Ĺ
示ĤǤ⡢Ʊ褦ʡ
Ѥ顡 1216ڡ 0:05:36 HomePage:åȬ24218
ҡΤ
ꤲȡ7C2/7!Ǥʡ
̲ΤDz¾οͤ...ʾ
ɥ 1216ڡ 0:07:13 24219
tomh
ΤǤϡƱɤ2³ƽФ뤳Ȥ⤢ΤǤϡ?
ȡޥ뤵ΰտޤΤȰäƤ褦ʡ
ԡ 1216ڡ 0:09:20 MAIL:tomh@yahoo.co.jp HomePage:H to M24220
ȥȥ
󡢣ʬ٤줿ǰ
(1+2+3+4+5+6+7)/7!
ʼ˸лԡ 1216ڡ 0:09:33 MAIL:h-sakai@zb3.so-net.ne.jp 24221
Ҥ
1/2,1/2,1/4,1/12,1/48/1,240
1/1,1/2,1/3ܡˤʤäƤǤ
1216ڡ 0:09:37 24222
ԤԤΡά
1/240äĤ꤬1/2ǻߤޤäƤ
72/7!ʤǤ͡ƬθǤϼ¸ʤ󤫤äꡦʴ
̤̪ 1216ڡ 0:11:45 MAIL:ishizaki@qa.so-net.ne.jp 24223
tomh
#24220

ޤ᤹פΤǤϤʤơ
ְ㤦ȢפΤ
פǤ͡餷ޤ (^^;
ԡ 1216ڡ 0:11:59 MAIL:tomh@yahoo.co.jp HomePage:H to M24224
ޥ
#24220
ʸޤǤ礦...
MacOS X 1216ڡ 0:12:05 MAIL:masaru-y@kt.rim.or.jp HomePage:24225
ޥ
#24224
ۥá
MacOS X 1216ڡ 0:12:29 MAIL:masaru-y@kt.rim.or.jp HomePage:24226
ߤ
ΤƤġΤȤˤʤΤǣΣ̤
ΤƤġΤ줫ˤʤΣ̤
ĤȤäˣΤƤޤǿ夲ȷף̤ꡣ
ݡ᣷ꡢΨϣᣱ
繥ؤϷġ 1216ڡ 0:16:36 24227
N.Nishi
ʺǹ̤Σ̴򤷤Ǥ˲ꡢǼĤǤϤͤ줿Τǡ⤦ͤľȤǤ
ΤƤΤϣΡΣ
ΤƤΤϣΣ
ȹͤȤǣΤƤΤϤɤɤ󾯤ʤʤäƤΤ
ʣܣܣܣܣܣ/1/240
1216ڡ 0:13:47 24228
Ĺ
#24218
ܤƤ
ߣᣴ礢ΤȻפäƤޤ
㤢ʤ
Ѥ顡 1216ڡ 0:15:55 HomePage:åȬ24229
ҡΤ
äѤˡ񤤤Ƥ鿲ޤʵ
1,2,3,4,5,6,77ΥɤΤ2Υɤ֤
ɤ餫礭ϤǤ
Ǥ礭Υɤ˽ФơΥɤõȤΤͤޤ
...ĤޤΤƤ륫ɤȡθ륫ɤ֤櫓Ǥ

Ȥ13Ȥ2314567¤֤ޤ

Ʊͤ271345672¤֤ޤ

äơ1ΤƤ褦ʥɤ¤7C2̤Ǥ櫓Ǥ
..ȤʤΤǤ......ȿȤ뤫⡩ʡ
ɥ 1216ڡ 0:23:13 24230
tomh
7ΰ֤ͤơ1ܤ5ܤޤǤ7ȡ
θϤ٤ƼΤƤʤФʤΤǡǤʤ

6ܤ7ȡ



16Τɤ줬ƤɬΤƤΤǡ
ǼΤƤʤ褦˻ĤΥɤ
ξ¤٤6̤.

6ܤ7ȡ



ȡ¤Ӥ1ΤƤʤ
ʤʤʤΤǡ٤6ΰ֤ͤơ(ʲƱ)

ɡ6+5+4+3+2+1=21̤.
ԡ 1216ڡ 0:24:50 MAIL:tomh@yahoo.co.jp HomePage:H to M24231
takaisa
ؤǡ7C2/7! ޤϡ
(6+5+4+3+2+1)/7!=1/240
줷ϤʤΤʡ
1216ڡ 0:27:57 24232
uchinyan
ϤФϡ
ľˡİĹͤޤ
1ܤϡ12OK
1ܤ2ξϡ1ɬΤƤ뤳Ȥˤʤꡢ¾ΤƤʤο6̤ꡣ
1ܤ1ξϡ2ܤ23OK
2ܤ3ξϡ2ɬΤƤ뤳Ȥˤʤꡢ¾ΤƤʤο5̤ꡣ
2ܤ2ξϡ3ܤ34OK

ȤäƤɡοϡ6+5+4+3+2+1 = 21 ̤ꡣ
Τϡ7!̤ʤΤǡΨϡ21/7! = 1/(6*5*4*2) = 1/240

ޤϡ

1ΤƤʤ硢Ĥޤꡢ17ޤǤ򾮤¤٤礫顢ɤ2սؤ롢ȹͤƤ⤤Ǥ͡
ȡ7ս꤫2ս٤ФΤǡ7C2̤ǡΤ7!̤ǡ
7C2/7! = 7!/5!2!7! = 1/5!2! = 1/(120*2) = 1/240
äñʡ
ͥνȡ 1216ڡ 0:57:51 MAIL:uchi@sco.bekkoame.ne.jp 24233
uchinyan
#24233
Ѥߤޤ󡣺Ƕᴪ㤤¿Ƥʤ
1ΤƤʤ硢Ĥޤꡢ17ޤǤ򾮤¤٤礫顢ɤ2սؤ롢ȹͤƤ⤤Ǥ͡
䤹ȡ7ս꤫2ս٤ФΤǡ7C2̤ǡΤ7!̤
ϡΤǤ
#24230Ρ֥ҡΤפƱȤäΤǤ
äȡʤʤäƤ
ͥνȡ 1216ڡ 1:17:11 MAIL:uchi@sco.bekkoame.ne.jp 24234
¼ŵ
1ΤߤΤƤΤǤ顢ΰϡΤɤ줫ο

1ΤƤο6̤ꡣ
ΤƤοϣ̤ꡣ
ΤƤοϣ̤ꡣ
ΤƤοϣ̤ꡣ
ΤƤοϣ̤ꡣ
ΤƤοϣ̤ꡣ

21̤ꡣȤϣβʬˡ
1216ڡ 4:14:23 MAIL:tedksya@r02.itscom.net 24235
Ŵ
⤫󤿤äΤǤ
줫Ƥ
Կ¶˿عɤ 1216ڡ 7:39:24 24236
ʤ
ƱʣܣܣܡܣˡȤޤ
ʤߤˡΤƤȤγΨʬۤϡ

Ȥʤ褦Ǥʬϣ
̳ƻ 1216ڡ 7:57:03 MAIL:naka@sansu.org HomePage:naka's Home Page24237
M.Hossie
ˤϡΤϤ餤ñǤ͡ʬDz򤱤ޤ衣
ȹͤϳƱ(1+2+3+4+5+6)/7! Ǥ
Τꡡ 1216ڡ 9:19:42 24238
kasama
Ϥ褦ޤץǤޤ(*^_^*)

import java.util.*;
public class Question431 {
public static void main(String[] args) {
int count = 0;
List list = new Permutation(Arrays.asList(new Integer[]{//#18624
new Integer(1), new Integer(2), new Integer(3), new Integer(4),
new Integer(5), new Integer(6), new Integer(7)})).getList();
for (Iterator iter = list.iterator(); iter.hasNext(); ) {
List eList = (List) iter.next();
Integer maxNo = new Integer(Integer.MIN_VALUE);
int discard = 0;
for (Iterator eIter = eList.iterator(); eIter.hasNext(); ) {
Integer no = (Integer) eIter.next();
if (no.compareTo(maxNo) > 0) maxNo = no;
else ++discard;
}
if (discard == 1) ++count;
}
System.out.println(count);
}
}
1216ڡ 9:48:23 24239
uchinyan
Ϥˤϡϼפޤ

7C2βǤäȤϼΤȤǤ

1ΤƤʤ硢Ĥޤꡢ1 7 ޤǤ򾮤¤٤礫顢ɤ2սؤ롢ȹͤƤ⤤Ǥ͡
ξ硢1 ... (m-1) m (m+1) ... (n-1) n (n+1) ... 7 ˤơm n (m < n) ȤؤȤޤ
ȡ1 ... (m-1) n (m+1) ... (n-1) m (n+1) ... 7 ˤʤޤ
ǡm ΤƤޤ¾ΤΤΤƤƤϤʤʤΤǡ
1 ... (m-1) (m+1) ... (n-1) n m (n+1) ... 7 Ȥɬפޤ
ϤǺ𤷤ΤǤ
1 ... (m-1) (m+1) ... (n-1) n (n+1) m ... 7, 1 ... (m-1) (m+1) ... (n-1) n (n+1) (n+2) m ... 7, ...
ʤɤ̤ˤOKǤ
ϡm (n+1) Ȥؤʤɤǿ뤳ȤˤʤΤǡϿɬפϤޤ
ơȤοؤФơդĤο¤Ӥб뤳Ȥˤʤޤ
ǡ7ս꤫2ս٤ФΤǡ7C2̤ǡΤ7!̤ǡ
7C2/7! = 7!/5!2!7! = 1/5!2! = 1/(120*2) = 1/240

֥ҡΤפήξϡǽ7Ĥο2ĤοȤäƤơ... n ... m ... Ȥ¤Ӥͤޤ
θιͤƱȻפޤ
ͥνȡ 1216ڡ 11:31:22 MAIL:uchi@sco.bekkoame.ne.jp 24240
⡼ޥ
ͤۤѤǤ͡
ͧͤФ줿ǤŨʲˡ˴ưޤ
ֱ߼100Ĥ¤Ǥꤽ¤1ǤĤϢ³ν򺿤Ȥ֤Ȥˤȡ¤äƤ뺿θĿ衣
1216ڡ 13:57:56 MAIL:kennji72001@yahoo.co.jp 24241
⡼ޥ
ͤۤѤǤ͡
ͧͤФ줿ǤŨʲˡ˴ưޤ
ֱ߼100Ĥ¤Ǥꤽ¤1ǤĤϢ³ν򺿤Ȥ֤Ȥˤȡ¤äƤ뺿θĿ衣
1216ڡ 15:45:35 MAIL:kennji72001@yahoo.co.jp 24242
⡼ޥ
Ǥޤ
ߤޤƱʸϤʣƤޤޤ
1216ڡ 15:51:10 MAIL:kennji72001@yahoo.co.jp 24243
weapon
>>24241
4951?
1216ڡ 15:57:58 24244
weapon
>>24241
4951?
1216ڡ 16:01:22 24245
n

1216ڡ 17:20:31 24246
⡼ޥ
>>24241 weapon Ǥ
ûǤΥСϤäѤꤹʤ
1216ڡ 18:23:27 MAIL:kennji72001@yahoo.co.jp 24247
uchinyan
#24241
ǶФΤ㤤¿ְäƤ뤫⤷ޤ󤬡
ߤ뺿ءʳϡAФƱߤAʬ⺿ˤʤޤ
BȤޤȡA + B = 1
äơA >= 1 <-> B <= 0 абޤ
ǡؤ¤1ʾ塢ʤκθĿ¤ʲκθĿȤϰפޤ
ؤϡ99 * 100 = 9900 ʤΤǡθĿϡؤξ礬Ǥ뤳Ȥθơ
9900/2 + 1 = 4951
ʤĤξ⺿ȤƤޤϤΤǤ͡
1216ڡ 19:34:38 24248
ʤ
󤹤Ǥ͡
줬Ȥϻפޤ󡣡
ǰ˽񤭹ߤޤ
1216ڡ 19:47:28 24249
⡼ޥ
>> 24248
uchinyan 󡢹ͤϤޤˤ̤Ǥ( 1002 + 1 )
ߤʤ󤵤Ǥͤ
1216ڡ 21:21:18 MAIL:kennji72001@yahoo.co.jp 24250
̾õ
ߤʤޤƱǤ

Ȥǡΰ̹ࡢ
ʤޤǤˤĤơ
ΤƤĤǤοA(n,k)Ϥɤɽޤ

A(7,5)=6C1*5!*0!+6C2*4!*1!+6C3*3!*2!+6C4*2!*3!+6C5*1!*4!+6C6*0!*5!
Ƚ񤤤ƤϸΤΡA(7,4)ʤɤؤθ̤褯ޤ
A(7,4)=6C2*4!+6C3*3!*3+6C4*2!*11+6C5*1!*50+6C6*0!*255
1216ڡ 22:28:00 24251
⡼ޥ
>> 24248
uchinyan 󡢹ͤϤޤˤ̤Ǥ( 1002 + 1 )
ߤʤ󤵤Ǥͤ
1216ڡ 23:35:13 MAIL:kennji72001@yahoo.co.jp 24252
⡼ޥ
ߤޤ󹹿ޤƱʸ񤭹ޤƤޤޤ
ǤʤʤǤ
1216ڡ 23:39:11 MAIL:kennji72001@yahoo.co.jp 24253
uchinyan
#24251
괺ϡ
A(n,k) = (i=0,k) [C(n-1,k-i) * (k-i)! * A(n-k+i-1,i)]
ʡ
ͥνȡ 1217ʶ 0:31:24 MAIL:uchi@sco.bekkoame.ne.jp 24254
X
ϤּΤƤ뤫ޤˤɤפ򷫤֤ȴ㤤Ƥޤ轵ͤޤǤꡣ䤹ߤǤ
1217ʶ 13:53:21 24255
оϩ
7뤫ǹͤޤ
ΤȤ15̤
ΤȤ6̤
ʳϤʤΤǡפǤ21̤
äơ21/5040=1/240Ǥ
Ψ϶ʤΤǤʤ
γ 1217ʶ 20:05:22 MAIL:pctakada@mail.goo.ne.jp HomePage:Ĥ줭24257
Ф
Ǽ֤ϣ̤ꡢ˿¤٤ƤơĤĿɤưФФ褤ۤοͤäƤΤƱǤ͡Ĥޤ(1+2+3+4+5+6)/7!
1218ڡ 5:56:39 24258
̾õ
#24254 ꤬Ȥޤ
Ǥ͡ˤʤޤ͡
ȤС
A(7,4)=A(6,4)+6*A(5,3)+6*5*A(4,2)+6*5*4*A(3,1)+6*5*4*3*A(2,0)

ˤ
A(n,0)=1, A(2,1)=1
A(3,1)=A(2,1)+2*A(1,0)=3
A(4,1)=A(3,1)+3*A(2,0)=6
A(5,1)=A(4,1)+4*A(3,0)=10
A(6,1)=A(5,1)+5*A(4,0)=15
A(7,1)=A(6,1)+6*A(5,0)=21
äơΨ=21/5040=1/240

1218ڡ 8:08:37 24259
uchinyan
#24254ڤ#24259
ǰʤ顢ΰ̹ϡΤȤƤޤ
A(n,k) = (i=0,k) [C(n-1,k-i) * (k-i)! * A(n-k+i-1,i)]
ޤȤƤޤ
ޤ餫ˡA(n.0) = 1 Ǥˡ̣ꡢA(k+1,k) = k! ⤤ޤ
ˡ
A(n,k) = A(n-1,k) + (i=0,k-1) [C(n-1,k-i) * (k-i)! * A(n-k+i-1,i)]
ʤΤǡA(n,k-1) ʬСA(n,k) n ˴ؤ­뤳ȤǸŪˤϵޤޤ
äơA(n,1), A(n,2), ... Ƚ֤˷׻ǽǤ
ʤA(n,1) ϡΰñʳĥˤʤäƤޤ
ϡ#24230ڤ#24240ΥåΤޤ޻ȤơA(n,1) = C(n,2) ȵޤޤ
Τ褦ˤޤޤ
A(n,1) = A(n-1,1) + C(n-1,1) * 1! * A(n-2,0) = A(n-1,1) + C(n-1,1) = ...
= A(2,1) + C(2,1) + C(3,1) + ... + C(n-2,1) + C(n-1,1)
= 1 + C(2,1) + C(3,1) + ... + C(n-2,1) + C(n-1,1)
ǤäȥȥåǤC(2,2) = 1 Ǥ뤳ȤȡC(n,r) = C(n-1,r-1) + C(n-1,r) Ǥ뤳ȤȤȡ
A(n,1) = C(2,2) + C(2,1) + C(3,1) + ... + C(n-2,1) + C(n-1,1)
= C(3,2) + C(3,1) + ... + C(n-2,1) + C(n-1,1) = ...
= C(n-1,2) + C(n-1,1) = C(n,2)
ƱͤˤơA(n,2) ϡ
A(n,2) = A(n-1,2) + C(n-1,2) * 2! * A(n-3,0) + C(n-1,1) * 1! * A(n-2,1)
= A(n-1,2) + C(n-1,2) * 2 + (n-1) * C(n-2,2)
줫ޤޤάޤ
ͥνȡ 1218ڡ 13:50:25 MAIL:uchi@sco.bekkoame.ne.jp 24260
uchinyan
#24260
ءۤǤ
A(n,1) = 1 + C(2,1) + C(3,1) + ... + C(n-2,1) + C(n-1,1) = 1 + 2 + 3 + ... + (n-2) + (n-1)
= n(n-1)/2 = C(n,2)
Ǥ (^^;
ͥνȡ 1218ڡ 18:09:16 MAIL:uchi@sco.bekkoame.ne.jp 24261
arijune
Ƥ顣
󥿡ޤǸ塦orz
1220ʷ 1:29:42 24262
̾õ
A(n, k) = (i=0 to k) [P(n-1, i)*A(n-1-i, k-i)]顢ޤ
A(n, 0) = 1
A(n, 1) = 1/2*(n-1)n
A(n, 2) = 1/24*(n-2)(n-1)n(3n-1)
A(n, 3) = 1/48*(n-3)(n-2)(n-1)^2n^2
A(n, 4) = 1/5760*(n-4)(n-3)(n-2)(n-1)n(15n^3-30n^2+5n+2)

1220ʷ 16:45:48 24263