٥륯åĥ
եܥʥå13Ǥ͡

䤼󤼤㤤ޤ
¤Ǥ͡ܤƤ褦ʤΤ˿ޤ
1212ڡ 0:13:17 48593
鯤ο
ǽ˽񤫤ƤäΡΡȤιͤA(n)Ȥȡ
+1n+1ʬˤꡢA(n+1)=A(n)+n, A(2)=2顢
˷׻ƤȡA(13)78ȤʤΤǡ13
//
1212ڡ 0:11:22 48594
ǯ
12ޤ­78ʤΤ13
ä12äƤ

ΡΡȤ˽񤤤8μ1???
Ф餯ǺǤ

1212ڡ 0:17:10 48595
鯤ο
>>48593
եܥʥå78ϽФƤޤ󤬡
1212ڡ 0:18:16 48596
٥륯åĥ
亣ǯԤ
21+1111ǤϤʤǤ礦Ѥߤä餺ߤޤ
鯤οͤ
ο¤׻ƤΤˡʤǼĤˤϥեܥʥåȽ񤤤Ƥޤ󤷤äƤޤ󡢼ʬǤ̣Ǥ

1212ڡ 0:30:40 48597
Sueh
ʬǽ黰ѿȻפäΤǤʬλˤäưабǤϤʤ褦Ǥ
ǼŪ˷׻
ĤκǽοΡȤο
10
21
33
45, 6
59, 10
614, 15
720, 21
826, 27, 28
934, 35, 36
1043, 44, 45
1153, 54, 55
1263, 64, 65, 66
n(n-1)n/2-[n/4] (n-1)n/2
1212ڡ 0:27:25 48598
alice
ɽ2,3,4,äΤǷ׻21,33,46äΤnC2Ȼפޤ
1212ڡ 0:32:51 48599
alice
48598
42+2(4)1+1+1+1(4+1+1)
43+1(3)2+1+1(3+2)1+1+1+1(3+2+1)
ȤʤΤʬλ˸¤餺1ĤȻפޤ
1212ڡ 0:40:35 48601
alice
48598
42+2(4)1+1+1+1(4+1+1)
43+1(3)2+1+1(3+2)1+1+1+1(3+2+1)
ȤʤΤʬλ˸¤餺1ĤȻפޤ
1212ڡ 0:40:35 48602
ǯ
48597٥륯åĥ
꤬ȤޤˤʤäȽޤ
1212ڡ 0:41:35 48603
٥륯åĥ
>Sueh
a+ʬȡ1a-1ޤǤ+1-1ޤǤ+abɬ1餢-1ޤǤ¤ˤʤȻפޤŪǼˡǤ
1212ڡ 0:46:49 48604
鯤ο
ǽ˽񤫤ƤäΡΡȤιͤA(n)Ȥ롣
n=1,2ξϡʬλ1̤ʲʤΤǡ
A(1)=0A(2)=1
()ǤդnˤĤơʬλ˰ͤ餺A(n)n(n-1)/2Ȥʤ뤳ȤǼˡǼ

()Ǥդ1<=k<=nkˤĤơʬλ˰ͤ餺A(k)k(k-1)/2Ȥ롣

ΤȤn+1ˤĤơ1<=m<=nʤǤդmˤĤơn+1m+(n+1-m)ʤʬ
ͤ롣
ȡ()ˤꡢʬˤΡȤιB(n,m)ϡ
B(n,m)A(m)+A(n+1-m)+m(n+1-m)
׻ά
n(n+1)/2
ȡm˰ͤ餺n(n+1)/2ˤʤޤ

äơn+1ξˤ⡢A(n+1)n(n+1)/2Ȥʤ롣
//
1212ڡ 1:16:02 48605
ֿء׾ι
n(n+1)/2ޤ
1212ڡ 6:14:57 48606

nĤͭꡢǤդ2ǤĤʤäƤ
n(n-1)/2ܤͭ뤳Ȥˤʤޤ
򣲤ĤΥ롼פʬȤ
ۤʤ륰롼פˤʤäƤޤä
ƱΤĤʤڤȤȡ
ڤäܿΡȤ˽񤤤Ƥ뤳Ȥˤʤޤ
ǽŪˤ٤Ƥڤޤ³Τ
ΡȤοιפn(n-1)/2Ȥʤޤ

äơɤǸȤǤ
1212ڡ 8:48:43 48607
Ѥ
(1/2)n(n-1)ǵޤʬ򣱤Ȥ
¤ϣn-1ޤǤμ¤ɽΤ
(1/2)n(n-1)=78򤭤ޤ
1212ڡ 9:23:01 48610
ޤ
ʬλ˸¤餺դˤʤꤽäΤǡ
16 ̤äƥߤĤ֤ġʲˡǤ
1112β˴ؤơkyorofumiޡ¾ޡˤ
𤹤ɬסꡢȤꤢäƤޤ(^^;
ۤɡ򥢥åפޤ

kyorofumi
򸫤¤ꡢֿءʻŪطʡפϤʤ
ߤĤ֤ˤʤdzǧȤά롢
Ȥ٤ΰ̣礤Ȼפޤ


ޥ뤵󡢤ޤ륱󤵤¾طγ͡񤤤ǤƤ褫äǤ
ǯڤߤˤƤޤ

somewhere in the world 1212ڡ 19:31:52 48611
Ϣ
151~5¤ȵŤΤǤ
Ȥ78ޤ6.7.8...­Ƥޤ
1212ڡ 13:55:22 48612
Ϣ
151~5¤ȵŤΤǤ
Ȥ78ޤ6.7.8...­Ƥޤ
1212ڡ 13:56:57 48613
ϥ饮㡼ƥ
ʬޤǤ

Ȥͤ뵤Ϥ̵ʤäƤޤ
ԡ 1212ڡ 15:15:43 MAIL:tfuruya@aria.ocn.ne.jp HomePage:湩ؤ˥48614
ˤ⡼
ͤ12¤78ȤȤǡ13饹Ȥơƥեn+n-1ˤ򤹤Ф󡪤ȻפĤDz
򤳤줫ͤ
¡ 1212ڡ 21:51:54 HomePage:˥ͥäΥڡ48615
٥륯åĥ
ïޤ褻Ƥʤ褦ʤΤǡ73+4341234פξοޤ򡣡ߤθĿΡȤ˽񤫤ˤʤޤ


ߡߡ
ߡߡߡ
ߡߡߡ
ߡߡߡ

ʤʤǤ

1213ʶ 22:50:23 48616
Sueh
ޤΤŦɤꡤ㤤Ƥޤޤ򤷤㤤ޤ

>>48607 >>48616
ʤۤɡn(n-1)/2ˤʤ̣狼ꡤٶˤʤޤ
1214ڡ 0:15:03 48617
ˤ
ΡȤοܤ­ȻפäƤޤ
Ķļˡ 1214ڡ 7:32:19 HomePage:ޤޤ48618
Mr.ǥ
ԼΤ褦ʹͤϤɤǤ礦

㤨С6ΤȤǹͤޤ
a,b,c,d,e,fΡͤȤ
Σͤ{a,b,c,d}{e,f}2롼פʬȤΥƱΤɬ򤹤ȡβϷס428ʲˡʥΡȤ˵
ˡ
{a,b,c,d}{a,b}{c,d}2롼פʬȤ
βϡ224
{a,b}{a}{b]ʬȤβϡ1

ͤĤˤʤޤǷ֤Ȱβ¤ϡˤͤ¤Ȥʤޤ
aǹͤȤΥƤä5ͤ٤ƤȰ򣱲󤺤ĤȤˤʤ
ɡ6ͤ٤Ƥ¾ΣͤĤ1󤺤İ򤷤Ƥ뤳Ȥˤʤ
ϡ65/215ʲ
ͤξȡʥΡȤ˵ͤ¡ˤ
n(1)/2

ˤȤŤ13Ȥޤ
1214ڡ 12:21:47 48619
RSI
ޤˤñä
1214ڡ 11:24:12 48620

Mr.ǥβ⤬ӰǤޤȤϤäȥԥȤʤΤǤ
1214ڡ 17:05:19 48621
٥륯åĥ
ޤʬˤȤΤȤʤΤǡؤäݤ

Ĥ˽񤫤Ƥ2ΤȤΡȤ˽񤫤줿¤11ޤǤμ¡ˤˤʤޤ

Ĥ˽񤫤ƤaΤȤΡȤ˽񤫤줿¤a-1ޤǤμ¡Ĥ˽񤫤ƤbΤȤΡȤ˽񤫤줿¤b-1ޤǤμ¤ǤСĤ˽񤫤Ƥ(a+b)ΤȤΡȤ˽񤫤줿¤ϡa-1ޤǤμ¡+b-1ޤǤμ¡+ab(a+b-1)ޤǤμ¡פˤʤޤʿޤa=3b=4ξ

ӭꡢƤμnˤĤơĤ˽񤫤ƤnΤȤΡȤ˽񤫤¤1n-1ޤǤμ¤ˤʤޤ
1214ڡ 23:55:08 48622
٥륯åĥ
¤¤Ǥʤ0¤ˤСʸˤֿ1ˤʤä齪λ1ΤȤϽ񤫤줿¤0פƱɽޤ͡

0¤ľơϡ1ΤȤ00ޤǤ¡פˤۤ褫ä
ޤ٤ϵˤʤͤ餪ꤤޤ
1215 13:44:31 48623

x(x1)/2=78
1215 0:39:06 48624
ޤ
1112θͥβǤ
Ŭ٤˴äơξ˥åפ褦ȻפäΤǤ
Ѥʤ顢ǤƤޤ̡ġ

Ѱդ˴ȤʤȤʤꤽʤΤǡ
̿˼Ƥۤɥåפޤm(__)m

somewhere in the world 1217ʲС 1:45:39 48625
ֿء׾ι
#48616 ͭ񤦤ޤȤäǤ͡åǤ
1217ʲС 16:43:40 48626
kyorofumi
#48611
虜虜ĺѤ꤬Ȥޤ
ץʤΤǿDz夲ƤȤϻפΤǤĤޤ͡
1217ʲС 19:55:16 48627
ޤ
ޤ򥢥åפǤʤΤǡˤǤ礦
Τޤޥ٥Ǥޤ

ꡧξĤμa,b,c,d,e,f Ȥͤ롣
aϡǤ⾮ƤĤˤʤ뤳ȤǤ뤫
[] a > b > c > d > e > f ǡa-b, b-f, c-eʤɡɤΣκۤʤ롣


a-b=P, b-c=Q, c-d=R, d-e=S, e-f=T ġȤ롣
a,b,c,d,e,f ΣˤĤơκ 6C2 = 15Ĥ롣

ǡ15ĤκP,Q,R,S,Tɽȡʳˡ
a-c=P+Q
b-d=Q+R
c-e=R+S
d-f=S+T
a-d=P+Q+R
b-e=Q+R+S
c-f=R+S+T
a-e=P+Q+R+S
b-f=Q+R+S+T
a-f=P+Q+R+S+T Ȥʤ롣
[]ˤϡ15Ĥο٤ưۤʤФ褤

ǤȤꤢ
P,Q,R,S,T
P+Q, Q+R, R+S, S+T ĭΣĤοۤʤPTȤͤ롣

ޤ a Ǥ⾮ˤϡ
P+Q+R+S+TǤ⾮Ф褤顢
P,Q,R,S,T˾Ƥ

(i) 1, 2, 3, 4, 5 Ȥ
ͤϣʾǤʤФʤʤΤǡ
ͤȤ߹碌ϡ
1+5, 2+4 ; 2+5, 3+4 ; 3+5 ; 4+5 Σ̤ꤢ롣
ǡPTϣ󤷤ȤʤȤͤȡ
1PTΤɤ餫Ǥ롣
P=1ȤQ=5ΤȤ R=2ȤȡS=4 ȤʤꡢP+Q=R+Sǥᡣ
R=3,4ξᡣT=1ΤȤƱ顢ȹ礻ǤϥǤ롣

(ii) 1,2,3,4,6 Ȥ
(i)Ʊͤ˹ͤơͤȹ礻ϡ
1+4, 2+3 ; 1+6, 3+4 ; 2+6 ; 3+6 ; 4+6 7̤ꤢ롣
ǸΣĤμˤϡɤ⣶äƤ뤬
6¿Ƥ2󤷤Ȥʤ¤ˤʤϣ̤ꤢ뤬
1+6֤ȡ1+42+3Τɤ餫ĤȺǸΣĤμΤΣĤ
ȤʤǤ롣äơ3+4ФʤФʤʤ
ΤȤȤΤϣĤʤ顢1+4Ф롣
ȡP,Tξ
P=1, Q=4, R=3 ĭR=3, S=4, T=1ĭ
ͤ졢ΤȤS=6, T=2 ΤȤP=2, Q=6 Ȥʤ롣

ȤΤȤ줾
P+Q+R = S+T, R+S+T = P+QǤꡢ[]ʤ顢
ȹ礻Ǥ롣

(iii) 1,2,3,5,6 Ȥ
Ʊͤ 1+3 ; 1+6, 2+5 ; 2+6, 3+5 ; 3+6; 5+6 Σ̤ͤ롣
Ϥꣶܤȡ2+5 ФʤФʤ餺
1+3ɬŪФ롣ĤŬȹ礻Ф褤

ΤȤȤơP=1, Q=3, R=6, S=2, T=5 ĭꡢ
¤17Ǥ롣
PT¤ϡǾ15Ǥ뤬(i) ξ礷ʤΤ̵
16ξ(ii)ξ礷ʤΤǡ̵Ǥ롣
äơ17ǾȤʤ롣
f ϤɤΤ褦ʿǤɤaǤʤ褦ˤȡ
f=1ΤȤa = f+17 = 18

somewhere in the world 1218ʿ 23:18:07 48628
ޤ
;̤Ǥϡع⹻ؤοء٤ΡֽסʺιԥåˤǤ
äΤǤ31̾Ԥ1̾ΤߡȤ̤Ǥ
¿ʬˤˤ⡢1̾ȤΤϡʤΤǤϤʤǤ礦ġ

ʤߤˡԤ6䤬ʻƱ͡˾ƤϤ
äȤΤȤǤ

񤭼̤Ǥ뤫ȻפޤޤǤޤorz

somewhere in the world 1218ʿ 23:25:57 48629