Ȥ
basic

LET s=0
FOR a=1 TO 14
FOR b=a+1 TO 14
FOR c=b+1 TO 14
FOR d=c+1 TO 14
IF a+d=b+c THEN LET s=s+1
NEXT d
NEXT c
NEXT b
NEXT a
PRINT s
END

f9161()
927ڡ 0:06:19 MAIL:fttnm528@ybb.ne.jp 39827

ǽ21,21,31,72,311,12ȷƲ̤ꤢ뤫׻ȡ11+9+7++1+10+8++2++3+1+2+1=161(̤)Ȥʤ

29%ȯǤƥƥ󥷥夬äƤ
ϵ塡 927ڡ 0:23:15 39828

¤Ϻ㤬ǹ⤬Σѥ󡣣ˤʤΤϡʣˡʣˤΣ̤ꡢˤʤΤʣˡʣˤʤΤǣ̤ꡢˤʤΤϡʣˡʣˡʣˤʤΤǣãǣ̤ꡢʣˡʣˡʣˤʤΤǣ̤ꡢդ¤ȣοоΤˤʤͽۤǤΤǡʣܣܣܣܣܣܣܣܣܣˡߣܣᣱȤʤޤ
927ڡ 0:29:22 39829

Ǥãǣ̤ꡣ⡦̤Ǥ
927ڡ 0:31:16 39830
ͣ.ǥ
㤨Сʥ,ˤ1,8ˤΤ褦˺Ȥϡ7̤ꡣΤȤ֤(,)Ȥϡ3̤ꤺġ7*3̤
Τ褦ˡ313ޤǤΤȤȤοФ
(11*1)(10*1)(9*2)(8*2)(7*3)(6*3)(5*4)(4*4)(3*5)(2*5)(1*6)161
1,2ʬФƤȤȤϡäȥޡȤʲˡΤǤ礦͡
927ڡ 8:22:03 39831
⡼ޥ
ξü¡᤽¦......
Ϣ³...14Ĥ1̤ꡣ
134ĤΤΤ...оΤޤǤ...^^;

14...7C2=21
13~4...
2*2*(6C2+5C2+4C2+3C2+2C2)=4*(15+10+6+3+1)=140
21+40=161

äȾꤤˡꤽ...^^;
927ڡ 0:39:41 39832
ߤ
ȣĤκλȣĤ̤ߣ¤ȣä̤᣶̤
ȣĤκλȣĤ̤ߣ¤ȣä̤ᣱ̤
ȣĤκλȣĤ̤ߣ¤ȣä̤ᣱ̤
ʲƱͤˡ
ȣĤκλȣĤ̤ߣ¤ȣä̤ᣱ̤
ޤǷ׻Ƥ

ɡܣܣܣܣܣܣܣܣܣܣᣱ̤ꡣ
927ڡ 1:00:32 39833
HirotakaUEDA
ۡȿ夲ơΥѥɤǤȤϿ¬Фޤ
Ҥ̤Ȥ߹碌­Τ˺ʤäǤ͡
927ڡ 2:53:41 39834
ϥ饮㡼ƥ
Ϥ褦ޤץǤ
927ڡ 6:16:04 HomePage:湩ؤ˥39835
(Keigei)
ɤ ȤС
ΤȤ n(n2)(2n5)/24ΤȤ (n1)(n3)(2n1)/24
ˤʤޤ
927ڡ 7:51:15 39836
abcba@baLLjugglermoka
#39836

Τˤʤޤ͡¡ʿ¤θȤдñ˾Ǥޤ
927ڡ 9:03:20 39837
???
99basic1ԥץǡ
1 FOR A=1 TO 14:FOR B=A+1 TO 14:FOR C=B+1 TO 14:D=B+C-A:K=K-(C<D AND D<=14):NEXT:NEXT:NEXT:PRINT K
927ڡ 11:00:08 39838
δ
-ᥨ-ȤƤޤ¤ؤ
12C2+10C2+8C2+6C2+4C2+2C2161
ǤϤʤǤ
927ڡ 11:13:33 39839

ȥκξ硡ȥκξ硡ȥκξ
̤ꡡ̤ꡡ̤
̤ꡡ̤ꡡ̤

̤ꡡ̤ꡡ̤

ȥκξ
̤
(11+10+9+8+7+6+5+4+3+2+1)+(9+8+7+6+5+4+3+2+1)+(7+6+5+4+3+2+1)
(3+2+1)+1=161
Ȥޤ
927ڡ 11:29:06 39840

1Ȥκ4ξ20̤ȤơĤǺǤޤ
ȥκ3ξ硡11̤
ȥκ4ξ硡10̤
ȥκ5ξ硡18̤
ȥκ6ξ硡16̤
ȥκ7ξ硡21̤
ȥκ8ξ硡18̤
ȥκ9ξ硡20̤
ȥκ10ξ硡16̤
ȥκ11ξ硡15̤
ȥκ12ξ硡10̤
ȥκ13ξ硡6̤

ס161̤
927ڡ 11:51:11 HomePage:39841

󤬤줿ˤ狼ˤʤäƤޤä

11+10+9+8+7+6+5+4+3+2+1ȥκǥͤ򣱡9+8+7+6+5+4+3+2+1ȥκǥͤ򣱡
7+6+5+4+3+2+1ȥκǥͤ򣱡
5+4+3+2+1ȥκǥͤ򣱡
3+2+1ȥκǥͤ򣱡
1ȥκ

ס̤
927ڡ 11:51:46 39842

嵐ޤ󡦡

11+10+9+8+7+6+5+4+3+2+1ȥκǥͤ򣱡
9+8+7+6+5+4+3+2+1ȥκǥͤ򣱡
7+6+5+4+3+2+1ȥκǥͤ򣱡
5+4+3+2+1ȥκǥͤ򣱡
3+2+1ȥκǥͤ򣱡
1ȥκ

ס̤
927ڡ 11:54:19 39843
uchinyan
Ϥˤϡơϡ
ϡƻ˿вȤʤǤޤοĤꤽǤ
äȴñʲˡϤΤʡ

(ˡ1)
= 1 ξ硤 = 4 14 Ф 11223344556 ̤ǡ36 ̤ꡣ
= 2 ξ硤 = 5 14 Ф 1122334455 ̤ǡ30 ̤ꡣ
= 3 ξ硤 = 6 14 Ф 112233445 ̤ǡ25 ̤ꡣ
= 4 ξ硤 = 7 14 Ф 11223344 ̤ǡ20 ̤ꡣ
= 5 ξ硤 = 8 14 Ф 1122334 ̤ǡ16 ̤ꡣ
= 6 ξ硤 = 9 14 Ф 112233 ̤ǡ12 ̤ꡣ
= 7 ξ硤 = 10 14 Ф 11223 ̤ǡ9 ̤ꡣ
= 8 ξ硤 = 11 14 Ф 1122 ̤ǡ6 ̤ꡣ
= 9 ξ硤 = 12 14 Ф 112 ̤ǡ4 ̤ꡣ
= 10 ξ硤 = 13 14 Ф 11 ̤ǡ2 ̤ꡣ
= 11 ξ硤 = 14 Ф 1 ̤ǡ1 ̤ꡣ
ʾǤ٤ƤʤΤǡפ 161 ̤ꡣ

(ˡ2)
+ = + - = - ȸС
- = 1 ξ硤 = 1 11 Ф 1110987654321 ̤ǡ66 ̤ꡣ
- = 2 ξ硤 = 1 9 Ф 987654321 ̤ǡ45 ̤ꡣ
- = 3 ξ硤 = 1 7 Ф 7654321 ̤ǡ28 ̤ꡣ
- = 4 ξ硤 = 1 5 Ф 54321 ̤ǡ15 ̤ꡣ
- = 5 ξ硤 = 1 3 Ф 321 ̤ǡ6 ̤ꡣ
- = 6 ξ硤 = 1 Ф 1 ̤ǡ1 ̤ꡣ
ʾǤ٤ƤʤΤǡפ 161 ̤ꡣ

ϡ - = ξϡ + 1 14 - 14 - * 2 ĤΤΤ 2 ǡ
򥤡礭򥦡Ȥ (14 - * 2)C2 ̤ꡤȤͤޤ
С
12C2 + 10C2 + 8C2 + 6C2 + 4C2 + 2C2 = 66 + 45 + 28 + 16 + 6 + 1 = 161 ̤
ȤƤ⤤Ǥ͡

ޤǽڤʵ⤹뤱ɡ

(ˡ3)
- ʬहС
- = 3 ξ硤 = 1 11 Ф - = 1 11 * 1 = 11 ̤ꡣ
- = 4 ξ硤 = 1 10 Ф - = 1 10 * 1 = 10 ̤ꡣ
- = 5 ξ硤 = 1 9 Ф - = 12 9 * 2 = 18 ̤ꡣ
- = 6 ξ硤 = 1 8 Ф - = 12 8 * 2 = 16 ̤ꡣ
- = 7 ξ硤 = 1 7 Ф - = 123 7 * 3 = 21 ̤ꡣ
- = 8 ξ硤 = 1 6 Ф - = 123 6 * 3 = 18 ̤ꡣ
- = 9 ξ硤 = 1 5 Ф - = 1234 5 * 4 = 20 ̤ꡣ
- = 10 ξ硤 = 1 4 Ф - = 1234 4 * 4 = 16 ̤ꡣ
- = 11 ξ硤 = 1 3 Ф - = 12345 3 * 5 = 15 ̤ꡣ
- = 12 ξ硤 = 1 2 Ф - = 12345 2 * 5 = 10 ̤ꡣ
- = 13 ξ硤 = 1 Ф - = 123456 1 * 6 = 6 ̤ꡣ
ʾǤ٤ƤʤΤǡפ 161 ̤ꡣ

Ǥ(ˡ2)ֳڤʤ
§ΤʤΤ 1 n ΰ̲ưפǤ͡

n = ξ
[i=1,n/2-1]{[j=1,n-2i-1}{j}}
= [i=1,n/2-1]{(n-2i-1)(n-2i)/2}
= (n(n-1) * (n/2-1) - 2(2n-1) * (n/2-1)(n/2)/2 + 4 * (n/2-1)(n/2)(2(n/2)-1)/6)/2
= (n(n-1)(n-2)/2 - n(n-2)(2n-1)/4 + n(n-1)(n-2)/6)/2
= (6n(n-1)(n-2) - 3n(n-2)(2n-1) + 2n(n-1)(n-2))/24
= n(n-2)(2n-5)/24 ̤

n = ξ
[i=1,(n-1)/2-1]{[j=1,n-2i-1}{j}}
= [i=1,(n-1)/2-1]{(n-2i-1)(n-2i)/2}
= (n(n-1) * ((n-1)/2-1) - 2(2n-1) * ((n-1)/2-1)((n-1)/2)/2 + 4 * ((n-1)/2-1)((n-1)/2)(2((n-1)/2)-1)/6)/2
= (n(n-1)(n-3)/2 - (n-1)(n-3)(2n-1)/4 + (n-1)(n-2)(n-3)/6)/2
= (6n(n-1)(n-3) - 3(n-1)(n-3)(2n-1) + 2(n-1)(n-2)(n-3))/24
= (n-1)(n-3)(2n-1)/24 ̤
ͥνȡ 101ʷ 14:22:56 39844
uchinyan
ǼĤɤߤޤ
󡤷ɤϿ夲Τ褦Ǥ
ʤƱƼԤƤƱΤϡ§ǽƤ򵭺ܤƤޤ

θɲä줿#39850#39857ʤɤñʤ夲ǤϤʤ̲ưפʲˡΤ褦Ǥ

#39828
ʬषƿƤˡ

#39828
+ ʬषƿƤˡ

#39831#39833#39841#39844(ˡ3)
- ʬषƿƤˡ

#39839#39840#39844(ˡ2)
- ʬषƿƤˡ

#39844(ˡ1)
ʬषƿƤˡ

#39832
ξü¡᤽¦......
Ϣ³...14Ĥ1̤ꡣ
134ĤΤΤ...оΤޤǤ...^^;
ʤɤ˹ͤˡǽιԤǤθϡʤ褯ʬ餺 (^^;

ȤʤΤʡ

+ = + ( + )/2 = ( + )/2
ĤޤꡤͤĤο򡤺ǾȺʿѤȴ֤ĤʿѤ褦֤Ȥˤʤޤ
ϡʿѤˤͤᡤФƾ礭оΤˤʤ褦֤ȤǤ
ĤޤꡤȾʬο饢ȥӡȥʿѤη᤿ͤˤʤ褦ˤͤоΤ˷뤳Ȥˤʤޤ

ǡ
ʿѤ 7.5 ξ硤1 7 饢ȥ٤ФΤ 7C2 ̤ꡣ
ʿѤ 7 8 ξ硤1 6 2 7 饢ȥ٤ФΤ 6C2 * 2 ̤ꡣ
ʿѤ 6.5 8.5 ξ硤1 6 3 8 饢ȥ٤ФΤ 6C2 * 2 ̤ꡣ
ʿѤ 6 9 ξ硤1 5 4 8 饢ȥ٤ФΤ 5C2 * 2 ̤ꡣ
ʿѤ 5.5 9.5 ξ硤1 5 5 9 饢ȥ٤ФΤ 5C2 * 2 ̤ꡣ
ʿѤ 5 10 ξ硤1 4 6 9 饢ȥ٤ФΤ 4C2 * 2 ̤ꡣ
ʿѤ 4.5 10.5 ξ硤1 4 7 10 饢ȥ٤ФΤ 4C2 * 2 ̤ꡣ
ʿѤ 4 11 ξ硤1 3 8 10 饢ȥ٤ФΤ 3C2 * 2 ̤ꡣ
ʿѤ 3.5 11.5 ξ硤1 3 9 11 饢ȥ٤ФΤ 3C2 * 2 ̤ꡣ
ʿѤ 3 12 ξ硤1 2 10 11 饢ȥ٤ФΤ 2C2 * 2 ̤ꡣ
ʿѤ 2.5 12.5 ξ硤1 2 11 12 饢ȥ٤ФΤ 2C2 * 2 ̤ꡣ
ʾǤ٤ƤʤΤǡ
7C2 + (6C2 + 5C2 + 4C2 + 3C2 + 2C2) * 2 * 2 = 21 + (15 + 10 + 6 + 3 + 1) * 4 = 21 + 140 = 161 ̤
ˤʤޤ

ʤβˡϤ˲ɤǽʤ褦Ǥ#39857

#39850
+ = + = + - ȸȡ
٤ ޤΤǡ 1 14 ٤ФǤ
ˤ = = ( + )/2 ȤʤΤޤΤǤ > ʤΤȾʬˤ롤ȹͤˡ

#39834
ۡȿ夲ơΥѥɤǤȤϿ¬Фޤ
Ȥˡܺ٤

#39827#39835#39838
ץˤˡ

ʤ

#39836
䥫ɤ ȤС
ΤȤ n(n2)(2n5)/24ΤȤ (n1)(n3)(2n1)/24
ˤʤޤ
#39837
Τˤʤޤ͡¡ʿ¤θȤдñ˾Ǥޤ
ϤǤ͡ɬפϰϤǡ#39844κǸ⻲ȤƤߤƤ

θɲä줿#39850#39857ʤɤϡ η׻ʤ˰̲ǽʲˡǤ
ͥνȡ 930 15:59:26 39845
Taro
ɤǻ褦긫Ȼפä裴Ǥ
927ڡ 15:18:52 39846
ޥ
䡢åΤ.....ФƤޤǤߥޥ...m(__)m
iMac 927ڡ 15:40:54 HomePage:֥39847
⡼ޥ
#39845
uchinyan ^^
496丫ޤƱǤͤ...^^;

Τ錄Τ...¤βˡ5ƱͤǤ^^;v...Orz
927ڡ 16:06:11 39848
uchinyan
#39847
䤲䡢åΤ.....ФƤޤǤߥޥ...m(__)m
#39848
uchinyan ^^
496丫ޤƱǤͤ...^^;
ءۥȤƱ դʤäʤ
ޤĹ³ƤΤ顤ޤˤϤʤȤ⤢Ǥ礦



#39848
亣Τ錄Τ...¤βˡ5ƱͤǤ^^;v...Orz
ۤޤƱ פФޤǤ
ǡƱȤʿѤȤäƺƹƤޤޤ (^^;
#39845Ρ#39832ΤȤ⡼ޥ󤵤βˡΤȤ
ͥνȡ 927ڡ 16:47:09 MAIL:uchi@sco.bekkoame.ne.jp 39849
(Keigei)
īϻ֤ʤƽ񤱤ޤǤ#39836βˡǤ
ޤ ֤ȡᥢܥݥ Ƿޤޤ
n3n(n1)(n2)/6 Ǥ
ˤ ᥦ(ܥ)/2 ȤʤΤꡢ
ϡ饢֤饢֤Ȥˤʤ뤫顢
ΤȤϡ2(n/2)22(n/2)(n/21)/2n(n2)/4
ΤȤϡ{(n1)/2}2{(n1)/2}2{(n1)/2}{(n3)/2}/2{(n1)/2}{(n1)/2}/2(n1)^2/4
ơ㥦䥦 Ʊ뤳ȤդС
ΤȤϡ{n(n1)(n2)/6n(n2)/4}/2n(n2)(2n5)/24
ΤȤϡ{n(n1)(n2)/6(n1)^2/4}/2(n1)(n3)(2n1)/24 ˤʤޤ

ʤΤȤ a0 ΤȤ a1 ȤС
{n(n2)a}/4n(n2)/4a/4 顢
ϡ{n(n1)(n2)/6n(n2)/4a/4}/2n(n2)(2n5)/24a/8[n(n2)(2n5)/24] Ǥ

927ڡ 20:58:44 39850
⡼ޥ
#39845
uchinyan ^^
496丫ޤƱǤͤ...^^;

Τ錄Τ...¤βˡ5ƱͤǤ^^;v...Orz
927ڡ 20:13:56 39851
⡼ޥ
......
ʤȤ...^^;
λ狼ޤ...̵뤷Ƥޤ...m(_ _)m
927ڡ 20:16:19 39852
ޤԤ
ޤȤ˽񤭽Фʹ֤Ǥ
927ڡ 21:20:34 39853
ޤ륱
ȥκǾ櫓ƿʤ顢ˡ§򸫤Ĥ
ruby Υ饤ʡ(68ʸ)dzΤޤ
p (1..14).to_a.combination(4).to_a.delete_if{|a,b,c,d|a+d!=b+c}.size
927ڡ 23:06:34 MAIL:take4310@mobile.email.ne.jp 39854
fumio
Ϥ褦ޤʤȤ򤱤ޤϤϤϡ
ǤϤǤϡ
929ڡ 6:42:25 39855
Ф
ܥᥤܥʤΤǥݥᥤݥͤȤƣᣱ
ˤĤƤĤ뤫
ãܣãܣãܣãܣãܣã161
929ڡ 10:21:50 39856
uchinyan
#39850
ʤۤɡϤޤˡǤ͡

ˤϵڤӤޤ󤬡
#39845Ρ#39832ΤȤƹͤơΤ褦ʲˡפդޤ
εƧޤơ1 n ξǹͤȡ

+ = + ( + )/2 = ( + )/2ȸȡ
ͤĤο򡤺ǾʿѤȴ֤ĤʿѤȤʤ褦֤Ȥˤʤޤ
ϡʿѤˤͤᡤФƾ礭оΤˤʤ褦֤Ȥˤʤޤ
ĤޤꡤȾʬο饢ȥӡȥʿѤη᤿ͤˤʤ褦ˤͤоΤ˷뤳ȡϤεաˤʤޤ

ʿѤ (n + 1)/2 ΤȤϡ
ͤβ¦ ӡʿѤ˴ؤоΤ˾¦ 뤳Ȥˤʤꡤ
(n + 1)/2 겼¦ˤ뼫ĤǤФȤˤʤޤ
ʿѤʳͤΤȤϡ
(n + 1)/2 겼¦ʿѤ (n + 1)/2 ˴ؤоΤʾ¦ΰ֤ʿѤȤϡοƱˤʤޤ
ˡ¦ͤƤ⡤ʿѤͤξ μ - 1/2 ξοƱǤ
ơ¦ǤäʿѤͤξϡ
(n + 1)/2 겼¦ˤ뼫黰ĤǾ ʿ ȤФȤˤʤޤ

ʾΤȤƧޤơ

(n + 1)/2 Ǥʤ硤Ĥޤ n ξ
ʿѤ (n + 1)/2 ΤȤϡ(n/2)C2 ̤ꡣ
ʿѤʳͤΤȤϡ(n + 1)/2 ΤʿѤʤΤǡ
ۤɤΤޤޤιͤǡ(n/2)C3 * 2 * 2 ̤ꡣ
ǡΤǤϡιפǡ
(n/2)C2 + (n/2)C3 * 2 * 2 = ((n/2)(n/2 - 1))/2 + ((n/2)(n/2 - 1)(n/2 - 2))/6 * 4
= n(n-2)(2n-5)/24 ̤

(n + 1)/2 ξ硤Ĥޤ n ξ
ʿѤ (n + 1)/2 ΤȤϡ((n-1)/2)C2 ̤ꡣ
ʿѤʳͤΤȤϡ(n + 1)/2 ΤʿѤ - 1/2 ʤΤǡ
ˤʿѤˤʤ褦 (n + 2)/2 ˹ͤȡ((n+1)/2)C3 * 2 * 2 ̤ꡣ
ºݤˤʿѤ (n + 1)/2 ΤȤ ((n-1)/2)C2 ̤ ­᤮Ƥޤ
ǡΤǤϡʬơ
((n+1)/2)C3 * 2 * 2 - ((n-1)/2)C2 = (((n+1)/2)((n+1)/2 - 1)((n+1)/2 - 2))/6 * 4 - (((n-1)/2)((n-1)/2 - 1))/2
= (n-1)(n-3)(2n-1)/24 ̤

ˤʤޤ
ͥνȡ 930 20:38:24 39857
ݤ
פ֤Ǽ
礳ä
꽸򣲺ޤ
http://www21.ocn.ne.jp/~hopes/hon.htm
ɤꤤפ޼
102ʲС 10:14:30 MAIL:hopes@mba.ocn.ne.jp 39858
粬ҹ
äݤʬޤ󤬡Υɤλ
̤
̤ꡡܣ̤ʿοȹ
̤ꡡܣܣ̤ʡ
̤ꡡܣܣܣ̤ʡ
̤ꡡܣܣܣܣʡ
̤ꡡܣܣܣܣܣʡ




ܣܣܣܣܣܣܣܣܣܣʡ

äε§򸫤ĤƺϽФޤäݤȸĿŪˤϻפäƤޤ
102ʲС 22:59:36 39859