Taro
˽ͤĸǤޤ뤫˽ͤĸߤ˸Ǥޤ뤷ʤȤ
Ф餯ŤޤǤ
saka 1127ڡ 0:09:27 MAIL:tarox@nifty.com HomePage:⤦ҤȤĤʥ죲19943

ȴ

åץǽ֤դˤʤ뤳Ȥ˺Ƥ
̤̪ 1127ڡ 0:09:32 MAIL:kentaro@qa2.so-net.ne.jp 19944

ǽ˽ߤ¤ǤΤͤƤޤ
ߡߡߡߤǤ⤤ΤǼ͡
äѤꤪϼ
äѤ餤ŷ񡡡 1127ڡ 0:10:20 MAIL:hopes@mba.ocn.ne.jp HomePage:HOPES19945
̥
פ֤˥ꥢ륿ǻä顢դξοʬǤȤޤ
ͤĸǤޤäƤȡåץ뤬ߤƱΤˤʤäƤȤʬƹͤޤ
1127ڡ 0:11:33 19946
ϣ
פ֤̤GETȻפä.....
124860̤ǵǤ夫
Ųδۡ 1127ڡ 0:11:45 MAIL:tora@ansas.org HomePage:Ver319947
ߤ
㥤ͤǤޤäƺ¤碪ߣߣߣᣴ̤
ͤǤޤäƺ¤ꡢθˤ͸Ǥޤäƺ¤
ߣߣࣲᣱ̤
äƣܣ᣶
ʤǤΤʡ
1127ڡ 0:12:40 19948
ΤϤ
ͣͤȤƤޤοꡣ
1127ڡ 0:13:35 MAIL:unotakaharu@anet.ne.jp 19950
ȥȥ
ޤ48̤˵ŤǺǤޤ
ʼ˸лԡ 1127ڡ 0:13:58 MAIL:h-sakai@zb3.so-net.ne.jp 19951
naopapa
ƱåץνֵդΣأ˺Ƥޤ
1127ڡ 0:14:51 19952
ΤϤ
ͣͤȤƤޤοꡣ
1127ڡ 0:15:07 MAIL:unotakaharu@anet.ne.jp 19953
ѥ
˽2ͤĤ¤֤Τ6x2=12̤
4ͤʬΤ24x2=24̤
碌12+24=60̤ꡡְ㤨
˿ꡡ 1127ڡ 0:15:47 MAIL:dr-yasu@nifty.com 19954
Ϥʤ
(;)
äΤ
ޤ¤٤ƤʤȤȤȤäƻˤƤޤޤ

ߡߡߡߤߡߡߡߡʤΤǤŤ⤷ޤǤ

ääҤɤ

ڥȤ
££ããģģȤ

ޤ¤٤ƣ̤

ǼA2¤٤ȤȡϤǽΤȤϣ̤ꡢ̤ꤺĤ˾ʬ

٤ˤʤʤ
ȤУ£ȣãδ֤ξ硢ưŪˣ£ȣãϷޤΤǡģФ褤Ȥģϣξ٤Τɤ餫ǤΤǣ̤

٤ξ
ˣΤ⤦٤£Ȥȡ£ϼưŪ˷ޤΤǣãģɤ£֤뤫ʽƱˣãģ֤ˤϤ뤫ʤϽƱˤʤΤǣ̤

ʾꡢ
¤¤Ĥ¤ȹͤ
ܣ᣶

1127ڡ 0:20:43 19955

äȤо
1127ڡ 0:16:51 19956
DrK
ξϡåץβƱǤʤȤʤȤ󤬤ĤƱ4¤־2Ȥϥåץ뤬٤ʤȤʤäơ2ȤΥåץ̤4C2=6Ǹ2Ȥˡåץ˶ޤʹˤʤꡢǤ¤Ϥ줾2̤ꡢ˥åץ֤ؤϲǽʤΤ2̤Ǥξ6222=48
Ʊ3¤־硢2ȤΥåץβƱˤʤ뤬2ͤ˶ޤ줿ʪȯΤԲġ
Ʊ2¤־ϡåץ뤬4ȤȤ٤礦˸¤졢ν3!=6̤ꡢåץǤ¤ӤؤϲǽǤ뤬1Ȥؤä¾ȤϤΤȰ֤ޤΤ2̤ꡣξȤ߹碌62=12̤ꡣ
Ʊ¤Ӥʤ¾ΰ٤礦ΤԲġ
ä48+12=60
狼дñǤ뤬ճ񤷤⤷ʤ
񤷤ǴñȤ桹ǤϤʤȻפ
ϳڱफʡ 1127ڡ 0:19:03 MAIL:satoka@star.odn.ne.jp 19957
⤢ꤹ
ܤ12äƣܤ48äƣܤˤä(^^;
οϤऺ
1127ڡ 0:20:28 19958
DrK
3Ϣ٤ֺȤ4ȤʤꡢΤޤ޻͹ϤޤǯΥեߤΤȤ˹Ԥä³ԤݵޤǹԤä֤Ǻ˽Фơ餷ޤʤ߳ƻԤޤޤʤ߳ƻԤǤϤʤ줾ޤ290kmǤ23Ǥ϶줷Ȥפޤ34ʤ餤뤫ʡ
ʤߤ˻2ǹԤͽ꤬2Ⱦݤޤ
4ԵΥ395kmǤ
ϳڱफʡ 1127ڡ 0:24:51 MAIL:satoka@star.odn.ne.jp 19959
ȥȥ
39̤40̤ƱͤǤ衣
ʼ˸лԡ 1127ڡ 0:26:04 MAIL:h-sakai@zb3.so-net.ne.jp 19960

̤κƣ뤵äƤޤƱʪǤ
1127ڡ 0:26:55 19961

֤ä
1127ڡ 0:27:28 19962
ޥ
Ŧ꤬Ȥޤɽη

ǡʥʤʤäˡľƤޤ
MacOS X 1127ڡ 0:29:07 MAIL:masaru-y@kt.rim.or.jp HomePage:19963
ޤ륱
ŦĤǤ
֤νλˤʤäƤޤ
1127ڡ 0:46:09 MAIL:take4310@mobile.email.ne.jp HomePage:ޤ륱19964
CRYING DOLPHIN
񤷤ͤ
ˤϣϣ£ãĤ̾դ뤳Ȥˤơ
LoveLoveʤΤϣ¡áĤäǡ

ץ󣱡
դࡢϤäȰɮ񤭤˵Ǥ
ͤ߷¤١ƱΤ˺¤äƤ褤ͤǷ֡
ʤʤʿޤˤʤä硣㤢򥹥ȤȤơ
ġĤ㤴
ʽʬˤ狼󡣡

ץ󣲡
Ϳ򸺤餷
ȡȤξϴñ
η̤ˣȤΤȤξοʤ
ġĤ㤰
ʬˤࡢäѤ狼󡣡塼

ץ󣳡
פˤդġ˹ͤΤ
ξ٤褿ޥ櫓顢˽κ¤ȤƤϡ
áˣͤ͡Ǥޤäƺ¤롡ˣͽͤߤ˺¤
Σѥ󤷤ʤΤ⡢ˤȽƱΤˤʤȤ
LoveLoveʣͤƤϤʤäĤȤϡ
ʻʬˡá12̤ꡡ48̤ꡡ60̤

۾ҤͤΤΥϥޥǤ
ǯԥ奦ȡ 1127ڡ 1:50:18 HomePage:θ³äƤɤΤ餤19965
ϥ饮㡼ƥ
Ϥ褦ޤ
߽ȤnHmȤ⤫Ӥޤ˺ƤΤ
åǤ
̶彣 1127ڡ 5:41:26 HomePage:ϥ饮㡼ƥ湩ؤ˥19966

ᤦޤ
ͣͤͤĤΣѥ󤷤ʤΤǡ
ߣܡ42ߣ^2ᣴܣ᣶Ǥ
ϳڤǤ
طʤɿؤεǢϲɤΡƤϤ
ļˡ 1127ڡ 5:47:16 19967
̾õ
ABCDd**a ȡABbcCDdaΣġϥ󥰤դơ
4!*2+4!/2ˤʤޤ
Υåץ2n>=4ΤȤ
2n!*(2n-2)!+2n!/nˤʤΤǤ礦
1127ڡ 7:09:47 19968
¼
̲^^;

ʡˡߡᡡ
ʡˡߡᡡ
ʡˡߡᡡ
ʡˡߡᡡ
ʡˡߡᡡ
ʡˡߡᡡ
ʡˡߡᡡ
ʡˡߡᡡ
ʡˡߡᡡ
ʣˡߡᡡ
ԡ 1127ڡ 8:02:12 MAIL:naka@sansu.org HomePage:naka's Home Page19969
M.Hossie
Фˤ㡣ʤ鸭˥Ǥ͡
ʣˣǸǤޤѥ
ˣ¤ϣ̤ǡξüˤϤ줾Τǰաʤϸ򴹲ǽʤΤǤܡäơᣴ̤ꡣ
ʣˤĤǣ¤֥ѥ
ĤȤ¤ϱ߽ǣ̤ꡣĤ˽ϸ򴹲ǽʤΤǤܡäơᣱ̤ꡣ
Ρʣˡʣ˰ʳˤդΩʤΤǣܣ᣶̤.....Final Answer
˿ꡡ 1127ڡ 9:46:06 19970
CRYING DOLPHIN
>ʤϤ 1 2 6 60 960 ϥǡ١ˤ¸ߤޤ

˿󥵥Ȥˤ¸ߤʤǡ

ïο򸦵椷ƤΥȤäƤ
ǯԥ奦ȡ 1127ڡ 11:31:57 HomePage:θ³äƤɤΤ餤19971
ߥߥϤ
˽ʬ
ѥ󤷤̵ʬиϴñǤ͡
4322̤ꡢ322̤ꡣ

Ǥ⤢ο󥵥ȤˤФƤʤȤϡäޤ

ɤߤܤäΤǡ򿩤٤Ƥ
ͤޤΤҤȤȤɤǤ
ää3桡 1127ڡ 13:03:31 MAIL:mae02130@nifty.com 19972
ߥߥϤ
֡ˤϤɤ˺¤äƤ⤤ɡ¾ˤοͤ٤ϤȤ
֤ιȤɤʤ뤫ȹͤޤƱȤǤ

γ󡢤ʤ
ää3桡 1127ڡ 13:16:33 MAIL:mae02130@nifty.com 19973
ʸ
ʤäǤä

12:00ϤäѤĤǤä

οϤäѶǤä

٤ϤȵǤä
դä񡡡 1127ڡ 18:50:56 HomePage:ʸ19974

ɤʤꤤޤ
ؤεǢϲɤΡƤϤm(_ _)m
ļˡ 1128ʶ 10:59:39 19975
̾õ
ʤءŦ˴ա줿ͳǧޤ
1128ʶ 16:40:31 19976
̾õ
ʸA,B,C,DǼб뾮ʸ a,b,c,dǼޤ
ǥեȤǤޤ4ͤˤĤȤ3*26̤ꡣ
abcd ɽȤˤޤ
4ͤΤޤabcdˡ
a/b/c/d/Τ褦4Ĥǡ2ͤؤǽΤ4*28̤ꡣ
2ͤĤˡ
ab/cd/a/bc/d2̤ꡣ
ޤȤ6*8+2̤ꡣ
1128ʶ 17:27:11 19977
̵ͭ
2-2-2-2ʬΤMIRRORޤ֤Τ˺ơ6̤ȤƤޤ
where i am 1128ʶ 17:27:17 MAIL:ancoromochi@ba.wakwak.com HomePage:̵ͭ19978
̵ͭ
åץ뤤ơʤ顢̾õ夵Τ褦ˡ19968ˡ
m!*(m-2)!+(m-1)!*2̤ꡢ
m=ʤ顢2-2-...ξ礬äm!*(m-2)!̤
ˤʤޤ󤫡
where i am 1128ʶ 17:44:58 MAIL:ancoromochi@ba.wakwak.com HomePage:̵ͭ19979

m=Ǥ⡢ʤ顢㤨УǣݣݣݤȤǤΤǡ
m=ǿΤȤʣ礭ˤȤm!*(m-2)!ʤ
ޤͤƤʤΤDzְäƤ饴Ǥ
ļˡ 1128ʶ 21:27:16 19980

äѰ㤦ϡǿǤ
m=7ǣݣݣݣȤݣݣݣȤǤޤ͡ʴ
ļˡ 1128ʶ 21:32:08 19981
YB
ĥ
ȡ̻ϳؤη׻ǻȤޤ
1128ʶ 22:28:21 19982

YB
ꥬȡ
ļˡ 1128ʶ 23:12:43 19983
omega
ޤ˿󥵥ȤäƤɤǤ
˵ˤʤΤǤ
1129ڡ 10:54:06 19984
̾õ
19968ͽۤϸǤ
αǤϡ2ʾƱΤޤʬȽˤϥåץǷҤޤȤФ֤ξοΰ̲ʬޤ
㤨С10ȤΥåץξ硧
10ͤαν9
10ͤ2ͰʾΤޤʬ
10ˡüεϤޤοɽޤ
82ˡ73ˡ64ˤޤϡ55
622ˡ532ˡ523ˡ442ˤޤϡ433
4222ˡ3322ˤޤϡ3232
22222
Ф֤ξο10*8403200
Ф֤ξο10*3*7+5*1*7176400
Ф֤ξο10*5*15*418000
Ф֤ξο10*2*10*2+5*1*10*2500
Ф֤ξο2
598102̤
äơ9*598102̤Ǥ
1129ڡ 12:10:27 19985
̾õ
䡧ƱﲼǡȤΥåץФ֤ξοA(n)ˤĤơ
ФơA(n)/((n-1)!)^2Ϥ˼«ʤǤ礦?
1129ڡ 12:12:38 19986
Ф
פ֤Ǥפ֤Ǥä񤷤꤫¾οͤȤɤäǤ硣
1129ڡ 12:16:23 19987
YB

ɤޤ

ե˽񤤤ȡʲˤ˸꤬äΤʬä
äݵ
1129ڡ 20:31:45 19988
Ƥä
ʤ#19969 ̲^^; ˤο͡
ǧƤޤ
10!*{8!+6!*(24+1/2)+4!*75+2!*25+0!*1/5}=217039253760
Ȥ߹碌DZ߽󤬿ˤʤꡤ̲Ǥ
Ĥ⡤äȤäȤ 1130 0:11:35 19991
¼
#19984 omega

>ޤ˿󥵥ȤäƤɤǤ

The On-Line Encyclopedia of Integer Sequences
http://www.research.att.com/~njas/sequences/
ԡ 1130 23:30:11 MAIL:naka@sansu.org HomePage:naka's Home Page19992
¼
ʹߤ⥢ɥ쥹ΰǤ
ԡ 1130 23:38:55 MAIL:naka@sansu.org HomePage:naka's Home Page19993
ޥ
http://ǻϤޤURL򵭻˽񤤤νǡ~ʥ˰ʹߤڤ㤦褤ޤǤ򤪤ޤm(__)m
MacOS X 121ʷ 0:55:06 MAIL:masaru-y@kt.rim.or.jp HomePage:19995
¼
#19995 URL 󥯤Υƥ
The On-Line Encyclopedia of Integer Sequences
http://www.research.att.com/~njas/sequences/
ԡ 121ʷ 1:53:02 MAIL:naka@sansu.org HomePage:naka's Home Page19997
¼
̲λ

#19985 ̾õ夵βϤ³Ǥ

Ȥξ⤦ȡ
ʣˡߣᡡߣᡡ
ʣˡߣᡡߣᡡ
ʣˡߣᡡߣᡡ
ʣˡߣᡡߣᡡ
ʣˡߣᡡߣᡡ
ס̤Ȥʤޤ

׻ΰ̣ʣˤޤ

򣴤ĤΤޤʬο
ʣˤ̤
ʣˤ̤
ʣˤ̤оˤ꣱ǤʤȤաˡ

ˤ˶ޤԱˣ֤ͤǡ
ȣᣵãᣵᣲ
ȣϡĤΤޤ꤫飲ĤֽʣȤ߹碌
Ϥˣͤν

ꡧͤؤ򡢣ͰʾκĤڤʬο
Ǥ뤳Ȥ򡢤äȾǤʤΤ
ԡ 121ʷ 1:54:59 MAIL:naka@sansu.org HomePage:naka's Home Page19998
ۤ
(4)ξ̤ʹͤ
Ȥǡ9Ƥ׻ǤϤޤ

ޤ٤礦ͤӱ߷¤٤ޤ10C87
ˤ٤˽򣸿ޤ2̤
ȤaABbcCDdeEFfgGHh߷ˤʤȤAaBCcdDEefFGghH
߷ˤʤ礬ޤ͡
Iδ֤Τ̤
Jδ֤Τ̤

iδ֤Τ̤
ˣꤵδ֤Τ̤

ʾ夫鼰ϡ10C2724(54)2=5009!Ȥʤޤ



121ʷ 14:25:59 MAIL:micci@sansu.org 19999
ۤ
Ĥδ֤ˤåäƤ
Ʊ褦٤礦ͤӡ߷¤١֤¾οͤͤù
(1)10C21!2(8!)2=108!9!
(2)10C43!2(234ߡġ7)2=1764009!
(3)10C65!2(3456)2=180009!
(5)10C109!2=29!Ȥʤޤ

̤αȡ 121ʷ 14:39:15 MAIL:micci@sansu.org HomePage:ߤäα20000
¼
ۤ󡢤䤫Ǥ
⡢Υ롼ȤƱˤɤĤޤ

ǤˤؤˤʤäͤνĤκڤäơ
ڤܤˡ䤭ʤ򶴤οϡ

B(n,k)={(n-k-1)!/(k-1)!}^2/(n-2k)!*n/k

n=10
B(10,1)=(8*7*6*5*4*3*2*1)^2/8!*10/1=403200
B(10,2)=(7*6*5*4*3*2)^2/6!*10/2=176400
B(10,3)=(6*5*4*3)^2/4!*10/3= 18000
B(10,4)=(5*4)^2/2!*10/4= 500
B(10,5)=1/0!*10/5= 2

η
ȤΥåץ䤭ʤ¤٤οϡ
A(n) = (n-1)!*B(n,k)
= (n-1)![{(n-k-1)!/(k-1)!}^2/(n-2k)!*n/k]

ûϰϡk=1,2,3,,,[n/2]

n=5
B(5,1) = (3*2*1)^2/3!*5/1 = 30
B(5,2) = (2)^2/1!*5/2 = 10
A(5) = 4!*(30+10) = 960

#ʸΤᵭޤ
<PRE></PRE>Ȥʤʤ
ԡ 121ʷ 23:51:44 MAIL:naka@sansu.org HomePage:naka's Home Page20001
¼
ʤ顢BASIC Ǥ׻Ǥޤ
ο󥵥Ȥˤ⿽ǤʱѸǥ᡼񤱤뤫ʤ

( 2) 2
( 3) 6
( 4) 60
( 5) 960
( 6) 24000
( 7) 861840
( 8) 42104160
( 9) 2686763520
(10) 217039253760
(11) 21651071904000
(12) 2614084251609600

# ץɵޤ

OPTION ARITHMETIC DECIMAL_HIGH
FOR n=2 TO 50
LET b=0
FOR k=1 TO INT(n/2)
LET b=b+(FACT(n-k-1)/FACT(k-1))^2/FACT(n-2*k)*n/k
NEXT k
LET a=FACT(n-1)*b
PRINT "(";n;")";a
NEXT n
END
ԡ 121ʷ 23:39:39 MAIL:naka@sansu.org HomePage:naka's Home Page20002
ʸ
ۤ20000ܤƤǤȤޤ!!!
դä񡡡 121ʷ 17:46:29 HomePage:ʸ20003
̾õ
1999920002Τۤ󡢤ʤ󡢤䤭ʤαA(n)ΰ̲ãǤ󡢿󥵥Ȥ˿Ƥ
122ʲС 8:02:54 20004
̾õ
ФA(n)/(n-1)^2ͤ
1/(0!*1!)+1/(1!*2!)+1/(2!*3!)+,,,+1/((n-1)!*n!)
ˤ
ˤȤ1.590636854...ȹͤɤΤǤ礦
122ʲС 8:05:50 20005
¼
#20005 ̾õ夵

>1.590636854...ȹͤɤΤǤ礦

줤Ǥ͡ɤΤ褦Ƴ줿ΤǤ礦
¸ŪˤϰʲΤȤꡢޤְ㤤ޤ

1.6482087743 * ( 9 !)^2 = A( 10 )
1.5974438702 * ( 99 !)^2 = A( 100 )
1.5913250049 * ( 999 !)^2 = A( 1000 )
1.5907057415 * ( 9999 !)^2 = A( 10000 )
1.5906437440 * ( 99999 !)^2 = A( 100000 )
1.5906375436 * ( 999999 !)^2 = A( 1000000 )
1.5906369235 * ( 9999999 !)^2 = A( 10000000 )
1.5906368615 * ( 99999999 !)^2 = A( 100000000 )
Muroran 122ʲС 17:08:14 MAIL:nak@sansu.org HomePage:naka's Home Page20007
̾õ
200071/ (n-1)!*B(n,k)ˤơ1n/(n-1)1˼«
21*B(n,2)/B(n,1)n/(n-1))*(n-3)/((n-2)*1*2)1/(1*2)˼«
31*B(n,3)/B(n,1)n/(n-1))*(n-4)*(n-5)/((n-2)*(n-3)*1*2*2*3)
1/(1*2*2*3)˼«ʲƱͤˤƵޤ
122ʲС 19:13:40 20008
ʸ
ܣǣţԡǣ!!!

ʤꤦ줷Ǥä

äڤɤȤäʤ
äȤɤǤä



ۤȡ򤤤Ǥä
դä񡡡 122ʲС 19:59:00 HomePage:ʸ20009
Ƥä
©Ǥޤ
̾õ夵¼󡤤ۤˤ̲ؤ
ɥޥåήƻdzڽƤޤ

ۤ(#19999)10ȣnk˽񤭴
nͤĤ˽򤽤줾죲Ͱʾ夫ʤk([n/2 ])ͤĤ
ޤʬơ䤭ʤ¤٤¤οA(n,kˤȤ
A(n,k)=nC2k*(2k-1)!*2*{(n-k-1)!/(k-1)!}^2
äơ䤭ʤ¤٤¤A(n)Ȥ
A(n)ᦲ{k=1,[n/2ϡA(n,k)
ȤߤȤ˰̲ΤǤ͡
ʤ(#20001)ƱȤ̵̽񤭤ƺѤߤޤ;ˤ
䤫äΤǡʤ񤭤Ƥޤޤ ^^;

Ѹǥ᡼񤤤ơ󥵥Ȥ˺ܤƤ
ΤڤߤǤ
Ĥ⡤äȤäȤ 123ʿ 6:44:09 20011
CRYING DOLPHIN
>>ϢΤ䤭ιͻ

ҡĸȤ褦ΤʤͻǤ


󥵥ȤθäڤȤƤϾ𤱤ʤ¤ʤΤǤ
ʤȤ䤬Ϥǹͤ褦ʤΤǤϤʤȤȤ
ν񤭹ߤ򸫤Ƥ狼ޤ
ǯԥ奦ȡ 123ʿ 11:50:25 HomePage:θ³äƤɤΤ餤20012
粬ҹ
աáäȲ򤱤ޤʡ˾ʬƷ׻ޤ
ĤĥåץξʬաäƴǤ͡
123ʿ 12:21:00 MAIL:toshi009@land.hokuriku.ne.jp 20013
ݥϥ륫
ܣǣ̤ȷ׻ޤ
123ʿ 17:28:39 20014
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󥵥Ȥ˿ƤߤޤĤƤ Author Ϣ̾ǡ
Akemi Nakamura(naka(AT)sansu.org),Michihiro Takahashi, Shogaku Meitantei
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Muroran 123ʿ 19:08:01 MAIL:nak@sansu.org HomePage:naka's Home Page20015
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դä񡡡 123ʿ 19:31:35 HomePage:ʸ20016