4ξޤǤ񤭽Фǡ12612ȤʤꤽäΤǡn(>1)ΤȤn(n-1)ˤʤפȻפޤ45=20
125ڡ 0:14:09 41177

ΰ̣򤹤Τˣʬۤorz
飳İסİפޤ
İס53 ᣶
İס52 ߣᣴ
ݣᣲ
裲롼ס 125ڡ 0:17:59 HomePage:41178
⡼ޥ
ߤгˡ򿮤ơ^^;
12345
23451
34512
45123
51234
13524
24135
35241
41352
51413
14253
25314
31425
42531
53142
15432
21543
32154
43215
54321
褦Ǥ͡^^;
ٶĺޤä ^^
125ڡ 0:22:40 41179

Фϡ

MβˡߤԤͤޤ
⡼ޥ󤵤ȤۤƱͤǡġ
1٤ƥӥåꤹۤɼʤäǤ
ٶƤޤ
125ڡ 0:58:27 41180
abcba@baLLjugglermoka
NΤȤϡN(N-1)̤Ǥ͡
125ڡ 1:02:18 41181

轵˺ƤĴäǤ͡
򤭤ä

ϥǤ
ޤ޹礤ޤ
125ڡ 3:49:50 HomePage:41182
ǯ
ͤޤȤޤ餺ޤȹ礻Ĵ٤ޤ
θǡƱΤʤܣĤƱȹ礻ݣƱݣƱȿޤޤäƤޤ󡣷ǼĤ򻲹ͤٶƤ餤ޤ
125ڡ 9:37:47 41183
takasi
̲ǤϤʤǤ5ǿǤ뤳ȤѤ

1a5,1b4Ǥ뼫a,bȤ(a,b)ɽޤ
(a,b)򼡤Τ褦ޤ
1ܤaȤ
(n+1)ܤnܤοb­Ȥ롣6ʾˤʤ5Ҥ

ξ뤳ȤǤޤ
(a,b)20̤뤳ȤǤΤǤ줬Ǥ
125ڡ 9:44:39 41184
и
14Ǥɤΰ̤פʤΤ 1234,2143,3412,43214̤ꡢ줾ξüȴ֤5Τ
45=20
125ڡ 10:27:33 41185
uchinyan
Ϥˤϡơϡ
ࡤϤ褯ʬޤǤʤꤤøȤְäƤǽ硤Ȼפޤ

ο 120 ĤǤΤǡΤ顤5 ġ4 ġ3 ġ2 ġοפФʡȻפ
5 İסʬȤʤΤ̵̣
4 İס5 İפƱ
3 İסʬȤʤ褦դơ5C3 * 6 * 1 = 60
2 İסʬȤʤ褦դơ5C2 * 2 * 2 = 40
120 - 60 - 40 = 20

ιͤޤ褯ʬʤȤϴĤޤ
ʬȤʤ褦դơ3 İס2 İסȤ
Dz­ʤƤΤ
ʤɡȤǤ

θ塤Ժǡɤ 20 ĤݤʡȻפäǧڤȯǤ
嵭ιͤ϶äǽޤ

äȤ⡤ǼĤɤȤ#41178ƱǤ͡

ϤɤʤΤʡ
ͥνȡ 125ڡ 13:27:21 41186
ޥ
Ǥ.֤룲ˡ52=20̤פʤΤǡ21̤ȡȷ㸶ǡɬŤʤ꤬ƤޤΤNGäƤꤨȤ20̤ꡣȤϡºݤΥѥͤơĤȤǤºݤΥѥͤΤʤʤݤʤΤǤġ
ҡ 125ڡ 13:57:56 HomePage:41187
ϥ饮㡼ƥ
sum(2n,n=1,5)Ȼפä.ճ˾ʤΤˤӤäꤷ
125ڡ 14:12:16 HomePage:湩ؤ˥41188
uchinyan
#41187
֤룲ˡ52=20̤פʤΤǡ21̤ȡȷ㸶ǡɬŤʤ꤬ƤޤΤNG
äƤꤨȤ20̤ꡣ
ʤۤɡåʤʤޤǤͤʬϻԺˤʤǤ͡
ͥνȡ 125ڡ 15:50:24 MAIL:uchi@sco.bekkoame.ne.jp 41189

ΰ̣ǤʥȥˡϤۤäƤơ٤ߤ˹ͤޤʤϤäꤻȤǤ
٤ưۤʤΤϤȤ




Σ
İۤʤΤϤΣĤФ˰ĤĿ
ʣĤΣܤΣĤΣܤΣĤΣܤΣĤΣܤΣĤΣܤΣΤ
äƼФӤʣˤΣ
ФᣱФӤʣˤΣ
ФᣲФӤʣˤΣ
ФᣳФϤ٤ƱˤʤäƤޤΤǤʤ
äƣܣܣܣᣲ̤ˤʤޤ
125ڡ 16:30:54 41190

ǤäƲƤߤ
#41179⡼ޥ󤵤ƱǤ;ʬʾȤäƤޤ
Ф˸ƤˡгˡȤǤ
ȤʤäƤˡΤȤǤïͤˡۤȤɤʤǤ͡
125ڡ 16:40:42 41191
uchinyan
դࡣɤΤȤ

ޥ뤵#41187ǺĿθ򼨤
⡼ޥ󤵤#41179Jޥޤ#41180#4119ʤɤμˡгˡǼºݤ򼨤

ȤΤ褵Ǥ͡
ͥνȡ 125ڡ 17:19:09 MAIL:uchi@sco.bekkoame.ne.jp 41192

takasi#41184ΤäȤǿġ N=5ˤʤ
N-1ĤΥ롼 (12345) (13524) (14253) (15432) 򤽤줾ơ󤵤
Ū N(N-1)ĤβǤǤ͡
ǿǤʤ N=6 ξϤɤΤġĶŪ˹ͤ褦Ȥǰ
125ڡ 18:07:25 41193
ޤ륱
ȤǡΡ㤨СפΤȤȤäοˤʤäƤޤ
ǡN(N-1)ǤѤΤõƤߤǤ
ɤ飶ξϣĤ³Τ褦ʵƤޤ
ʤߤˡϣġϣĤ¿ϸĤäƤޤ
꤬Ǥ褫ä
ʤ硡 126ʶ 11:13:04 MAIL:take4310@mobile.email.ne.jp HomePage:ޤ륱41194
uchinyan
#41184
takasi󡤺ϤäƷǼĤФɤߤԽʬǤ
βˡϡǿξˤɬ׽ʬʲͿƤ褦Ǥ͡פޤ
ޤ⡼ޥ󤵤#41179ʤɤгˡμˡϤβˤʤäƤ褦Ǥ

ǡǿʳξϤɤʤΤǤ礦͡Τˡn = 4 Ǥ⤦ޤʤ褦Ǥ
ޥ뤵#41187μˡǿǤʤȤȤΤ n(n-1) ĿθʤΤϴְ㤤ʤǤ
줬¸ǤΤɤ¸ǤʤˤϹʹߤΰϤΤȤ
ͥνȡ 126ʶ 11:31:41 MAIL:uchi@sco.bekkoame.ne.jp 41195
uchinyan
#41194
ޤ륱󤵤󡤣ʾĴ꤬Ȥޤ
塤ϡޤʤΤʡȻפޤ
7 * (7 - 1) = 42 ǤϤʤȾʬ 21 ĤʤΤǤ
#41184μʳĥ 42 ĤȻפäΤǤ㤦Τʡ
ͥνȡ 126ʶ 11:45:20 MAIL:uchi@sco.bekkoame.ne.jp 41196
ޤ륱
˴ؤ
μ˰֤˿Ȥäơ

Ȥȡμˤ
ȸäƤޤΤǡߣȻפޤ

ΤĤФơ
Τ褦ˤȡ١ο̤Ǥơ줾ơ󤷤ƣߣᣴĤ뤳Ȥǧޤ
餷ޤ

ġĥäƤޤ

1234567 2345671 3456712 4567123 5671234 6712345 7123456
1473625 4736251 7362514 3625147 6251473 2514736 5147362
1357246 3572461 5724613 7246135 2461357 4613572 6135724
1765432 7654321 6543217 5432176 4321765 3217654 2176543
1526374 5263741 2637415 6374152 3741526 7415263 4152637
1642753 6427531 4275316 2753164 7531642 5316427 3164275

ʤ硡 126ʶ 15:36:54 HomePage:ޤ륱41197
uchinyan
#41197
ޤ륱󤵤󡤣γǧ꤬ȤޤϤ 42 Ĥޤ
takasi#41184ϡ n ǿξˤŪȻפΤǡʡȻפޤ
¿ʬn ǿξ n(n-1) ĤǷޤǤ礦
n ǿǤʤǡޤ륱󤵤η̤򸫤ȡ̤ˤ n(n-1) ϾʤꤽǤ
ϼʵޤΤʸĿΤ񤷤Τʡ
ͥνȡ 126ʶ 15:54:24 MAIL:uchi@sco.bekkoame.ne.jp 41198
ǯ
#41199Ȥְ㤨ƺƤޤޤľޤ
ε§ȽˤȤϡʤηΤʤΥåȡʣĤΥåȡˤͭꡢγơΥåȤФơƱΤΣĤбƤȤȤˤΤʤȴƤޤ

ĤηˤĤơƱʪʤĿĤƱη夬ĿƤߤޤƱΤʤΥåȤФơΤƱΤȤƵޤΤǡΤߤʤƱΤӤǤƤޤ󡣤ƱΤʤΥåȤϳƷˣޤǿޤǤޤΤǡˡǤ褤ΤǤϤʤȻפޤʴְäƤ餴ʤ
塡Ʊη夬ʤΡġƱΡġס
塡Ʊη夬ʤΡġƱΡġס
塡Ʊη夬ʤΡġƱΡġס
ʿϣʤΤǡʸǹԤäȹͤɤǤ礦
Ʊη夬ʤΡġƱΡġס
ȣϡ#41179⡼ޥ󤵤#41184takasi#41190ᤤ󤿤εܤƤˡФˤĤƤΤ߳ǧΤǤ

ǿξϡʣݣˤΩǤ͡

§̵ȻפäƤäƤߤ̤ǤäѤǤ


127ڡ 0:11:46 41200
̴
äȡΰ̣㤨ɤƣǤϤʤΤȡ
ܸٶɬפ˴Ǥ
ٻΤ桡 127ڡ 15:50:38 41201
takasi
12345678 13574286 14768523 15487362 16253847 17826435 18632754
21436587 24683175 23857614 26378451 25164738 28715326 27541863
34127856 31752468 32586741 37265184 38471625 35648217 36814572
43218765 42861357 41675832 48156273 47382516 46537128 45723681
56781234 57138642 58324167 51843726 52617483 53462871 54276318
61872143 68247531 67413258 62734815 61528374 64351782 63185427
78563412 75316824 76142385 73621548 74835261 71284653 72458136
87654321 86425713 85231476 84532637 83746152 82173564 81367245

8ξ56̤Ǥޤ
127ڡ 19:01:07 41202
takasi
ޤ󡣽꡹ߥޤ

12345678 13574286 14768523 15487362 16253847 17826435 18632754
21436587 24683175 23857614 26378451 25164738 28715346 27541863
34127856 31752468 32586741 37265184 38471625 35648217 36814572
43218765 42861357 41675832 48156273 47382516 46537128 45723681
56781234 57138642 58324167 51843726 52617483 53462871 54276318
65872143 68247531 67413258 62734815 61528374 64351782 63185427
78563412 75316824 76142385 73621548 74835261 71284653 72458136
87654321 86425713 85231476 84512637 83746152 82173564 81367245
Ȥʤޤ
127ڡ 19:20:09 41204
kitaji
ФǤ餹ޤ
ޤϰܤλʬޤǹͤФ褤Τǡ54ȹͤޤ
128 1:58:36 41207
ǯ
#41204takasiη̤ߤ48ľƤߤޤ
ߤ˳Ʒοۤʤȹ礻ȡˤʣȤꡢȤϤߤȻפäƤޤɤǤϤʤ褦Ǥ
8ˤĤƤΡ㤨12345678, 21436587, 34127856, 43218765, 56781234, 65872143, 78563412, 87654321Ȥ饹ȤȡΤ56Ĥη̤ˤʤޤǤ䤹ȤǤ롢12345678, 23456781, 34567812, 45678123, 56781234, 67812345, 78123456, 81234567ȤǤϡ8Ĥޤ840320ĤοȤ̡ϤˤʤäƤޤˡ
ΤȤ4Ǥ12ġ4*(4-1)]ǧǤޤ1234, 2341, 3412, 4123ȤǤ4ĤǤ#412004ʤ餯6˴ְ㤤Ǥ
ޤǧǤ4塢5塢8οǤϡߤ˳Ʒοۤʤȹ礻ȡˤǹƤޤ6ϤޤäƤޤ
4
(1) 1234, 2143, 3412, 4321
(2) 1342, 2314, 2431, 4213
(3) 1423, 2314, 3241, 4132
5
(1) 12345, 23451, 34512, 45123, 51234
(2)1 13524, 24135, 35241, 41352, 52413
(3)2 14253, 25314, 31425, 42531, 53142
(4)3 15432, 21543, 32154, 43215, 54321
8
#41204οɽνĤȤˤʤäƤޤ
128 12:19:31 41208
uchinyan
#41204
takasi󡤣ξ򤢤꤬Ȥޤ56 Ĥޤ
ξϡ㤨С
1234 1342 1423
2143 2431 2314
3124 3241 3412
4132 4321 4213
12 ĤΤǡ̤ n(n-1) ĤβǽФƤޤ͡

ξϤɤʤ
ͥνȡ 128 12:39:34 MAIL:uchi@sco.bekkoame.ne.jp 41209
ǯ
#412084ξοְ̤㤨Ƥޤ
4
(1) 1234, 2143, 3412, 4321
(2) 1342, 2431, 3124, 4213
(3) 1423, 2314, 3241, 4132
128 14:57:25 41210

takasi#41204
ֺΥ֥å8Ĥ
01234567 γƷ 0,1,2,3,ġ,7 XOR +1 Τǡ
ˤ 23547862 ִ12󡢡ġĤȷ֤ƤȤ
2֤7֤Υ֥åǤ͡
̤ N=2^n ʤ N(N-1)ĺ줽ͽ
128 22:16:09 41211

takasi#41204
ֺΥ֥å8Ĥ
01234567 γƷ 0,1,2,3,ġ,7 XOR +1 Τǡ
ˤ 23547862 ִ12󡢡ġĤȷ֤ƤȤ
2֤7֤Υ֥åǤ͡
̤ N=2^n ʤ N(N-1)ĺ줽ͽ
128 22:56:34 41212

N=2^n ξͤƤߤޤ
ʰʲXOR 䤹褦
Nο 0,1,2,ġ,N-1 ¤ؤǹͤޤ

{0,1,2,3,ġ,N-1} Ф {0,0,,0},{1,1,,1},ġ,{N-1,N-1,,N-1} XOR
{0,1,2,3,ġ,N-1}
{1,0,3,2,ġ,N-2}
{2,3,0,1,ġ,N-3}
{3,2,1,0,ġ,N-4}
ġ
{N-2,N-1,N-4,N-3,ġ,1}
{N-1,N-2,N-3,N-4,ġ,0}
NĤȤޤǤ OK

ˤ 0 1,ġ,N-1 ִ f 缡ä N(N-1)Ĥ䤷ޤ
ִ f εʲΤ褦˹ͤޤ

(1) a(0)=1, a(1)=2, a(2)=4, ġ, a(n-1)=2^(n-1) Ȥ
(2) a(n) ʹߤϼǷꤹ
a(k) = a(k-n) XOR a(k-n+1)
(3) f(a(n)) = a(n+1) Ȥ

ȡa(k) ϼ N-1 μŪˤʤޤ
⤷ a(k) μ N-1 ˤʤäƤСf 1,ġ,N-1 Τ󤹤ִȤʤޤ

Ȥ
n=3 (N=8) ΤȤ f : 12436751 ʼ 7
n=4 (N=16) ΤȤ f : 1248361211510714151391 ʼ 15
Ȥʤޤ
f Ȥä 1Ĥ {0,1,2,3,ġ,N-1}
{0,1,2,3,ġ,N-1}
{0,f(1),f(2),f(3),ġ,f(N-1)}
{0,f^2(1),f^2(2),f^2(3),ġ,f^2(N-1)}
ġ
{0,f^<N-2>(1),f^<N-2>(2),f^<N-2>(3),ġ,f^<N-2>(N-1)}
N-1Ĥ䤹Ȥޤ

ƺä N(N-1)Ĥοϸߤˤ 1սꤷʣޤ󡣡ʤξά

ִ f ¸ߤ뤫ʤΤǤġ
n=3,4 Ͼ嵭ΤȤOKʤΤǤʹߤ
n=5 ϼ 21ʡ31 NG
n=6 ϼ 63 OK
n=7 ϼ 127 OK
n=8 ϼ 63ʡ255ˤ NG

n=9 ϼ 73ʡ511ˤ NG
n=10 ϼ 889ʡ1023ˤ NG
n=11 ϼ 1533ʡ2047ˤ NG
n=12 ϼ 3255ʡ4095ˤ NG
n=13 ϼ 7905ʡ8191ˤ NG
n=14 ϼ 11811ʡ16383ˤ NG
n=15 ϼ 32767 OK
ȷ̤ɤޤ
f ȤäѤƤ
n=5 ϡ a(k) = a(k-n) XOR a(k-n+2) Ǽ 31
n=9 ϡ a(k) = a(k-n) XOR a(k-n+4) Ǽ 511
n=10 ϡ a(k) = a(k-n) XOR a(k-n+3) Ǽ 1023
n=11 ϡ a(k) = a(k-n) XOR a(k-n+2) Ǽ 2047
Ŭڤ f ⤢ޤ
n=8,12,13,14 Ǥμ㴳ѹǤ f ޤǤ

Ȥ櫓ǡN=2^n Ǥΰ̲ʤޤϲԺߤξˤϴñǤϤʤ褦Ǥ

1210ʲС 11:35:22 41213
uchinyan
#41213
󤵤N = 2^n ξξܤͻ򤢤꤬Ȥޤ
ɡN(N-1) ĤȤʤ⤢뤬ʤ뤫褯ʬʤ빽롤ȤȤǤ礦

⡤ǿξʳϡδ֤θФ֤Ʊͤ˰̲񤷤Ǥ͡
ͥνȡ 1210ʲС 17:59:02 MAIL:uchi@sco.bekkoame.ne.jp 41214
a
ξ


夹٤Ʊ
Ʊ
Ʊߣ1/2ߣãᣲ
Ʊߣ2/6ߣãᣱ
Ʊߣ3/24ߣã᣶
Ʊߣ4/120ߣãᣱ

衡ݣݣݣݣᣴ
1211ʿ 8:56:42 41215
粬ҹ
ʤʤ˲򤱤ޤǤʡ
ơǤβˡǤݤǤ
1211ʿ 14:12:13 41216
kitaji
5ξ硢1ΰ̤1λΰ̤254̤ꡣ
1ΰ̤2λΰ̤1,3,4,54̤Ťȹͤ1ΰ̤ˤ5̤οΤǡ54ȹͤޤnξƱͤ˹ͤСn(n-1)Ǥ
1211ʿ 15:26:04 41217
kitaji
ޤn9ʲμξǤ
1211ʿ 15:34:12 41218
kitaji
١ޤnϤɤʿǤn(n-1)Ǥޤ
1211ʿ 21:08:54 41219