ߥƥ
100 p=0
110 for a=1 to 11
120 for b=a+1 to 12
130 for c=b+1 to 13
140 for d=c+1 to 14
150 if a+d-b-c=0 then p=p+1
160 next d
170 next c
180 next b
190 next a
200 print p
210 end

161̤
ϤʤᤤȻפäɡġġʤ||
46ڡ 0:06:30 27100
kasama
import java.util.*;
public class Question496 {
public static void main(String args[]) {
Integer nos[] = new Integer[14];
for(int i = 0; i < 14; ++i) nos[i] = new Integer(i+1);
int count = 0;
List list = new Combination(Arrays.asList(nos), 4).getList();//饹Combination#19625
for (Iterator iter = list.iterator(); iter.hasNext(); ) {
List eList = (List) iter.next();
int a = ((Integer) eList.get(0)).intValue();
int i = ((Integer) eList.get(1)).intValue();
int u = ((Integer) eList.get(2)).intValue();
int e = ((Integer) eList.get(3)).intValue();
if (a + e == i + u) ++count;
}
System.out.println(count);
}
}
²λ 46ڡ 0:07:49 27101
Ȥ
餫Ģ˺äƤΤǤäѷ
ʲΥץ(basic)

10 FOR a=1 TO 14
20 FOR b=1 TO 14
30 if b=a then goto 290
40 FOR c=1 TO 14
50 if ((c=a) or (c=b)) then goto 280
60 FOR d=1 TO 14
70 if ((d=a) or (d=b) or (d=c)) then goto 270
100 LET x=a+d
110 LET y=b+c
120 IF x=y AND a<b AND b<c AND c<d THEN PRINT a;b;c;d
270 next d
280 next c
290 next b
300 next a
END
˭ԡ 46ڡ 0:08:10 MAIL:fttnm528@ybb.ne.jp 27102

ܡʣܣܣˡܡʣܣܣܣܣˡܡʣܣܣܣܣܣܣˡܡʣܣܣܡܣˡܡʣܣܣܡܣˡᣱܣܣܣܣܣᣱ
46ڡ 0:18:23 27104

ܥᥤܥꡤݥᥤݥ
ݥᥤݥ1ΤȤȥ213ޤǤ椫֤Ȥˤʤ롥12C2=66̤
ʲƱͤˡ
ݥᥤݥ2ΤȤ312ޤǤ椫210C2=45
ݥᥤݥ3ΤȤ411ޤǤ椫28C2=28
ݥᥤݥ4ΤȤ510ޤǤ椫26C2=15
ݥᥤݥ5ΤȤ69ޤǤ椫24C2=6
ݥᥤݥ6ΤȤ78ޤǤ椫22C2=1
66+45+28+15+6+1=161̤

äȤ줤ʲꤽ
46ڡ 0:21:21 MAIL:kaitoexe@green.livedoor.com HomePage:ؼ Kaito's Lab.27105

36+30+25+20+16+12+9+6+4+2+1=161
ľ˹ͤФ褫äOTL
ӥå 46ڡ 0:24:27 HomePage:θ27106
إ饯쥹ԡ
¿ΤǺƤӽľ

ΥץǽʤΤƻ˵ޤ
ܥʥܥˤθϡ飲Σ̤ꡣ
ΣоΤˤʤΤͽۤĤΤ
ģ
ģ
ģoror
ģoror
ģororororor
10ģororororor
ʲάȤޤ
ºݤϥȤ߹碌ͤơб륤õޤ
ǵ§˵Ťޤ
ǽŪʼϡʣܣܣܣܣˡߣܣᣱ

ޤ׻ǣʬǽ褿­
軲̻ԡ 46ڡ 0:26:47 HomePage:ɥԥ27108
ݤ
ϼǤٴְ㤨Ȥ
ȤǤ褪ǤȤ
Ƹɡ 46ڡ 0:28:09 MAIL:hopes@mba.ocn.ne.jp HomePage:ȣϣУţӤ褤Ȥ٤Ϥ27109
ߤ
14 13 12 11 10 09 08 07 06 05 04ο
ݡݡݡݡݡݡݡݡݡݡݡݡݡݡݡݡݡݡݡݡ
06 05 05 04 04 03 03 02 02 01 01 (1)
05 05 04 04 03 03 02 02 01 01 (2)
05 04 04 03 03 02 02 01 01 (3)
04 04 03 03 02 02 01 01 (4)
04 03 03 02 02 01 01 (5)
ɽϰʲάäƤȤǡ()ϥο򼨤

ɽοȤ߹碌ˤ­
ߣܣߣܣߣܣߣܣߣܣߣᣱ̤ꡣ

46ڡ 0:29:03 27110
ä
ƻ˷׻ޤ
ܥᥤܥk ֤ȡ
k 525Τɤ줫

k5ΤȤ
1,4ˡ2,3ˤȤ߹碌ʤΤǡդƤϤޤΤ1̤ꡣ

k6ΤȤ
1,5ˡ2,4ˤȤ߹碌ʤΤǡդƤϤޤΤ1̤ꡣ

k7ΤȤ
1,6ˡ2,5ˡ3,4ˤȤ߹碌ʤΤǡդƤϤޤΤ123̤ꡣ

ȤޤǷ׻ơ§˵դ
k5,25ΤȤ1̤
k6,24ΤȤ1̤
k7,23ΤȤ12̤
k8,22ΤȤ12̤
k9,21ΤȤ123̤
k10,20ΤȤ123̤
k11,19ΤȤ1234̤
k12,18ΤȤ1234̤
k13,17ΤȤ12345̤
k14,16ΤȤ12345̤
k15ΤȤ123456̤

{1(12)(123)ܡ1234ˡ(12345)}2(123456)161
Ȥޤ(^^;)ե
Ϥ 46ڡ 0:35:55 27111
ޡ
¤5or6or24or252C2
¤7or8or22or233C2
Ʊͤˤ4C2,5C2,6C2
¤157C2
ꡤ2C2+3C2+4C2+5C2+6C2ˡ4+7Cᣱ̤
46ڡ 0:36:13 27112
ä
#27111
Ǹη׻ְäƽ񤭤ޤ(^^
ˡ 2
ˡ 4
Ϥ 46ڡ 0:40:32 27113
⡼ޥ
錄ƻˡ
1*6+(2+3)*5+(4+5)*4+(6+7)*3+(8+9)*2+(10+11)*1=161
äȡȤޤˡʤ
46ڡ 5:21:01 MAIL:kennji72001@yahoo.co.jp 27114
ʤ
#27105 Ȥ˰ɼ
ᥨĤȤʤΤ(14-2D) 2 Τǡ
12C2 * 10C2 + 8C2 + 6C2 + 4C2 + 2C2 = 161
̹񡡡 46ڡ 6:56:26 MAIL:naka@sansu.org HomePage:naka's Home Page27115

ϡȤƱͤʾʬǵޤʿϻŪ˥ȥκλȤ˾ʬޤ
޷Ū˹ͤȡݤ򡡡ȣ¤١֤ΰ֤򺸤飱Ȥ롣򣴸ɤĤ֤ĤоΤʿ޷ˤʤФ褤оΤоΤμΰ֤..ΤȤϡ¦ͤ22̤ꡢΰ֤..1ΤȤϡ32̤ꡢΰ֤..ΤȤϡ42̤ꡢΰ֤..ΤȤϡ52̤ꡢΰ֤..ΤȤϡ62̤ꡢΰ֤ΤȤϡ72̤ꡣɡ2232425262ˡߣ72ᣱ̤ꡣ
46ڡ 8:44:19 27116

Ȥ󡢸ƤӼΤƤˤƤߤޤ󡣥ѥɤꤷƤʤǤޤǤͤӤޤ
46ڡ 8:51:19 27117
ϥ饮㡼ƥ
Ϥ褦ޤ

ץǤ
̶彣 46ڡ 9:48:45 HomePage:ĩ27118
DrK
櫓򤷤ޤ
â羮طꤵƤ뤳ȤȤơ2Ԥޤ
2Ĥο¤15(=1+14)ФоݤˤʤäƤ뤳Ȥ˵ŤйפФƤξ櫓򤹤Ф
פ327ꤦ
34ˤĤƤ1̤ꤷʤΤԲ
562̤ǡ2ĤȤ߹碌֤Τ1̤
783̤ǡ2ĤȤ߹碌֤Τ3C2=3
9104̤ꡢ4C2=6
11125̤ꡢ5C2=10
13146̤ꡢ6C2=15
15ξ7̤ꡢ7C2=21
ʾ夫
(1+3+6+10+15)22+21=161
٤Ͼγڱࡡ 46ڡ 11:55:53 MAIL:satoka@star.odn.ne.jp 27119
Ҥ
ƱȻפΤǤ
̤
̤

̤
ޤȤ̤
ƱޤΤϣܣܡܣᣳ̤
Ȥϵ§Ūˡ
ܣܣܣܣܣܣܣܣܣܣȡ
46ڡ 12:39:02 27120
Ҥ
ʤߤˡ飱ޤǤο˶ǻѷĤˡƱΤ褦Ǥ

http://www.research.att.com/~njas/sequences/Seis.html
46ڡ 12:59:39 27122
Ҥ
󥯴ְ㤨ޤ

http://www.research.att.com/~njas/sequences/?q=1%2C3%2C7%2C13%2C22%2C34&language=english&go=Search
46ڡ 13:03:09 27123
uchinyan
ϤˤϡϡϤʤ˵ޤäΤΡǽϡɤ⺣ĤǤ
θ塢ͤФ顢ȤʲˡפĤޤ
ƱȤȻפޤ޳ѤʤΤǡ񤤤Ƥޤ

ޤϡīƬǹͤˡ顣

(ˡ1)
ҤᤫʤäΤǡƻ˿ޤ
(1) 1 ξ硧ϡ4 14 Ǥ
(1-1) 4 ξ硧 + = 5 ǡ < ʤΤǡ1 ̤ꡣ
(1-2) 5 ξ硧 + = 6 ǡ < ʤΤǡ1 ̤ꡣ
(1-3) 6 ξ硧 + = 7 ǡ < ʤΤǡ2 ̤ꡣ
(1-4) 7 ξ硧 + = 8 ǡ < ʤΤǡ2 ̤ꡣ
(1-5) 8 ξ硧 + = 9 ǡ < ʤΤǡ3 ̤ꡣ
(1-6) 9 ξ硧 + = 10 ǡ < ʤΤǡ3 ̤ꡣ

(1-9) 12 ξ硧 + = 13 ǡ < ʤΤǡ5 ̤ꡣ
(1-10) 13 ξ硧 + = 14 ǡ < ʤΤǡ5 ̤ꡣ
(1-11) 14 ξ硧 + = 15 ǡ < ʤΤǡ6 ̤ꡣ
Ĥޤꡢ(1 + 2 + 3 + 4 + 5) * 2 + 6 ̤ꡣ
ǡΡ§ƤƤޤ
(2) 2 ξ硧ϡ5 14 Ǥ
(2-1) 5 ξ硧 + = 7 ǡ < ʤΤǡ1 ̤ꡣ
(2-2) 6 ξ硧 + = 8 ǡ < ʤΤǡ1 ̤ꡣ
(2-3) 7 ξ硧 + = 9 ǡ < ʤΤǡ2 ̤ꡣ
(2-4) 8 ξ硧 + = 10 ǡ < ʤΤǡ2 ̤ꡣ

(2-9) 13 ξ硧 + = 15 ǡ < ʤΤǡ5 ̤ꡣ
(2-10) 14 ξ硧 + = 16 ǡ < ʤΤǡ5 ̤ꡣ
Ĥޤꡢ(1 + 2 + 3 + 4 + 5) * 2 ̤ꡣ
Ǹ夬ĤΤݥȤǤ
Ʊͤˤơ
(3) 3 ξ硧ϡ6 14 Ǥ
(1 + 2 + 3 + 4) * 2 + 5 ̤ꡣ
(4) 4 ξ硧ϡ7 14 Ǥ
(1 + 2 + 3 + 4) * 2 ̤ꡣ
(5) 5 ξ硧ϡ8 14 Ǥ
(1 + 2 + 3) * 2 + 4 ̤ꡣ
(6) 6 ξ硧ϡ9 14 Ǥ
(1 + 2 + 3) * 2 ̤ꡣ
(7) 7 ξ硧ϡ10 14 Ǥ
(1 + 2) * 2 + 3 ̤ꡣ
(8) 8 ξ硧ϡ11 14 Ǥ
(1 + 2) * 2 ̤ꡣ
(9) 9 ξ硧ϡ12 14 Ǥ
1 * 2 + 2 ̤ꡣ
(10) 10 ξ硧ϡ13 14 Ǥ
1 * 2 ̤ꡣ
(11) 11 ξ硧ϡ14 Ǥ
1 ̤ꡣ
Ǥ٤ƤǤɡ
((1 + 2 + 3 + 4 + 5) + (1 + 2 + 3 + 4) + (1 + 2 + 3) + (1 + 2) + 1) * 4 + (1 + 2 + 3 + 4 + 5 + 6)
= (1 + 3 + 6 + 10 + 15) * 4 + 21
= 35 * 4 + 21
= 161 ̤

(ˡ2)
(ˡ1)Ʊͤ˿夲Ǥʬλ㤤ޤñ⤷ʤ
ȥȡȥϡȥδ֤ ܥᥤܥ 褦˷ƤФȤˤʤޤ
ǡݥ βǽϰϤʬहȡ
ݥ = 13 ξ
ݥ = 13 Ȥʤ륢ȥϡ1 ̤ꡣ
ȥϡĤ 12 Ĥ椫 ܥᥤܥ 褦˷Τ 6 ̤ꡣ
ݥ = 12 ξ
ݥ = 12 Ȥʤ륢ȥϡ2 ̤ꡣ
ȥϡĤ 11 Ĥ椫 ܥᥤܥ 褦˷Τ 5 ̤ꡣ
ݥ = 11 ξ
ݥ = 11 Ȥʤ륢ȥϡ3 ̤ꡣ
ȥϡĤ 10 Ĥ椫 ܥᥤܥ 褦˷Τ 5 ̤ꡣ
ݥ = 10 ξ
ݥ = 10 Ȥʤ륢ȥϡ4 ̤ꡣ
ȥϡĤ 9 Ĥ椫 ܥᥤܥ 褦˷Τ 4 ̤ꡣ
ݥ = 9 ξ
ݥ = 9 Ȥʤ륢ȥϡ5 ̤ꡣ
ȥϡĤ 8 Ĥ椫 ܥᥤܥ 褦˷Τ 4 ̤ꡣ
ݥ = 8 ξ
ݥ = 8 Ȥʤ륢ȥϡ6 ̤ꡣ
ȥϡĤ 7 Ĥ椫 ܥᥤܥ 褦˷Τ 3 ̤ꡣ
ݥ = 7 ξ
ݥ = 7 Ȥʤ륢ȥϡ7 ̤ꡣ
ȥϡĤ 6 Ĥ椫 ܥᥤܥ 褦˷Τ 3 ̤ꡣ
ݥ = 6 ξ
ݥ = 6 Ȥʤ륢ȥϡ8 ̤ꡣ
ȥϡĤ 5 Ĥ椫 ܥᥤܥ 褦˷Τ 2 ̤ꡣ
ݥ = 5 ξ
ݥ = 5 Ȥʤ륢ȥϡ9 ̤ꡣ
ȥϡĤ 4 Ĥ椫 ܥᥤܥ 褦˷Τ 2 ̤ꡣ
ݥ = 4 ξ
ݥ = 4 Ȥʤ륢ȥϡ10 ̤ꡣ
ȥϡĤ 3 Ĥ椫 ܥᥤܥ 褦˷Τ 1 ̤ꡣ
ݥ = 3 ξ
ݥ = 3 Ȥʤ륢ȥϡ11 ̤ꡣ
ȥϡĤ 2 Ĥ椫 ܥᥤܥ 褦˷Τ 1 ̤ꡣ
Ǥ٤ƤǤɡ
1 * 6 + 2 * 5 + 3 * 5 + 4 * 4 + 5 * 4 + 6 * 3 + 7 * 3 + 8 * 2 + 9 * 2 + 10 * 1 + 11 * 1
= 6 + 10 + 15 + 16 + 20 + 18 + 21 + 16 + 18 + 10 + 11
= 161 ̤

(ˡ3)
θ塢Żι֤˹ͤˡǤǤ⡢ǤϤʤǤ͡
= a, = b, = c, = d Ȥޤȡ
a + d = b + c, 1 <= a < b < c < d <= 14
Ǥѷơ
b + (c - b - 1) + (b + 1) = a + d
2 * (b - a - 1) + (c - b - 1) + 2 * a + 3 = a + d
(a - 1) + 2 * (b - a - 1) + (c - b - 1) = d - 4
(a - 1) + 2 * (b - a - 1) + (c - b - 1) + (14 - d) = 10
ǡx = a - 1, y = b - a - 1, z = c - b - 1, u = 14 - d Ȥȡ
x + 2y + z + u = 10, x >= 0, y >= 0, z >= 0, u >= 0
ˤʤޤβȤθĿФȤˤʤޤǰʤ顢y η 1 ǤϤʤΤǡʬޤ
ʥ֤ˤ 0 <= y <= 10 Ǥx >= 0, z >= 0, u >= 0 ˤդȡ0 <= y <= 5 ˤʤꡢ
x + z + u = 10 - 2y, x >= 0, z >= 0, u >= 0
y Ф롢(x,z,u) βθĿϡ(12-2y)C2 ĤʤΤǡɡβθĿϡ
12C2 + 10C2 + 8C2 + 6C2 + 4C2 + 2C2 = 66 + 45 + 28 + 15 + 6 + 1 = 161
ǡ ܥᥤܥ μФϡ161 ̤ꡣ

(ˡ4)
(ˡ2)(ˡ3)񤤤ƤƻפĤˡʤСȤʡ
ܥᥤܥ ݥᥤݥ ѷƤߤޤȡ1 14 ϰϤ¤ꡢϡ1 6 ꤨޤ
⡢򤳤ϰϤǰķȡ뤳ȤǡϰĤ˷ޤäƤޤޤ
1 ȤǤΤϡʥ֤ˤ 13 ̤Ǥ > ʤȤʤʤΤǡ٤Τ 12 ̤Ǥ
ǡȥ 12C2 ̤ꡣ
2 ȤǤΤϡʥ֤ˤ 12 ̤Ǥ > ʤȤʤʤΤǡ٤Τ 10 ̤Ǥ
ǡȥ 10C2 ̤ꡣ
3 ȤǤΤϡʥ֤ˤ 11 ̤Ǥ > ʤȤʤʤΤǡ٤Τ 8 ̤Ǥ
ǡȥ 8C2 ̤ꡣ
4 ȤǤΤϡʥ֤ˤ 10 ̤Ǥ > ʤȤʤʤΤǡ٤Τ 6 ̤Ǥ
ǡȥ 6C2 ̤ꡣ
5 ȤǤΤϡʥ֤ˤ 9 ̤Ǥ > ʤȤʤʤΤǡ٤Τ 4 ̤Ǥ
ǡȥ 4C2 ̤ꡣ
6 ȤǤΤϡʥ֤ˤ 8 ̤Ǥ > ʤȤʤʤΤǡ٤Τ 2 ̤Ǥ
ǡȥ 2C2 ̤ꡣ
Ǥ٤ƤǤɡ
12C2 + 10C2 + 8C2 + 6C2 + 4C2 + 2C2 = 66 + 45 + 28 + 15 + 6 + 1 = 161 ̤

(ˡ5)
(ˡ4)񤭾夲ơդȻפĤˡ(ˡ4)ǤϺܤޤ¤ΤޤޤǤǤޤ͡
äȤ⡢ϡ¤ϡ(ˡ1)Ǥ䤷ޤ (^^;
ܥܥܥ ͤȡ1 + 2 + 3 + 4 = 10 50 = 11 + 12 + 13 + 14 ʤΤǡܥᥤܥ ϡ5 25 ϰϤȤޤ
ơ5 14 16 25 Ȥϡ15 ˴ؤоΤȤʤȤĿ˴ؤƤƱˤʤޤ
ˡ¤ 5 15 ϰϤǰķȡ뤳ȤǡϰĤ˷ޤäƤޤޤ
¤ 5 ȤǤΤϡ2 ̤ˤʤꡢȥ 2C2 ̤ꡣ
¤ 6 ȤǤΤϡ2 ̤ˤʤꡢȥ 2C2 ̤ꡣ
¤ 7 ȤǤΤϡ3 ̤ˤʤꡢȥ 3C2 ̤ꡣ
¤ 8 ȤǤΤϡ3 ̤ˤʤꡢȥ 3C2 ̤ꡣ
¤ 9 ȤǤΤϡ4 ̤ˤʤꡢȥ 4C2 ̤ꡣ
¤ 10 ȤǤΤϡ4 ̤ˤʤꡢȥ 4C2 ̤ꡣ
¤ 11 ȤǤΤϡ5 ̤ˤʤꡢȥ 5C2 ̤ꡣ
¤ 12 ȤǤΤϡ5 ̤ˤʤꡢȥ 5C2 ̤ꡣ
¤ 13 ȤǤΤϡ6 ̤ˤʤꡢȥ 6C2 ̤ꡣ
¤ 14 ȤǤΤϡ6 ̤ˤʤꡢȥ 6C2 ̤ꡣ
¤ 15 ȤǤΤϡ7 ̤ˤʤꡢȥ 7C2 ̤ꡣ
ȡоΤ 16 25 Ǥ٤ƤǤɡ
((2C2 + 3C2 + 4C2 + 5C2 + 6C2) * 2) * 2 + 7C2
= ((1 + 3 + 6 + 10 + 15) * 2) * 2 + 21
= (35 * 2) * 2 + 21
= 161 ̤

ޤޤꤽʵ
Ǽɤٶޤ ^^/
ͥνȡ 47ʶ 9:04:09 MAIL:uchi@sco.bekkoame.ne.jp 27124
uchinyan
ǼɤߤޤϤꤤʲˡ褦Ǥڡ䤬դΤƱ˶ᤤ褦Ǥ
#27106, #27120ϡʬλ㤦褦Ǥ

#27100, #27101, #27102, #27118
ϡץࡣޤǥ󥰤ϰפǤ͡

#27104, #27105, #27115, #27116
ϡ#27124(ˡ4)(¤(ˡ3)Ȥ)Ʊ
#27116ϡ޷Ūʲ᤬򤤤Ǥ͡
ȡ#27115κǽΡ*פϡ+פδְ㤤Ȼפޤ

#27106, #27120
ϡƥȤ̤ξʬ򤷤Ƥޤ
äȤ⡢ϡݥ ƤȤȤˤϤʤΤǤʬ㤤ޤ͡

#27108, #27111, #27112, #27119
ϡ#27124(ˡ5)(¤(ˡ1)Ȥ)Ʊ

#27110
ϡŪˤϡ#27124(ˡ1)Ʊ
­λ㤦褦Ǥ

#27114
ϡ#27124(ˡ2)Ʊ
ͥνȡ 46ڡ 18:00:35 MAIL:uchi@sco.bekkoame.ne.jp 27125
???
3ʬлĤ1ĤϼưŪ˷ޤΤǡfor nextʸޤwhileʸ3ĤǤϤǤ
Option Explicit
Sub Macro1()
Sheets("Sheet1").Select
Cells(1, 1).Value = 0
Range("A1").Select
Dim a(4) As Integer
Call saiki(1, a())
Range("A1").Select
End Sub
Sub saiki(ByVal n As Integer, ByRef a() As Integer)
Dim j As Integer
If n = 1 Then
a(1) = 1
Else
a(n) = a(n - 1) + 1
End If
While a(n) <= 14 - (4 - n)
If n < 4 - 1 Then
Call saiki(n + 1, a())
Else
a(4) = a(2) + a(3) - a(1)
If a(3) < a(4) And a(4) <= 14 Then
Cells(1, 1).Value = Cells(1, 1).Value + 1
For j = 1 To 4
Cells(Cells(1, 1).Value, j + 1).Value = a(j)
Next j
Range("B" & Cells(1, 1).Value).Select
End If
End If
a(n) = a(n) + 1
Wend
End Sub
46ڡ 16:44:30 27126
uchinyan
#27124ؤɲ
(ˡ6)
(ˡ4)ΤäȤѷǤʬѤꡢ§ϤΤΡޤñǤϤʤ褦Ǥ
ޤǤ⡢Ӥΰ̣ǤΡ͡

ܥᥤܥ ݥᥦݥ ѷƤߤޤȡ1 14 ϰϤ¤ꡢϡ2 12 ǽǤ
򤳤ϰϤǰķȡ뤳ȤǥϷޤޤϥȥδ֤뤳ȤǽǤΤȤϷޤޤ
ϡ礭褦ˡμοľʤǽǡ
üΤȤǤϥμƤ뤳ȤդޤŪˤϡ
2 ȤǤΤϡ12 ̤ˤʤꡢȥ 11 * 1 ̤ꡣ
3 ȤǤΤϡ11 ̤ˤʤꡢȥ 9 * 2 + 1 ̤ꡣ
4 ȤǤΤϡ10 ̤ˤʤꡢȥ 7 * 3 + 2 + 1 ̤ꡣ
5 ȤǤΤϡ9 ̤ˤʤꡢȥ 5 * 4 + 3 + 2 + 1 ̤ꡣ
6 ȤǤΤϡ8 ̤ˤʤꡢȥ 3 * 5 + 4 + 3 + 2 + 1 ̤ꡣ
7 ȤǤΤϡ7 ̤ˤʤꡢȥ 1 * 6 + 5 + 4 + 3 + 2 + 1 ̤ꡣ
8 ȤǤΤϡ6 ̤ˤʤꡢȥ 5 + 4 + 3 + 2 + 1 ̤ꡣ
9 ȤǤΤϡ5 ̤ˤʤꡢȥ 4 + 3 + 2 + 1 ̤ꡣ
10 ȤǤΤϡ4 ̤ˤʤꡢȥ 3 + 2 + 1 ̤ꡣ
11 ȤǤΤϡ3 ̤ˤʤꡢȥ 2 + 1 ̤ꡣ
12 ȤǤΤϡ2 ̤ˤʤꡢȥ 1 ̤ꡣ
Ǥ٤ƤǤɡ
11 * 1 + 9 * 2 + 7 * 3 + 5 * 4 + 3 * 5 + 1 * 6 + (1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4) + (1 + 2 + 3 + 4 + 5)) * 2
= 11 + 18 + 21 + 20 + 15 + 6 + (1 + 3 + 6 + 10 + 15) * 2
= 91 + 35 * 2
= 161 ̤

ʤоꡢ
2 ϡ11 * 1
3 12 碌ȡ(9 * 2 + 1) + 1 = 10 * 2
4 11 碌ȡ(7 * 3 + 2 + 1) + (2 + 1) = 9 * 3
5 10 碌ȡ(5 * 4 + 3 + 2 + 1) + (3 + 2 + 1) = 8 * 4
6 9 碌ȡ(3 * 5 + 4 + 3 + 2 + 1) + (4 + 3 + 2 + 1) = 7 * 5
7 8 碌ȡ(1 * 6 + 5 + 4 + 3 + 2 + 1) + (5 + 4 + 3 + 2 + 1) = 6 * 6
Ȥʤޤ줬̣ΤɤϡʤȤ⡢λˤʬޤ
ͥνȡ 46ڡ 17:38:39 MAIL:uchi@sco.bekkoame.ne.jp 27127
uchinyan
ʤޤǤηǼĤε餫Ȼפޤ1 n ξˤϡ
f(n) = f(n-2) + (n-2)C2 for n >= 6, f(4) = 2C2 = 1, f(5) = 3C2 = 3
ˤʤ褦Ǥ͡
ͥνȡ 46ڡ 22:26:19 MAIL:uchi@sco.bekkoame.ne.jp 27128
fumio
Ф
46ڡ 23:27:06 27129
Revin
٤Perl

for($i = 1; $i <= 14; $i++){
for($j = 1; $j <= 14; $j++){
for($k = 1; $k <= 14; $k++){
for($l = 1; $l <= 14; $l++){
if($i == $j || $i == $k || $i == $l || $j == $k || $j == $l || $k == $l){
next;
}
@line = ($i, $j, $k, $l);
@line = sort{$a <=> $b} @line;
$calc = $line[0]*1000+$line[1]*100+$line[2]*10+$line[3];
if($record[$calc] != 0){ next; }
$record[$calc]++;
if($line[0] + $line[3] == $line[1] + $line[2]){ $count++; }
}
}
}
}

print $count;
47ʶ 2:17:41 27130
ʤ
PERL ʤ餳ʴǤɤǤ礦

for $i(1..14){
for $j($i+1..14){
for $k($j+1..14){
for $l($k+1..14){
if($i+$l == $j+$k){ $c++; }
}}}}
print $c;
̹񡡡 47ʶ 3:47:51 MAIL:naka@sansu.org HomePage:naka's Home Page27131
mhayashi
d(梦)b ƣ̤
47ʶ 8:22:04 HomePage:M.Hayashi's Web Site27132
⡼ޥ
ͧ䡦ϴñ

x1,x2,........xnϳơ1,0,-1Τ줫Ǥ롣
ο2ĤοѤ٤Ƥ¦xixjκǾͤ衣
1ijn٤ƤȡijˤˤĤƤ¤򤢤魯

ŷֻʤ(^^;)

ޤ꽸ְäƤ뤳Ȥ⤢뤷ܤˤꤤޤ(OrZ)
47ʶ 18:34:36 MAIL:kennji72001@yahoo.co.jp 27133
ERĹ
إ Excel VBA ץߥ(X_X;

Option Explicit

Sub إˡ()

Dim a As Integer, i As Integer, u As Integer, e As Integer, kosuu As Integer

With Worksheets("sheet1")

kosuu = 0

For a = 1 To 14
For i = 1 To 14
For u = 1 To 14
For e = 1 To 14

If (((a < i) And (i < u) And (u < e)) And (a + e = i + u)) Then kosuu = kosuu + 1

Next e, u, i, a

.Range("A1").Value = kosuu

End With

End Sub
47ʶ 23:22:39 27134
ERĹ
إ Excel VBA ץߥ(X_X;

Option Explicit

Sub إˡ()

Dim a As Integer, i As Integer, u As Integer, e As Integer, kosuu As Integer

With Worksheets("sheet1")

kosuu = 0

For a = 1 To 14
For i = 1 To 14
For u = 1 To 14
For e = 1 To 14

If (((a < i) And (i < u) And (u < e)) And (a + e = i + u)) Then kosuu = kosuu + 1

Next e, u, i, a

.Range("A1").Value = kosuu

End With

End Sub
47ʶ 23:25:52 27135
uchinyan
#27133
([i=1,n] xi)^2 = [i=1,n] (xi)^2 + 2 * [1 <= i < j <= n] xi * xj
ʤΤǡ
2 * P 2 * [1 <= i < j <= n] xi * xj = ([i=1,n] xi)^2 - [i=1,n] (xi)^2
դϡxi = -1 or 0 or 1 ΤȤϡ
([i=1,n] xi)^2 = 0 and [i=1,n] (xi)^2 = n
ΤȤǾǤ
n ΤȤ㤨Сx1 = 1, x2 = -1, ..., x_(n-1) = 1, x_n = -1 Ǽ¸ǽǡ2 * Pmin = - n, Pmin = - n/2 Ǥ
n ΤȤϡǰʤ顢ϤǤޤ
2 * P ʤΤǡĤ줿 - n + 1 ͤȡ
㤨Сx1 = 1, x2 = -1, ..., x_(n-2) = 1, x_(n-1) = -1, x_n = 1 Ǽ¸ǽǡPmin = - (n-1)/2 Ǥ
ǡޤȤȡ[ ] ̾ΥεȤơ
Pmin = - [n/2]
Ȥʤ褦Ǥ
βˡȡ0 ȤäƤʤǤ͡
ɤְäƤΤ
ͥνȡ 48ڡ 9:06:09 MAIL:uchi@sco.bekkoame.ne.jp 27136
⡼ޥ
#27136 uchinyan󡢤錄Ʊ

-1ο
0ο
1οȤ롣
¤ϡ
xC2+zC2-x*z=(x(x-1)+z(z-1))/2-xz
=1/2(x^2-x(2z+1)+z^2-z)
=1/2((x-(z+1/2))^2+z^2-z-(z+1/2)^2)
=1/2((x-(z+1/2))^2-2z-1/4)
Ĥޤꡢx=z 뤤ϡx=z+1 ΤȤ¤ϡ줾졢-z ǾȤʤ롣
x+y+z=n ʤΤǡy=0 ΤȤͤơ
2z=n ΤȤĤޤꡢn λ-n /2
2z+1=n ΤȤĤޤꡢnλ(-n+1)/2 줾ǾȤʤ롪

0ʤȤǾˤʤ뤳ȤϤǸޤ͡
48ڡ 14:04:11 MAIL:kennji72001@yahoo.co.jp 27137

ʤ󡡻ƱȤCǤޤ
ϣޤǡϣޤǡϣޤǤȤޤ
ߤޤ󡡾̤Ǥ
48ڡ 15:02:11 27138
uchinyan
#27137
Ϥ0 פʤ褦Ǥ
Ȥǡ n(n-1)/2 ǤΤǤ礦

ȡĤꤷĺƤФʤΤǡޤˤϡɤǤ礦
ȤϡWebǸΤǤ(1)(3)­ƣdzä褦ʡäȻפޤ
򸵤ˡꤷƤߤޤ

ꡧ(դΤˤ뤿˾Ѥޤ)
0 ʾ 100 ʲοͤޤͤϰϤˤ롢
(1) ʬ줬 3 Ǥʬ2/3 Ȥ 10/3 ȤǤιפƤ
(2) ʬ줬 12 ǤʬιפƤ
⤷ǽʤСϰϤ0 ʾ a b Ф a ʾ b ʲȤơͤϰϤˤ롢
(3) ʬ줬ǿ p ǤʬιפƤ
(4) ʬ줬 1 Ǥʤ c ǤʬιפƤ

(1)(2)ϡȻפޤäƤߤСϸĤǤ礦
(4)ϡ뤳ȤΤʤȡ񤭲Τ񤷤⤷ޤ󤬡ˡηǼĤˤʤäȤޤ

(1)(2)դϡβˤäꤷơ
ͥνȡ 49 11:33:11 MAIL:uchi@sco.bekkoame.ne.jp 27140
⡼ޥ
#27140
ꤢ꤬Ȥޡ
ͤƤߤޤ


˦(1~100)-(3*(1~33))/3=(100*101-3*33*34)/6=6734/6
=3267/3=1089
12=2^2*3 顢2,3dzΤСˤϡ4,6,12dzΤƤ롣
ʬ줬3ΤΤϵƤΤǡ
ʬ줬2ΤΡΤȡ
줾졢(1~100)-(2*(1~50)=(100*101-2*50*51)/2=2500
(1~100)-(6*(1~16))=(100*101-6*16*17)/2=4234

Ĥޤꡢ3267-2500+4234=5001 ʤΤǡΤϡ5001/12=1667/4
((a~b)-p*((1~[b/p])-((1~[a/p]))/p
ǤΤʡ
ˤϡʤ䤳ʤꤽ
48ڡ 19:24:15 MAIL:kennji72001@yahoo.co.jp 27141
uchinyan
#27141
󡢻ǰʤ㤦褦ǤäȤ줤ͤˤʤޤ
ޤ0 1 ξ硢0 2 ξ硢0 10 ξʤɤͤƤߤƤ
ͥνȡ 48ڡ 21:18:02 MAIL:uchi@sco.bekkoame.ne.jp 27142
⡼ޥ
#27142
ʬ줬3Ǥ褦ʵʬǡͤ0100äƤȤǤ͡
錄ϡˡʬҤ1100ȻפäƤޤ

ʤ顢
ˤϡ(1~300)-3*(1~100)=(300*301-3*100*101)/2=30000
顢Τϡ30000/3=10000
ˤϡ2*(1~600)=2*600*601/2=1200*601/2
3*(1~400)=3*400*401/2=1200*401/2
6*(1~200)=6*200*201/2=1200*201/2
(1~1200)-1200*601/2-1200*401/2+1200*201/2=1200(1201-601-401+201)/2=1200*400/2=240000
ͤϡ240000/12=20000
ʴǤ礦ʳΤ
ʬǿĤʤ10000mĤʤ顢m*10000 ʡ

3ˡ4ˤϡ⤦äȹͤƸʬн񤭹ߤƤޡ
48ڡ 23:08:14 MAIL:kennji72001@yahoo.co.jp 27143
uchinyan
#27143
ʬ줬3Ǥ褦ʵʬǡͤ0100äƤȤǤ͡
ϤΤĤǤ­餺äʡ
(1), (2) ȤˡǤ
פϡ
(1)ϡ0 1 1/3 + 2/3 = 11 2 4/3 + 5/3 = (1 + 1/3) + (1 + 2/3) = 2 + (1/3 + 2/3)ȤʤΤǡ
ϡ򤦤ޤ­ФǤ
(2)Ʊͤǡ0 1 1/12 + 5/12 + 7/12 + 11/12 = 2
1 2 13/12 + 17/12 + 19/12 + 23/12 = (1 + 1/12) + (1 + 5/12) + (1 + 7/12 + (1 + 11/12) = 4 + (1/12 + 5/12 + 7/12 + 11/12)
ݥȤǤ͡
ϡ(3), (4)ΥҥȤˤʤäƤޤ ^^;
ͥνȡ 49 0:06:28 MAIL:uchi@sco.bekkoame.ne.jp 27144

uchinyan
(1) 10000
(2) 20000
(3) 5000(P1)
(4) 1ʾCʲǡCȸߤǤʿ(1ޤ)θĿ¤Ȥ
4950*100*/C
ˤʤꤽǤŪʸΤʡ
49 1:26:38 27145
uchinyan
#27145
󡢲꤬Ȥޤ
(1), (2)ϡ
(3)ϡa = 0, b = 100 ξǤ͡ΰ̣ǡ򡣰̤ a, b ξͤƤߤƤ
(4)Ǥm n c ǽ񤱤ޤ¤ϡä񤷤Ǥn ׻Ǥޤ
[äɲ]
ַ׻ǤפȤΤϡc ͿȤ n ׻Ǥˡ롢Ȥ̣Ǥ
ǡn c δؿn = (c) Ǥǰʤ顢n c ľܤ˽񤭲ȤϤǤʤ褦Ǥ
äȤ⡢c ѷơΤȤ˸ΤȤС񤯤ȤǤޤ^^;
äơϡnĤޤ (c) c ȤɽǤСOKǤ
[ɲý]
470βԷǼġλν񤭹ߤդ˥ҥȤޤ
ǽʤС(̤ a, b Ǥ⡢)󥸤ƤߤƤ
ͥνȡ 49 11:25:29 MAIL:uchi@sco.bekkoame.ne.jp 27146

uchinyan
(3) a,b ξϡ
(a+b)*(-a+b)*(p-1)/2
Ǥ礦
(4) ϡΤȤû֤Ǥ(֤򤫤Ƥ⡩)򤱤ˤޤ
ˤʤȤuchinyanν񤭹ߤɤǹͤƤߤޤ͡
򤢤꤬Ȥޤָ˹ԤäƤޡ
49 10:21:47 27147
uchinyan
#27147
(3)Ǥ
(4)ϡʤҥȤȤơν񤭹#27146ɲʬ(3)μʳĥˤʤäƤޤ
ͥνȡ 49 11:29:09 MAIL:uchi@sco.bekkoame.ne.jp 27148

uchinyan

(4) ̤򸫤ƤӤäꡪʤ˴ñʼɤΤǤ礦
(ab)*(ab)*(c)/2
ˤʤޤ

ν񤭹ߤθ狼ʤơäɤޤ
uchinyan󤢤꤬Ȥޤ

410ʷ 17:46:10 27149
⡼ޥ
#27140 0 ͤʤȤʤǤ͡

3) (((0~pb)-(0~pa)+pa)-p((0~b)-(0~a)+a)/p
=((pb(pb+1)-pa(pa+1)-p(b(b+1)-a(a+1))/2p
=(p(b^2-a^2)-(b^2-a^2))/2
=(p-1)(b^2-a^2)/2

Ǥ⡢4) ϡɤǤ褯ʬޤ󡣡(^^;)
49 14:45:52 MAIL:kennji72001@yahoo.co.jp 27151
uchinyan
#27149
(ab)*(ab)*(c)/2
ϤǤ줤ʷ̤Ǥ礦 ^^/
ָϡɤǤ

#27151
(3)ϡǤ

(4)ϡ⡼ޥ󤵤Τȡĥ饤Ȼפޤ
#27144ȯŸ봶ǹͤƤߤƤ
c = 12 ΤȤ
0 1 1/12 + 5/12 + 7/12 + 11/12 = 2
1 2 13/12 + 17/12 + 19/12 + 23/12 = (1 + 1/12) + (1 + 5/12) + (1 + 7/12 + (1 + 11/12) = 4 + (1/12 + 5/12 + 7/12 + 11/12)

Ǥ͡
ƶ֤Ƿ׻˸ʬθĿc ȸߤǤ c ʲμθĿ (c) ˡʬҤ鼫ˡʤޤ
ޤc ȸߤǤ c ʲμ¤ȤΤϡ470˷ǼĤǵΤǤ1/2 * c * (c) ˤʤޤ
#25898, #25903, #25908 դ
塢[i=a,b-1]{i} = [i=1,b-1]{i} - [i=1,a-1]{i} 򤦤ޤȤäƤߤƤ
(٤Ȥȡa = 0,1, b = 0,1 ǤϾέμϻȤޤ󡣤̤ưפʬȻפޤ)

ʤߤˡc = p ΤȤ(p) = p-1 ˤʤäơ(4)(3)μʳĥǤ뤳ȤʬȻפޤ
ͥνȡ 49 16:04:42 MAIL:uchi@sco.bekkoame.ne.jp 27152
⡼ޥ
#27152
ҥȤ򤽤Τޤ޻Ȥäơ
ˤϡ
0~b ΤȤ(0~b)*(c)+2*1/2*c*(c)/c=((0~b)+1)*(c)
0~a ΤȤ((0~a)+1)*(c)
Ĥޤꡢ
弰=((0~b)-(0~a))*(c)
=((b(b+1)-a(a+1))*(c)/2
=(b-a)(b+a-1)*(c)/2
ɤä
49 18:23:32 MAIL:kennji72001@yahoo.co.jp 27153
ERĹ
ʤΤϤɤǤ礦

aʾbʲμqapbǿpȤ롣
pʬ,qʬҤȤʬ q/p ȤȤǤˤǴʬιפ
Ƥ

49 18:47:32 27154
uchinyan
#27153
դƹͤƤ­ϰϤ̯˰㤤ޤޤ1/2 * c * (c) ιϡ(b-a) ĤĤϤǤ
c = 12 ΤȤϡ
0 1 1/12 + 5/12 + 7/12 + 11/12 = 2
1 2 13/12 + 17/12 + 19/12 + 23/12 = ... = 4 + (1/12 + 5/12 + 7/12 + 11/12)

Ǥ̤͡ c Ǥϡ
0 1 ǡ0 * (c) + 1/2 * c * (c) * 1/c
1 2 ǡ1 * (c) + 1/2 * c * (c) * 1/c

a-1 a ǡ(a-1) * (c) + 1/2 * c * (c) * 1/c
a a+1 ǡa * (c) + 1/2 * c * (c) * 1/c

b-1 b ǡ(b-1) * (c) + 1/2 * c * (c) * 1/c
ΥϥǤ
ͥνȡ 49 22:02:05 MAIL:uchi@sco.bekkoame.ne.jp 27155
ERĹ
ʤΤϤɤǤ礦

aʾbʲμqapbǿpȤ롣
pʬ,qʬҤȤʬ q/p ȤȤǤˤǴʬιפ
Ƥ

49 18:54:57 27156
ERĹ
ηǼĤǤդƤޤΤǤꤤޤm(__)m
http://8915.teacup.com/tacky_bingo/bbs
49 18:55:59 27157
ERĹ
ηǼĤǤդƤޤΤǤꤤޤm(__)m
http://8915.teacup.com/tacky_bingo/bbs
49 18:56:21 27158
⡼ޥ
#27155
uchinyanء
äȵ뤳ȤǤޤ


0~b ΤȤ(0~(b-1))*(c)+b*1/2*c*(c)/c=((0~(b-1))+b)*(c)
0~a ΤȤ((0~(a-1))+a)*(c)
Ĥޤꡢ
弰=((0~(b-1))-(0~(a-1)+(b-a)*1/2)*(c)
=((b-1)b-(a-1)a+(b-a))*(c)/2
=(b^2-a^2)*(c)/2

Ǥ񤷤äʤ錄ˤ (^^;)
49 20:19:38 MAIL:kennji72001@yahoo.co.jp 27159
⡼ޥ
#27154
ERĹء
ͤƤߤޤ

((a~(p-1))+((p~b)-p(1~[b/p]))/p
=((a+p-1)(p-a)+(p+b)(b-p+1)-p(1+[b/p])([b/p]))/2p
=((b+a)(b-a+1)-p(1+[b/p])([b/p]))/2p

ޤ꤭줤Ǥʤ顢ޤְäƤ뤫ʤ

PS:ERĹΤŦǵդޤǸμ+-ľޤ(OrZ)
49 21:17:12 MAIL:kennji72001@yahoo.co.jp 27160
ţĹ
#27160
Ǥ(^O^)/
Ǥ(^_-)-
49 20:59:00 27161
ERĹ
#27160
ǤֺǸμ˰쥫椬㤦꤬ޤ(^^
49 21:02:27 27162
⡼ޥ
#27162
áˡľȤޤ
Ǥ褫äǤ͡
ۥ(^^)
49 21:18:34 MAIL:kennji72001@yahoo.co.jp 27163
uchinyan
ERĹǤp ϸꡢĤޤꡢp ˤĤƤ¤ϼʤƤȤդʤΤǤ
ȡa, b ˤäƤϡp ¸ߤʤ⤢ޤ͡
ͥνȡ 49 22:00:09 MAIL:uchi@sco.bekkoame.ne.jp 27164
⡼ޥ
#27164
錄ǽ顢a~b δ֤ˤ뤹٤Ƥ p ˴ؤƤȻפޤ
ñ˸ꤷƹͤޤ
p ⤢ΤȤơ

b ϾʤȤ⡢2a ʾʤɬĤ p ¸ߤ褦Ǥ͡
ϲοؼԥǥǤξߤȤޤ褯ʬޤǤ(^^;)
49 22:24:32 MAIL:kennji72001@yahoo.co.jp 27165
ERĹ
⡼ޥ󤵤λ򤷤ޤ(^^
pϸǤ͡ȤŦ̤ꡢabϰϤμˤäƤ¸ߤʤǤ(`) Ťä(>_<)
49 23:01:14 27166
ERĹ
Ϥäꤷʤۣǿޤm(__)m
49 23:06:26 27167
uchinyan
#27159
ʤäꤷƤޤ
(b^2-a^2)*(c)/2
ǤǤȤޤ ^^/
Ǥ񤷤äʤ錄ˤ (^^;)
(4)ϡͽμʤ񤷤Ȼפޤ
ʤˤ񤭤ޤ(c)ϡ顼ؿȸƤФͭ̾ʴؿǤ
470λν񤭹ߤΥ䡢WebĴ٤ĺСŪʷ׻λʬȻפޤ
ΤäƤȡǤ衣

#27165
b ϾʤȤ⡢2a ʾʤɬĤ p ¸ߤ褦Ǥ͡
Сޤ͡
ǰʤ顢ϾɤȤϤʤΤǤ
ͥνȡ 410ʷ 15:36:25 MAIL:uchi@sco.bekkoame.ne.jp 27168

c ȸߤǤ c ʲμ¤1/2 * c * (c) ˤʤȤϡ
ȤƤԻ׵Ĥ˴ޤǰ3ʲξϡ٥ޤ򤫤ꤷǼޤ
ȤϸʤΤǤ礦츫Ի׵ĤǤ⡢褯褯ͤȤʤۤɤǼǤ
ƱȻפޤΡʤۤɡȻפȤβǤ
ָϡζǤʤ껶äƤޤοͽФǤ
ָ͸ȤǤڤʿͤ򸫤ΤڤäǤ衣

410ʷ 18:10:39 27169

ʤ162ȿƵޤǤ
410ʷ 18:58:07 27170
uchinyan
äơ

#27128­
ʤޤǤηǼĤε餫Ȼפޤ1 n ξˤϡ
f(n) = f(n-2) + (n-2)C2 for n >= 6, f(4) = 2C2 = 1, f(5) = 3C2 = 3
ˤʤ褦Ǥ͡
#27124(ˡ3)(ˡ4)η̤䤹С餫פʤΤǤʥ֤˹ͤȤǤʤǤ
ǡʥ֤˹ͤ#27124(ˡ1)˽सˡǡ(ˡ7)ȤơƤޤ礦
ʤ§ΥݥȤϡ#27124(ˡ1)Ʊˤʤޤ

(ˡ7)
1 n ޤǤȤơΤȤμФ f(n) ̤Ȥޤ
ϡ1 n-1 ˡn ɲäȹͤޤ
餫ˡ n-1 ʲξˤ f(n-1) ̤ʤΤǡ˹ͤʤФʤʤΤϡ = n ξǤ
ǡܥᥢn ˴ؤơʬƤߤޤ
ºݤˤäƤߤȡn ǡʬƹͤɬפ뤳Ȥʬޤ
n ξ
(1) = 1 ξ硧ܥᥢܥn+1 Ǥ
2 n/2 n-1 (n+2)/2 ǽǤäơ(n-2)/2 ̤ꡣ
(2) = 2 ξ硧ܥᥢܥn+2 Ǥ
3 n/2 n-1 (n+4)/2 ǽǤäơ(n-4)/2 ̤ꡣ
(3) = 3 ξ硧ܥᥢܥn+3 Ǥ
4 (n+2)/2 n-1 (n+4)/2 ǽǤäơ(n-4)/2 ̤ꡣ
(4) = 4 ξ硧ܥᥢܥn+4 Ǥ
5 (n+2)/2 n (n+6)/2 ǽǤäơ(n-6)/2 ̤ꡣ

(n-6) = n-6 ξ硧ܥᥢܥ2n-6 Ǥ
n-5 n-4 n-1 n-2 ǽǤäơ2 ̤ꡣ
(n-5) = n-5 ξ硧ܥᥢܥ2n-5 Ǥ
n-4 n-3 n-1 n-2 ǽǤäơ2 ̤ꡣ
(n-4) = n-4 ξ硧ܥᥢܥ2n-4 Ǥ
n-3 n-1 ǽǤäơ1 ̤ꡣ
(n-3) = n-3 ξ硧ܥᥢܥ2n-3 Ǥ
n-2 n-1 ǽǤäơ1 ̤ꡣ
ǡ٤ƤǤɡɲäΤϡ
2 * (1 + 2 + ... + (n-4)/2) + (n-2)/2 = 2 + 4 + ... + (n-4) + (n-2)/2 ̤
Ǥ
n ξ
(1) = 1 ξ硧ܥᥢܥn+1 Ǥ
2 (n-1)/2 n-1 (n+3)/2 ǽǤäơ(n-3)/2 ̤ꡣ
(2) = 2 ξ硧ܥᥢܥn+2 Ǥ
3 (n+1)/2 n-1 (n+3)/2 ǽǤäơ(n-3)/2 ̤ꡣ
(3) = 3 ξ硧ܥᥢܥn+3 Ǥ
4 (n+1)/2 n-1 (n+5)/2 ǽǤäơ(n-5)/2 ̤ꡣ
(4) = 4 ξ硧ܥᥢܥn+4 Ǥ
5 (n+3)/2 n-1 (n+5)/2 ǽǤäơ(n-5)/2 ̤ꡣ

(n-6) = n-6 ξ硧ܥᥢܥ2n-6 Ǥ
n-5 n-4 n-1 n-2 ǽǤäơ2 ̤ꡣ
(n-5) = n-5 ξ硧ܥᥢܥ2n-5 Ǥ
n-4 n-3 n-1 n-2 ǽǤäơ2 ̤ꡣ
(n-4) = n-4 ξ硧ܥᥢܥ2n-4 Ǥ
n-3 n-1 ǽǤäơ1 ̤ꡣ
(n-3) = n-3 ξ硧ܥᥢܥ2n-3 Ǥ
n-2 n-1 ǽǤäơ1 ̤ꡣ
ǡ٤ƤǤɡɲäΤϡ
2 * (1 + 2 + ... + (n-5)/2 + (n-3)/2) = 2 + 4 + ... + (n-5) + (n-3) ̤
Ǥ
ޤȤȡ
n ΤȤ
f(n) = f(n-1) + 2 + 4 + ... + (n-4) + (n-2)/2
n ΤȤ
f(n) = f(n-1) + 2 + 4 + ... + (n-5) + (n-3)
ͤȤơf(4) = 1 Ǥ
ȤƤϤǽʬǤˤǤѷǤޤäȤ⡢̤ΤʤȤȤƤⵤդޤ (^^;
n ΤȤn-1 ϴʤΤǡ
f(n) = f(n-1) + 2 + 4 + ... + (n-4) + (n-2)/2
= f(n-2) + 2 + 4 + ... + ((n-1)-5) + ((n-1)-3) + 2 + 4 + ... + (n-4) + (n-2)/2
= f(n-2) + 2 + 4 + ...(ब (n-4)/2 Ĥ롪)... + (n-6) + (n-4) + 2 + 4 + ... + (n-4) + (n-2)/2
= f(n-2) + (2 - 1) + (4 - 1) + ... + ((n-6) - 1) + ((n-4) - 1) + (n-4)/2 + 2 + 4 + ... + (n-4) + (n-2)/2
= f(n-2) + 1 + 3 + ... + (n-7) + (n-5) + 2 + 4 + ... + (n-4) + (n-2)/2 + (n-4)/2
= f(n-2) + 1 + 3 + ... + (n-7) + (n-5) + 2 + 4 + ... + (n-6) + (n-4) + (n-3)
= f(n-2) + 1 + 2 + 3 + ... + (n-5) + (n-4) + (n-3)
= f(n-2) + (n-2)(n-3)/2
= f(n-2) + (n-2)C2
Ʊͤη׻ϡn ξǤǤơɡ٤Ƥ n Фơ
f(n) = f(n-2) + (n-2)C2
ޤʤξˤϡͤȤƤϡf(4) = 1, f(5) = 3 ɬפˤʤޤ
ͥνȡ 411ʲС 13:48:15 MAIL:uchi@sco.bekkoame.ne.jp 27171
issei
ʤȹͤƤޤ
412ʿ 16:02:07 27172