ߡ
̣˾ʬޤ
1545154040120120396(̤)

ȤʤֵջᤫäʤפȼǰĤġ

ʤߤ˼ǰ()ξ
720(1449090)396(̤)Ǥ
1218ڡ 0:16:31 33462
ڼ
324äƤޤʻǰ
͡ 1218ڡ 0:19:22 MAIL:iida@ae.keio.ac.jp 33463
纬İ
ߡαջǷ׻ޤ

ϻ󷫤֤ƸʽˤɤʤΤ̤ꤢΤͤޤ

ǤϤʤͤȣͤδ֤Ǥʤ۴Ĥȯȡ
ϻ󷫤֤Ȥ˸ʽʤΤǡξϤ줾졡

ʹ֤ν۴Ĥǡ6*5*3*2*1*1ᡡ180̤ꡢ
޿ʹ֤ν۴Ĥǡ6*4*3*2*1*1ᡡ144̤

ͤΤǡ٤ƤȤ߹碌720̤꤫餽򺹤ơ
720-180-144396Ȥʤޤ
1218ڡ 0:26:04 33464

Ǥν󷲤Ǥ͡

㤨6ͤƱ˽Ƹ6ܤ륫ɤϤ5!
ƱͤˤnͤnܤǸ륫ɤϤ(n-1)!
6ͤˤϤΤ褦nͤȤʣ¸ߤΤǤ(l,m,n,)ȵҤ롣

ʤ褦ʥɤϤ(1,5)(2,4)(1,1,4)ΤߡʤĤޤ6Ǥ̵ޤȤ߹碌ˤʤΤǡ
6!-(64!+6C23!+6C23!=396

ϻäݤޤʾС
1218ڡ 0:27:30 33465
Taro
ľˤäꡢʤˡǤͤƤߤޤ
4ͤǤΤȤʤ۴Ĥ6̤ȤƤޤ

ʤΤǷɥץǤorz
1218ڡ 0:28:24 33466
Ѥ
ƻ˾ƤϤޤΤʬƲ򤭤ޤ
(1,1,1,1,1,1)˵դʤä

ǼĤ佸ιͤ򸫤ƶäޤ
äꤤǤ͡ο϶Ǥ
֡ 1218ڡ 0:34:11 HomePage:33467
ڤפɡ
롼ʬǤ͡
ʤʤΤ˷׻Ǥʤä
6ǤȤȤȤϡ236ǽ۴ĤФ顢
ǥ롼פФ

ˡȤʤǤʤä
1,1,42,41,5720ޤorz
1218ڡ 0:40:08 33468
SUPER SPECIAL SEMTEX
̤Ǥ
׻ߥ³
ɣͤν۴Ĥȣͤν۴ĤդޤΤޤ
1218ڡ 0:42:54 33469
ϡ
Ǥν۴ĤĤγȻפǤơʤʤˤɤ失ޤǤֵջפDz򤤤褤Τ͡빽Ǥͤ
1218ڡ 0:43:11 33470
Mr.ǥ
Ĥγ󤫤ŬʤΤȤꡢʬϳ줿Ǵְ㤤ޤޤ
ɤϡߡƱ1545154040120120396(̤) Ȥˤʤޤ

ʤ¿ʤȤϻפ鷺ֵջפȯۤФƤޤǤƬ
1218ڡ 1:25:52 33471
翹˼
ݡʣˤξ˺졦
ʤۤɡۤ®ǤξϤɤˤ躬Ū˴ְäƤ
1218ڡ 2:59:29 33472
ϥ饮㡼ƥ
ץǤ
ľƷ׻ޤ
ܹѤʤޤ֤
ͭͤФ狼ΤǤϤʤȻפޤ
1218ڡ 7:33:19 HomePage:湩ؤ˥33473
abc
ʴ˽Ѥƿ褦ȤơʣͤäƤޤޤΤ褦ˡִѤ;ݤǵΤñǥ쥬ȤǤ͡
1218ڡ 8:17:18 33474
abcba@jugglermoka
#33464ȤƱǤ
ͤϤʬäΤǤ׻ְ㤨Ϣ³Ǥ
ʣˡʣˡʣˤǣ۴Ĥξϣ̤ꡢ
۴Ĥξϣ̤ʤΤ
-ʣߣ+ߣˡᣳ̤Ǥ
1218ڡ 11:00:22 33475
uchinyan
Ϥˤϡơϡ
ؤʤɤǹ󼰤ΰؤͤϡִ֤ʡפȻפꡤ㴳ͭ⤷ޤ
󡤾οη׻ˤϤμפǤѤǤ͡
ޤǤĹʤäƤޤäƿޤ󤬡

1, 2, ... ȥ a, b, ... ȹ礻 (1->a,2->b,...) ʤɤȽ񤯤Ȥˤ
1 ֤Υ A Ϻ2 ֤Υ B Ϻ¤äƤ֤˹碌ơ(A,B,...) ʤɤȽ񤯤Ȥˤޤ
(ִȤƤϡϺ A ֤ΥˡϺ B ֤Υˡ¤äƤ֤ (A,B,...) ʤɤȤǤ礦)
ϡ(1->2,2->3,3->5,4->1,5->4,6->6)(1,2,3,4,5,6) -> (4,1,2,5,3,6) -> (5,4,1,3,2,6) -> ... Ǥ
ơˡǤĴ٤Ƥߤȡ6 ؤ򤷤ƺǽ (1,2,3,4,5,6) äƤΤϡ
(1->a,2->b,3->c,4->d,5->e,6->f) 6 1, 2, 3, 6 Τ줫θĿοĤʬǤʬޤ
㤨С(1->1,2->2,3->3,4->4,5->5,6->6) ϡ1 Ǹޤäơ6 Ǹޤ
(1->1,2->3,3->2,4->5,5->6,6->4) ϡ(1->1) 1 (2->3,3->2) 2 (4->5,5->6.6->4) 3 ǡΤ 6 Ǹޤ
(1->2,2->3,3->4,4->5,5->6,6->1) ϡΤ 6 Ǹޤ
(1->2,2->3,3->5,4->1,5->4,6->6) ϡ1, 2, 3, 4, 5 ʬ 5 Ǹꡤ6 Ǥϸޤ
(ִη׻ηиȡε§ˤդǤ礦)
ǡʬΥѥ򸵤¤٤ [ ] dzäƽ񤯤Ȥˤޤ
(1->1,2->2,3->3,4->4,5->5,6->6) ϡ[111111]
(1->1,2->3,3->2,4->5,5->6,6->4) ϡ[123](1, 2, 3 ؤΤƱѥȤޤ)
(1->2,2->3,3->4,4->5,5->6,6->1) ϡ[6]
(1->2,2->3,3->5,4->1,5->4,6->6) ϡ[15]
ȡɡ6 ؤ򤷤ƸΤϡξǤ
[111111](1->1,2->2,3->3,4->4,5->5,6->6) ʤΤǡ1 ̤ꡣ
[11112]2 ֤Τ 6C2 = 15 ̤ꡤ2 ¤ؤ 1 ̤ǡ15 * 1 = 15 ̤ꡣ
[1113]3 ֤Τ 6C3 = 20 ̤ꡤ3 ¤ؤ 2 ̤ǡ20 * 2 = 40 ̤ꡣ
[1122]2 ֤Τ 6C2 * 4C2 * 1/2! = 45 ̤ꡤ2 ¤ؤ 1 ̤ǡ45 * 1 * 1 = 45 ̤ꡣ
[123]2 ֤Τ 6C2 = 15 ̤ꡤ3 ֤Τ 4C3 = 4 ̤ꡤ2 ¤ؤ 1 ̤ꡤ3 ¤ؤ 2 ̤ǡ15 * 4 * 1 * 2 = 120 ̤ꡣ
[222]2 ֤Τ 6C2 * 4C2 * 2C2 * 1/3! = 15 ̤ꡤ2 ¤ؤ 1 ̤ǡ15 * 1 * 1 * 1 = 15 ̤ꡣ
[33]3 ֤Τ 6C3 * 3C3 * 1/2! = 10 ̤ꡤ3 ¤ؤ 2 ̤ǡ10 * 2 * 2 = 40 ̤ꡣ
[6]6 ֤Τ 6C6 = 1 ̤ꡤ6 ¤ؤ 5 * 4 * 3 * 2 * 1 * 1 = 120 ̤ǡ1 * 120 = 120 ̤ꡣ
ǡ6 ¤ؤϡ1->a 5 ̤ꡤa->b 1,a ϥʤΤ 4 ̤ꡤb->c 1,a,b ϥʤΤ 3 ̤ꡤ
c->d 1,a,b,c ϥʤΤ 2 ̤ꡤd->e 1,a,b,c,d ϥʤΤ 1 ̤ꡤe->f f = 1 ʤΤ 1 ̤ꡤǤ
ʾǤ٤ƤʤΤǡ1 + 15 + 40 + 45 + 120 + 15 + 40 + 120 = 396 ̤ꡤˤʤޤ

ʤ 6! = 720 ̤ꡤ顤6 Ǻǽξ֤ʤ׻ڤǤ
6 Ǻǽξ֤ʤΤϼξǤ
[114], [24]4 ֤Τ 6C4 = 15 ̤ꡤ4 ¤ؤ 3 * 2 * 1 * 1 = 6 ̤ꡤ[11] [2] Ȥ碌 2 ̤ǡ15 * 6 * 2 = 180 ̤ꡣ
[15]5 ֤Τ 6C5 = 6 ̤ꡤ5 ¤ؤ 4 * 3 * 2 * 1 * 1 = 24 ̤ǡ6 * 24 = 144 ̤ꡣ
ǡ720 - (180 + 144) = 396 ̤ꡤˤʤޤ

¤ϡīϻȱɮ긵̵Ż򿴤뤷ʤǽˡǺޤޤΤˡDzȤǤޤ (^^;
ͥνȡ 1218ڡ 14:30:57 MAIL:uchi@sco.bekkoame.ne.jp 33476
???
Option Explicit
Dim a(6) As Integer
Sub Macro1()
Sheets("Sheet1").Select
Cells(1, 1).Value = 0
Range("A1").Select
Call saiki(1)
End Sub
Sub saiki(ByVal n As Integer)
Dim j As Integer
a(n) = 1
While a(n) <= 6
If onaji(n) = 0 Then
If n < 6 - 1 Then
Call saiki(n + 1)
Else
a(6) = 6
For j = 1 To 6 - 1
a(6) = a(6) + j - a(j)
Next j
Call check(1)
End If
End If
a(n) = a(n) + 1
Wend
End Sub
Sub check(ByVal x As Integer)
Dim b(6) As Integer
Dim dame As Integer
Dim j As Integer
For j = 1 To 6
b(j) = a(a(a(a(a(a(a(j)))))))
Next j
dame = 0
j = 1
While dame = 0 And j <= 6
If b(j) <> a(j) Then
dame = 1
Else
j = j + 1
End If
Wend
If dame = 0 Then
Cells(1, 1).Value = Cells(1, 1).Value + 1
For j = 1 To 6
Cells(Cells(1, 1).Value, j + 1).Value = a(j)
Next j
End If
End Sub
Private Function onaji(ByVal n As Integer) As Integer
Dim j As Integer
onaji = 0
j = 1
While onaji = 0 And j < n
If a(j) = a(n) Then
onaji = 1
Else
j = j + 1
End If
Wend
End Function
1218ڡ 12:49:11 33477
uchinyan
ǼĤɤߤޤ

#33462Ⱦ#33467#33471#33472#33476Ⱦ
6 ؤ򤷤ƺǽξ֤ľ˿ˡ

#33462θȾ#33464#33465#33468#33469#33475#33476θȾ
6 ؤ򤷤ƺǽξ֤ʤΤˡ

#33466#33473#33477
ץࡣ

ʤ

#33465
Ǥν󷲤Ǥ͡
դࡤŪªޤϤޤȤٶȤ̵Τ (^^;
μȤСñ˲򤱤㤦Τʡ

#33470
䣶Ǥν۴ĤĤγȻפǤơ
#33471
䣶Ĥγ󤫤ŬʤΤȤꡢ
#33474
ʴ˽Ѥƿ褦Ȥơ
Τ˳ȤȻפ;ʬʽʣθɬפޤ
#33476ȾŬѤƤߤȡ
ޤ a(n) ϡάޤ
a(n) = (n-1) * (a(n-1) + a(n-2))
a(1) = 0
a(2) = 1
a(3) = 2
a(4) = 9
a(5) = 44
a(6) = 265

[111111] ˤϻȤޤ󡣤ξ 1 ̤ꡣ
[11112][1113][1122][123] Ǥϡ2 ¤ؤ3 ¤ؤǻȤ a(2) ̤ a(3) ̤ꡣ
[222][33][6] ϡa(6) [24] ФǤ[24] [4] ¤ؤ [22] ʬʤȤʤΤǡ
a(4) ǤϤʤ a(4) - 4C2 * 2C2 * 1/2! * a(2) * a(2) ʤΤդǤ
ǡɡ
1 + 6C2 * a(2) + 6C3 * a(3) + 6C2 * 4C2 * 1/2! * a(2) * a(2) + 6C2 * 4C3 * a(2) * a(3)
+ (a(6) - 6C2 * a(2) * (a(4) - 4C2 * 2C2 * 1/2! * a(2) * a(2)))
= 1 + 15 * 1 + 20 * 2 + 15 * 6 * 1/2 * 1 * 1 + 15 * 4 * 1 * 2 + (265 - 15 * 1 * (9 - 6 * 1 * 1/2 * 1 * 1))
= 1 + 15 + 40 + 45 + 120 + (265 - 90)
= 1 + 15 + 40 + 45 + 120 + 175
= 396 ̤
ΤƱͤˤǤޤɬڤǤϤʤ褦Ǥ
6! - 6C4 * (a(4) - 4C2 * 2C2 * 1/2! * a(2) * a(2)) * 2 - 6C5 * (a(5) - 5C2 * 3C3 * a(2) * a(3))
= 720 - 15 * (9 - 6 * 1 * 1/2 * 1 * 1) * 2 - 6 * (44 - 10 * 1 * 1 * 2)
= 720 - 180 - 144
= 396 ̤
Ȥʤޤ
ͥνȡ 1218ڡ 14:20:28 MAIL:uchi@sco.bekkoame.ne.jp 33478
ϥ饮㡼ƥ
#33473
ƱȤǤ礦ͭ¿༰ˡݣȤʤΤοǤ͡
ؤͭ̾ʤΤϣͷǤ
1218ڡ 19:30:49 HomePage:湩ؤ˥33479
ϥ饮㡼ƥ
MATLABˤץ
aܹx,xd֤ɽѿ

ͤޤǤ

xd=[1 2 3 4 5 6]';
x=[1 2 3 4 5 6]';
m=0;
p=perms(1:6);
for k=1:720;
a=zeros(6);
b=p(k,:);
a(1,b(1))=1;
a(2,b(2))=1;
a(3,b(3))=1;
a(4,b(4))=1;
a(5,b(5))=1;
a(6,b(6))=1;
xd=x;
%
for ii=1:6;
xd=a'*xd;
end;
if xd==x, m=m+1;end;
end;
m
1219ʶ 7:39:38 HomePage:湩ؤ˥33480
ֿء׾ι
ץǤƤߤޤ
1221 0:38:09 33481
ֿء׾ι
Risa/AsirǼΤ褦ˤޤ

0 0 1 0 0 0
0 0 0 1 0 0
1 0 0 0 0 0
0 1 0 0 0 0 Τ褦ʣߣΤ褷ñ̹ˤʤ
0 0 0 0 0 1夲ޤ
0 0 0 0 1 0

M=0;
A=newmat(6,6);
E=newmat(6,6);

for(I=0;I<=5;I++){E[I][I]=1;}

for(I0=0;I0<=5;I0++){
for(I1=0;I1<=5;I1++){
for(I2=0;I2<=5;I2++){
for(I3=0;I3<=5;I3++){
for(I4=0;I4<=5;I4++){
for(I5=0;I5<=5;I5++){

A=newmat(6,6);

A[0][I0]=1;A[1][I1]=1;A[2][I2]=1;
A[3][I3]=1;A[4][I4]=1;A[5][I5]=1;

if(A^6==E){M++;}

}}}}}}
return M;

餫ŬʤΤˤĤƤ⣶褷Ĵ٤褦ˤʤäƤޤ
ޤץबñʤΤǡʡ
1221 0:45:24 33482
ϥ饮㡼ƥ
#33482
ʳط׻ڤˤʤޤफFORTRANǹ׻򤹤Τ
DOʸΥͥȤβˤʤäƸ񤤥ץˤʤäΤפФޤ

HPBASICǹ󤬰褦ˤơ٥ȥ뷿η׻ڤΤ
Ĥ졢ʳصѷ׻μήϥ٥ȥ롢ˤʤޤ
Ǥ

׷׻ʤ󤫤ŵŪʹ׻ȻפޤǤڤ
ʤäǥȤƬȤȤפȤʤޤ
äΤϼ󤷤Ƿ׻Ȥ졼㥬㤤äư
ΤȤοͤʹФäǤ

벽زҤˤϷ׻äƤˤϼ󤷤򤹤
⤬Ǥ׻ꤹȵμ󤷥
׻ʤ󤫤Ƿ׻Ʒ̤äƤǤΤ褦
äǤͤνλҤ̿󤹳ȤǤ
Ǥ
1221 13:33:45 HomePage:湩ؤ˥33483
⡼ޥ
äȤ狼ä...^^;

6Ĥλ265ˤ顢4Ĥλ (9*6C2=135)ҤΤϤ٤6롼פǸ롣
ȤϡưʤȤä롣

6ĤȤưʤ1
2ưȤ(4ưʤˡ6C4=15
3ưȤ3ưʤˡ2*6C3=40
4ưȤ2ưʤˡ6C2*4C2=90
5ưȤ1ưʤˡ2*6C3*3C2=120

=130+120+90+40+15+1=396̤
1221 17:38:57 33484