٥륯åĥ
4ͤABCDȤޤ
Aۤ4312̤ꡣ
Bۤ2ȤAƱ2ȤAȰ㤦1AƱǾʬƤ줾BCDۤޤ
ޤȤ(8+48+64)121440Ʃˤʤޤ
1211ڡ 0:10:52 42696
Ȥ
basic ֤ۤΥɤa,b,c,d,e,f,g,hȤ

for a=1 to 4
for b=1 to 4
for c=1 to 4
for d=1 to 4
for e=1 to 4
if a=e then goto 40
for f=1 to 4
if b=f then goto 30
for g=1 to 4
if c=g then goto 20
for h=1 to 4
if d=h then goto 10
if a+b+c+d+e+f+g+h=20 and a*b*c*d*e*f*g*h=576 then let s=s+1
10 next h
20 next g
30 next f
40 next e
50 next d
60 next c
70 next b
80 next a
print s
end

f9ơ1440̤ꡦ()
˭ԡ 1211ڡ 0:15:51 42697
CRYING DOLPHIN
ƻˡġ

1ܤϡۤʤ2ۤ4312̤ꡣ
ΤȤ12νۤäȤƤ⡢ϼʤ
2ܤϡۤ줿ɤˤĤƾʬƹͤ롣

)1ܤȤ2Ȥۤʤ륫ɤۤ줿Ȥ
2ܤˤ34ۤ롣ˡ2̤ꡣ
Ĥä2ͤ1234ʬ뤬Ϻǽ2ͤƱɤۤȤʤꡢ
(122)^2576̤ꡣ

)1ܤƱɤ1ۤ줿Ȥ
ɤȤ߹碌(13)(14)(23)(24)ǡ֤ͤ428̤ꡣ
ΤȤ(13)ȤƤϼʤ
Ĥä23442ͤʬˡϡ41示ʬ礦Ȥդƿ夲ȡ8̤ꡣ
äơ1288768̤ꡣ

)2Ȥ1ܤƱɤۤ줿Ȥ
12ۤ2̤ꡣ
Ĥä3344ۤϡɤ(34)ȼ뤷ʤΤǡ224̤ꡣ
äơ1222296̤ꡣ

פơ1440̤ꡣ

ǽϡȴطΤʤȻפäɡطϤʤäݤ
ï⤤ʤԳϡ 1211ڡ 0:31:32 HomePage:֥⤢42698
CRYING DOLPHIN
#42695
ĥޥ뤵줿⡢̵ʤ餺ˡ
ï⤤ʤԳϡ 1211ڡ 0:32:30 HomePage:֥⤢42699
ǯ
ĥ襷ϺϷʤǤ
夲ޤ
ͤ¡áĤȤơΥɤȣξˤĤƣ¡áĤȤ߹碌Ȥꡣ
ΥɤȤ߹碌ϣȤꡣ֤ͤȡ***
٤ۤɸȤ
ۤפ긵ɤμʤΤ֤ޤΤǺߡƥᡣܤƣȤ

1211ڡ 0:59:33 42701

Фϡ

1-2ܡ3-4ܡ5-6ܡ7-8
Ʊˤʤʤ褦
AABBCCDD¤٤Ͽޤ򡢰ʬ񤤤
Ȥо׻ޤ
ޤˡäɡʬʤäġ
ʬ⺮𤷤äΤǷɿ̤ˡ
ͤٶƤޤ

ޥ뤵ޡƱν⤯줰⤪ˡ

1211ڡ 1:02:15 42702
ޥ
ˡˤƻʤȤѥϤΤۤ¿ΤǤ˺ǯ»ܤޤ̣ä㤤ޤ顢 masaru-y@sansu.org ޤǥ᡼뤯ޤ
iMac 1211ڡ 1:19:16 HomePage:ARENA42703
4329ܤβ
Ƥξ8!/2!^4=2520
1ƱɤۤФ
4ͤȤƱɤۤïˤɤοۤ뤫ФʤΤ4!=24̤
3Ʊɤۤ줿Ĥ1ͤ⼫ưŪƱɤˤʤΤǤ礦3ͤƱɤˤʤ뤳ȤϤꤨʤ
2ͤƱɤξ硢Ʊɤۤ2ͤƤ餽2ͤۤлĤ2ͤۤ2ĤοޤΤǡ줾ɤۤ뤫ФΤ4C24P22^2=288̤
1ͤƱɤξ硢ޤƱɤۤ͵ڤӤοͤۤ
ȡĤ3ͤȤ߹碌ޤΤǡïˤɤȤ߹碌ۤ뤫ȡɤۤ뤫3ͳơФΤ443!2^3=768̤

ʾ˰㤦ۤο2520-24-288-768=1440̤
1211ڡ 3:18:18 42704
̴
äƤݤʷ׻򤷤ʤȤȻפ
12132434
12142334
13142324
21132443ͤ˵դʤΤä1152̤
12123434
13132424
14142323
21123443ͤ˵դʤΤä288̤
1440̤Ȥʤޤޤ
ٻΤ桡 1211ڡ 8:12:18 42705
algebra
ܣͤȤۤʤΤȤ
£ãģ£ã
̤ꡡäơߣᣲ̤

ܣͤƱΤȤ
£ãģ£ã
̤ꡡäơߣߣߣã
ᣱ̤

ܣͤĤƱΤȤ
£ãģ£ã
̤ꡡäơߣߣã
ᣲ̤

椨ˡ˿
ܣܣᣱ̤

ϤŤβˡǤ
1211ڡ 11:39:27 42706
uchinyan
Ϥˤϡơϡ
ϡñȤϸʤΤΡƻ˥ĥĿФǤ͡
äȤ⡤⤦ޡȤ˲򤱤ʤΤʡ
ޤʴǡ

(ˡ1)
ͤˣ󤺤ۤ櫓ǤܤȣܤȤʬƹͤޤܤϣܤȰۤʤˤޤ
ܤƱۤʤä
ܤ 4! = 24 ̤ꡣ㤨УȤƹͤޤ
ܤΣФƤϣ 3 ̤ꡣ㤨УȤƹͤޤ
ܤΣФƣʤС1 ̤ꡣܤΣФƣϣʤС줾Ф 1 ̤ꤺġ
ǡξϡ24 * 3 * (1 + 2) = 216 ̤ꡣ
ܤƱۤ줿
ܤ 4C3 * 3C1 * 4!/2!1!1! = 144 ̤ꡣ㤨УȤƹͤޤ
ܤǣܤΣΤ줫ФȤ 2 ̤ꡤ줾Фƣۤ 2 ̤ꤺġǡ2 * 2 = 4 ̤ꡣ
ܤǣܤΣФȤ 1 ̤ꡤФƣۤ 3 ̤ꡤǡ1 * 3 = 3 ̤ꡣ
ǡξϡ144 * (4 + 3) = 1008 ̤ꡣ
ܤƱۤ줿
ܤ 4C2 * 4!/2!2! = 36 ̤ꡣ㤨УȤƹͤޤ
ܤϣۤʤΤ 4!/2!2! = 6 ̤ꡣ
ǡξϡ36 * 6 = 216 ̤ꡣ
ʾǤ٤ƤʤΤǡ216 + 1008 + 216 = 1440 ̤ꡤˤʤޤ

(ˡ2)
̤ˡn ͤ 1 n Υɤ示Ĥ a(n) ̤ꡤȤޤ
ȡ餫ˡa(1) = 0a(2) = 4Ǥ
a(3) ϡ 6!/2!2!2! ̤꤫顤
ͤƱ 3C1 * 3C1 * a(2) ̤ꡤƱᣳͤȤƱ 3! ̤ꡤФΤǡ
a(3) = 6!/2!2!2! - 3C1 * 3C1 * a(2) - 3! = 90 - 3 * 3 * 4 - 6 = 90 - 36 - 6 = 48 ̤
a(4) ϡ 8!/2!2!2!2! ̤꤫顤
ͤƱ 4C1 * 4C1 * a(3) ̤ꡤۤ 2 ̤դƣͤƱ 4C2 * 4C2 * 2 * a(2) ̤ꡤ
ƱᣴͤȤƱ 4! ̤ꡤФΤǡ
a(4) = 8!/2!2!2!2! - 4C1 * 4C1 * a(3) - 4C2 * 4C2 * 2 * a(2) - 4!
= 2520 - 4 * 4 * 48 - 6 * 6 * 2 * 4 - 24 = 2520 - 768 - 288 - 24 = 1440 ̤
Τ a(4) ʤΤǡ1440 ̤ꡤˤʤޤ

ϷǼĤɤΤ٤ʤꤽǤ

ɲá

(ˡ3)(ˡ2)βǡˤäȤɡ
ޤʤۤ 8!/2!2!2!2! = 2520 ̤ꡣ줫˹ʤΤޤ
ͤƱξ
֤ͤΤ 4C1 = 4 ̤ꡤƱ֤Τ 4C1 = 4 ̤ꡤ
ĤΣͤ˻ĤΣĤοƱˤʤʤ褦ۤΤ (6C2 - 3) * (4C2 - 2) * 1 = 48 ̤ꡤǡ
ξϡ4 * 4 * 48 = 768 ̤ꡣ
ͤƱξ
֤ͤΤ 4C2 = 6 ̤ꡤƱ֤Τ 4C2 = 6 ̤ꡤΣĤο򣲿ͤۤΤ 2 ̤ꡤ
ĤΣͤ˻ĤΣĤοƱˤʤʤ褦ۤΤ (4C2 - 2) * 1 = 4 ̤ꡤǡ
ξϡ6 * 6 * 2 * 4 = 288 ̤ꡣ
ͤƱᣴͤȤƱξ
򣴿ͤۤФΤ 4! = 24 ̤ꡣ
ǡοϡ2520 - 768 - 288 - 24 = 1440 ̤ꡤˤʤޤ
ͥνȡ 1212ʶ 11:03:24 42707
⡼ޥ
äȤ^^;
ƻˡ
ХۤȤ
ڥΤȤ
ڥΤȤ
줾Dzͤ㤨Ƥޤ^^;;

4!*9+4C2*(4!/2!2!)^2+4C3*3*(4!/2!)*(1+2+4)
=24*9+6^3+12^2*7
=1440


ߤʤΤߤƤٶǤm(_ _)m
¨ ^^;v 1211ڡ 14:15:42 42708
uchinyan
ǼĤɤߤޤ
ޤϡݤ줿Ұ̵ǸɤĤʤȤΤȡ褫ä褫ä
ơꡣ

#42696#42698
ޥ뤵ؤ꤫ۤˤơȥ⥨ؤۤ
ޥ뤵ȡȤƱƱȤ㤦Ǿʬƹͤˡ

#42701
ޥ뤵ۤ륫ɤꤷ¾οͤۤο夲
ˡޥ뤵ؤ֤ۤۤθˡ

#42702
ޡоˤ夲ˡ

#42704#42707(ˡ2)#42707(ˡ3)
ΤʤΤʤοˡ
ܺ٤ˤϼ㴳ΥХꥨ󤬤ޤ

#42705
䭡12132434121423341314232421132443ͤ˵դʤΤä1152̤
䭢12123434131324241414232321123443ͤ˵դʤΤä288̤
1440̤Ȥʤޤ
ȤˡʤǤƤޤ
θ塤#42711ɲäޤ
ܤȣܤǿΰۤʤڥͤڥν֤θơ򣴤¤٤롤ȤͤΤ褦Ǥ
ʬäƤߤСŪʬ䤹򤤤Ȼפޤ

#42706#42707(ˡ1)#42708
ܤۤ륫ɤο٤ưۤʤ硤ͤƱ硤ͤƱ硤Ǿʬˡ

#42710
ΤʤΤ顤ͤƱɡͤƱɡͤƱɡͤȤƱɡˤʤ
ƱȤ߹碌νŤߤդθȤäƽˡ
¤Ϥβˡϡ#42707(ˡ2)ͤˤäȹͤˡǤ
ͤȿĤΥեäݤäΤǤƤޤޤ
ʤۤɡΤ褦ˤФޤΤǤ͡ٶˤʤޤ

#42713
Ψ١ˤͤȤ⣲礬ۤʤΨᡤΤˤƵˡ
Ψϻ˴ޤƤ褤äȵǤʤۤɡ򤤹ͤǤ
ȯۤϤʤäʡ

#42697
ץˤˡ
ͥνȡ 1212ʶ 17:37:53 42709
Mr.ǥ
8Τ٤Ƥۤϡ8!/(2!2!2!2!)2520̤
(ʤȤ)룱ͤƱɤˤʤۤ...4*(6!/2!2!2!)360̤
(ʤȤ)2ͤƱɤˤʤۤ...4*3*(4!/2!2!)72̤
(ʤȤ)3ͤƱɤˤʤۤ...4*3*2*(2!!/2!)24 ̤
4ͤȤƱɤˤʤۤϡ4*3*2*124̤
ä

2520(4C1)*360(4C2)*72(4C3)*24(4C4)*241440̤.....򡩡
ɡη׻˹Ԥ夭ޤ
ʳΨΤȤꤷּޤ
1212ʶ 9:23:58 42710
̴
uchinyanͤ
ä̤#42705 ϼȴǤƵפޤƱǤʤȤ߹碌ϡ12,13,14,23,24,34Ǥꤳ餫飴Ȥ֤ȡ12,13,24,34 12,14,23,34 13,14,23,24ΣȤȤʤ롣12,13,24,34 ͤȡν֤դǤɤ㤨21,13,24,34Ǥɤ¨֤դȤʤΤġġ2ġ3Ĥ4Ĥξͤ롣ȵդĤξϡ4!4=96,򷫤֤Ʒ׻ȡ241631152
ƱͤˣȤȤ߹碌12,12,34,34 13,13,24,24 14,14,23,23ǤɤҤƱͤη׻Ԥ963=288 1152+288=1440
ٻΤ桡 1212ʶ 7:03:53 42711
uchinyan
#42711
̴ɲ򤢤꤬Ȥޤ
ʤۤɡޤܤȣܤǿΰۤʤڥͤڥν֤θơ򣴤¤٤롤
ȤͤǤ͡
褯ʬޤ
ͥνȡ 1212ʶ 11:30:12 42712
Mr.ǥ
ˡϡ
ޥ뤵ΣܤȤȡܤȰۤʤΨϡ6/7
ۤ줿ͤˤʤɡʤ1ġˤȤ
⣲礬ȤͤʬΨϡ2/3
äơ4ͤȤ2礬ۤʤΨϡ(6/7)*(2/3)4/7
ۤϡ8!/2!2!2!2!2520̤ˤΤ
2520*(4/7)1440̤
1212ʶ 13:35:03 42713
⡼ޥ
#42713
ʤۤɤӥĥ
Mr.ǥȯۤϽ͡
aۤ줿ͤϤ⤦1ϲǤ⤢顢aۤƤʤ(2)ǡۤʤΨͤФǤ٤ƤäƤȤʤΤͤ
줬򤫤ʡ
ΨϤ䤳^^;...
¨ ^^;v 1212ʶ 12:27:34 42714
ǯ
Ѥ餺ޡȤǤϤʤǤ
1,1,2,2,3,3,4,4οƱڥˤʤʤ褦2Ĥ4ĤΥڥʬơȤ롣
ȴ֤ǡ4ڥιۤʤȤϰճ˾ʤä
2ڥĤƱǤ
1)12, 12, 34, 34
2)13, 13, 24, 24
3)14, 14, 23, 23
4ĤΥڥưۤʤ
4)12, 13, 24, 34
5)12, 14, 23, 34
6)13, 14, 23, 24
4ͤꤷƾ嵭γơȤ4ͤؤۤοˡ2^4ݤơ1440Ȥꡣ
1212ʶ 21:54:03 42715
???
Option Explicit
Dim a(8) As Integer, aa(10000) As String
Sub Macro1()
Cells(1, 1).Value = 0
Call saiki(1)
End Sub
Sub saiki(ByVal n As Integer)
Dim deta As Integer, max As Integer, j As Integer
a(n) = 1
While a(n) <= 8 + 4 * (n = 1)
If dame(n) = 0 Then
If n < 8 Then
Call saiki(n + 1)
Else
aa(0) = ""
For j = 1 To 8
aa(0) = aa(0) + Str(f(a(j)))
Next j
deta = 0: j = 1
While deta = 0 And j <= Cells(1, 1).Value
If aa(0) = aa(j) Then deta = 1 Else j = j + 1
Wend
If deta = 0 Then
Cells(1, 1).Value = Cells(1, 1).Value + 1
aa(Cells(1, 1).Value) = aa(0)
For j = 1 To 8
Cells(Cells(1, 1).Value, j + 1).Value = f(a(j))
Next j
End If
End If
End If
a(n) = a(n) + 1
Wend
End Sub
Private Function dame(ByVal n As Integer) As Integer
Dim j As Integer
dame = 0
For j = 1 To n - 1
If a(j) = a(n) Then dame = 1
Next j
If dame = 0 And n >= 5 Then
If f(a(n - 4)) = f(a(n)) Then dame = 1
End If
End Function
Private Function f(ByVal n As Integer) As Integer
f = n + 4 * (n >= 5)
End Function
1213ڡ 10:30:55 42716
ʪ
Ŭۤä礫ïƱɤľޤ
ޤƤ̤׻
1Ʊɤ3ͤϥХХ̤׻
3ͤХХ̤׻Ȥ
3Ŭ顢1Ʊɡ3Ʊɤ̤Ҥ
1ƱɤȤ
2Ŭ2ͤȤƱɤ̤Ҥ
ˡ2Ʊɤξ4ͤȤƱɤξ
8c2*6c2*4c2*2c2-4*4*(6c2*4c2*2c2-3*3*(4c2*2c2-2)-3!)
-4c2*4*3*(4c2*2c2-2)-4!=1440
ܡ 1215ʷ 15:11:40 42717