32	12	8	4	1	126
	6		4	4	12	20	28	16				84
	7			8	2	4	12	8	2			36
	8	1					4	4				9
	9						1					1

The average number of buttons needed to solve a position is obviously 4.5.

XL-25 Knights Game:

	Total	1	25	300	2,300	12,650	53,130	177,100	480,700	1,081,575	2,042,975	3,268,760	4,457,400	5,200,300	5,200,300	4,457,400	3,268,760	2,042,975	1,081,575	480,700	177,100	53,130	12,650	2,300	300	25	1	33,554,432
		Buttons
		0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	Total
L i g h t s	0																		1									1
	1												8			4		8		4						1		25
	2							8		8	16	32	52	72	32	16	36		24		4							300
	3					4		14		68	208	222	408	264	352	366	112	200	48	18			8		8			2,300
	4						12	40	112	520	640	1,432	1,420	2,240	2,200	1,272	1,276	664	532	152	60	56	2	16	4			12,650
	5					12	32	172	880	1,352	3,872	4,228	8,112	8,640	7,864	7,012	4,248	4,032	1,408	880	192	70	104	20				53,130
	6				14	24	144	672	1,954	6,880	9,416	20,240	22,644	28,560	26,624	20,808	19,780	8,808	6,736	2,152	1,162	352	80	40	10			177,100
	7					64	456	1,698	7,552	13,624	34,672	44,038	68,976	69,992	70,576	69,370	41,464	32,852	13,464	8,118	2,472	948	280	84				480,700
	8				16	192	972	5,488	12,748	39,776	61,794	118,200	134,416	168,312	171,852	133,344	112,424	59,384	39,728	13,720	6,648	1,816	620	96	28		1	1,081,575
	9			4	24	216	2,376	7,944	31,296	60,692	140,032	190,332	284,760	314,004	306,872	275,348	185,584	134,723	60,272	33,640	10,032	3,956	656	204		8		2,042,975
	0				30	584	3,080	17,544	41,234	114,352	192,568	338,744	431,380	506,240	497,440	419,040	332,492	190,504	113,864	43,608	19,502	4,728	1,576	184	58	8		3,268,760
	1				104	796	6,792	19,672	67,608	140,152	282,944	431,888	599,632	680,364	683,752	597,480	425,768	281,628	138,864	67,824	21,864	8,208	1,648	344	64	4		4,457,400
	2				88	1,688	6,696	28,368	74,136	171,640	316,368	509,472	685,464	804,528	812,204	688,936	502,912	313,496	172,264	72,752	29,200	7,704	1,984	376	24			5,200,300
	13			20	256	1,908	8,608	28,184	75,200	170,100	311,112	507,100	683,472	817,712	808,992	680,540	512,952	312,316	169,480	75,672	27,136	7,480	1,712	308	40			5,200,300
	14			8	298	2,128	8,620	24,040	67,330	137,392	277,344	414,864	602,052	688,504	686,240	608,600	425,508	280,208	137,792	66,312	22,010	6,808	1,156	176	10			4,457,400
	15			28	440	1,756	6,248	21,316	42,976	111,080	182,776	327,944	421,448	505,380	517,728	433,960	332,848	185,964	111,144	41,332	18,688	4,344	1,224	116	16	4		3,268,760
	16		1	72	444	1,424	4,820	10,224	34,272	56,912	129,272	184,872	274,960	317,240	322,144	282,512	189,440	132,112	56,654	32,384	8,340	4,008	708	144	16			2,042,975
	17			32	208	1,144	1,968	7,956	12,600	37,859	56,912	107,724	137,312	174,924	172,776	138,688	112,592	59,796	38,656	11,816	6,760	1,244	536	64	8			1,081,575
	18		4	40	214	296	1,788	1,944	8,166	11,584	30,032	42,760	68,752	74,696	73,112	66,704	44,624	32,792	12,420	7,904	1,538	1,096	124	96	14			480,700
	19			64	104	316	232	1,518	1,728	5,944	8,832	18,514	23,048	27,716	28,104	24,050	18,440	8,868	6,544	1,406	1,304	156	200	12				177,100
	20		8	16	52	56	262	208	820	1,232	3,472	4,696	6,820	8,224	9,176	7,488	4,524	3,776	1,180	856	96	144	8	16				53,130
	21		8	16	8	42		88	72	356	536	1,192	1,824	2,300	1,912	1,496	1,488	676	432	76	88	12	24	4				12,650
	22		4				24		16	32	144	224	392	344	312	320	208	152	52	72	4							2,300
	23							2		20	8	42	40	44	32	46	40	8	16	2								300
	24										5		8		4			8										25
	25	1																										1

The average number of buttons needed to solve a position is obviously 12.5.

Orbix (type 1):

	Total	1	12	66	220	495	792	924	792	495	220	66	12	1	4,096
		Buttons
		0	1	2	3	4	5	6	7	8	9	10	11	12	Total
L i g h t s	0	1													1
	1						12								12
	2							60				6			66
	3				40				180						220
	4					255				240					495
	5		12				600				180				792
	6			60				804				60			924
	7				180				600				12		792
	8					240				255					495
	9						180				40				220
	10			6				60							66
	11								12						12
	12													1	1

The average number of buttons needed to solve a position is obviously 6.

Jaap's Puzzle Page

Lights Out

Lights Out Classic:

Lights Out 2000:

Lights Out Cube:

Lights Out Deluxe:

The + move:

Lights Out Deluxe:

The × move:

Mini Lights Out:

Gamze Lights Out

The + move

Gamze Lights Out

The × move

Merlin Magic Square

Original version:

Merlin Magic Square

Reissued version:

XL-25 Knights Game:

Orbix (type 1):