å
褫ä111ĤǹäƤż֤ϥĥǤ
423ڡ 0:38:45 43204

ǯγ(2)˿꤬Ʊ꤬ޤͤ
423ڡ 0:41:23 43205
!!!
칩AOǤ礦ͥ
http://izu-mix.com/math/exam/toukou/2008_ao3.html
͡ 423ڡ 0:57:22 43206
CRYING DOLPHIN
10ǯʾˤǽФȤۤƱǤ뤳ȤˡὪ褦ȤƤ˵դޤ(
http://cdcdcd.sansu.org/pika/G/G-q51.htm
ï⤤ʤԳϡ 423ڡ 0:53:45 HomePage:֥⤢43207
٥륯åĥ
111Ǵְ㤤ʤȻפΤ̾ФʤȻפä顢ФƤʤǤ
ޤ̤¹Ԥ̤ڤäƣʤʬ롣ʤȤ˹ͤƤޤ
6ܤϡ̡μ̤¹Ԥ̤ڤäƤȡ1+2+3+4+5+621ʬ䤵ޤ
ƺǸ̤¹ԤڤäƤȡ줾13579ĤΩΤǤΤǡ1+3+5+7+925ơ6ܤϹ46ĤΩΤʬޤ
5ܤƱͤ˹ͤ+2+3+4+5+1+3+5+731ġ
6ܤ1ܤޤǤޤȤ48+31+19+10+4+1111ġ

ǽϲ򤷤餤Τʬ餺ٴְ㤨ƻܤǤäȤǤޤ
423ڡ 1:04:23 43208
ǯ
6*6*6=216äʤȤϤʤȹͤľơ
3ؤǤ⡢󤬤餬äơޤޤʤ
ϤäơTVߤơפ
2ؤξ4ĤȬ1Ĥ򻲹ͤˡ
6ؤڤäؤ΢¦ѷʬ䤷ơߤȬΤ̤ФƤȤơؤȬΤο
üΤʤΤǡȬΤϡ0+1+3+6+10+15=35ġ
ȬΤΤ4ܤѤʤΤǡ6*6*6-4*35=76ĤΤο
פ111ĤȽФʤꤤøǤ

423ڡ 2:22:23 43209
(Keigei)
1դĹ1ΤޤȬΤʬ䤵롣
ΤġȬΤĤȤС
ɽѤ¤ 1դĹ1ѷ
4x8y4{2(1^22^23^24^25^2)6^2}4146 ʬ顢x2y146
Ѥ¤ 1դĹ1Τ
x4y6^3 ʬ顢x4y216
x76y35 Ȥʤäơxy111 Ǥ
̲ȡn(n^21)/2 ˤʤޤ

423ڡ 7:39:56 43210
ǯ
6*6*6=216äʤȤϤʤȹͤľơڤäȤɤΤ褦ʷΩΤ뤫ͤäˤʤʤ
㥬Фơ3ؤڤäƤߤʤȤˤʤޤǤ˥㥬3ĤۤɤĤ֤
ˤϤޤڤʤäȬΤ餷礭Ρڤޤ10̤ʤɤĤäˤ4ĤǤ
ΤΤ褦ʾʤΤ10ǤäΤǡ2ΩΤˤʤ餷ȤȽä

423ڡ 8:31:57 43211

Ϥ褦ޤ

KeigeiΥޡȤʲˡ˷ޤäȸŪʲˡǤ

Ҥ٤Ƥ褦ˡΤȬΤʬޤ
̤ʿԤnʤΩΤŤͤȹͤޤ
ȬΤ2ܤ1
3ܤ1+2=3
4ܤ1+2+3=6ġĤȽиޤ
2ʤǹͤȤ΢ȬΡȤ
ȬΤѤ2^3-4=4ꢥ:=1:4

nnܡ
ѡ(ѡ)

1 1 1 0 1-04=1 1 1
2 8 7 1 7-14=3 4 5
3 27 19 3 19-34=7 10 15
4 64 37 6 37-64=1319 34
5 125 61 10 61-104=2131 65
6 216 91 15 91-154=3146111

̼᤿KeigeiƱ
n(n^2+1)/2 Ĥˤʤޤ

Ǥ

ɵ
#43209κǯԤȹͤƱǤ͡
ǯԤФƤƥåꤷƤޤ͢
423ڡ 11:56:16 43212
ߤ
#43207CRYING DOLPHIN
虜虜ѻڤäƻ湩򤷤ΤפФޤ
夫飳ܤϵդˤʤäΤФƤ뤱ɡʤʤ᡼Ť餤

ɡɤʲ򤷤פФǧߤǤ
423ڡ 16:16:13 43213
CRYING DOLPHIN
#43213
ꤷϡΤȬΤ椬1:4Ǥ뤳ȤѤƲ򤭤ޤϤʴΥ饤ޤ񤭤ޤ
ɤԤ˺Ƥ餷(
ttp://cdcdcd.sansu.org/pika/junkfoods/san1-q928-kirikiri48.png
ï⤤ʤԳϡ 423ڡ 13:35:49 HomePage:֥⤢43214
uchinyan
Ϥˤϡơϡ
ࡤפ֤˲򤤤ȤǤ
ǽɤ뤫¤ޤϤ̿ޤ͡Ȥ櫓ǡʴ
ǤȻפäƤΤǤ񤭽ФƤߤȤ󤬤餬äƤޤʤʤäƤޤ

ʿBCD ڤӤʿԤʿ̤ 6 ̤ޤ 塤Ĥޤ A˶ᤤ餽̤򸫤ȡ
1 ܡξѷ 1 ġξѷ 0 ġ 1 ġ
2 ܡξѷ 3 ġξѷ 1 ġ 4 ġ
3 ܡξѷ 6 ġξѷ 3 ġ 9 ġ
4 ܡξѷ 10 ġξѷ 6 ġ 16 ġ
5 ܡξѷ 15 ġξѷ 10 ġ 25 ġ
6 ܡξѷ 21 ġξѷ 15 ġ 36 ġ
ˤʤäƤޤ
ǡʤξѷι׸ĿʬʤξǤʬΤϴְ㤤ʤΤǡ
1 + 4 + 9 + 16 + 25 + 36 = 91 İʾʬΤϴְ㤤ޤ
ϳʤδ֤ɤʤäƤ뤫Ǥ
ʤξѷξ
ʤ΢ȤȬΤ 1 ĤǤǡʤ鸫Ȥ٤ƸĿޤ
ʤξѷξ
ʤȤ֤ˤҤä֤äΤ 1 ĤǤʤ鸫Ȥ٤ƸĿ 1 ޤ
ǡʤξѷʬ1 + 3 + 6 + 10 = 20 ġĿޤ
ꡤǤʬϡ91 + 20 = 111 ġˤʤޤ

äơǼĤɤΤϾ٤ʤꤽǤ

n ʬξϡƱͤˤơ
((1 + 3 + 6 + + n(n+1)/2) + (1 + 3 + 6 + + n(n-1)/2)) + (1 + 3 + 6 + + (n-1)(n-2)/2)
= (1 + 3 + 6 + + n(n-1)/2) * 3 + n(n+1)/2 - n(n-1)/2
= (n+1)n(n-1)/6 * 3 + 2n/2
= n(n^2 + 1)/2
Ǥ#43210ȰפƤΤפʡ
ͥνȡ 424ʶ 11:59:47 43215
uchinyan
ǼĤɤߤޤ
դࡤϤΤޤޤ빽Ǥͭ̾͡ȤȤǤ礦

#43208
ʿBCD ʿԤʿ̤ˤΤäƤʬ§θʤˡ

#43209#43212
ǤʬΤȬΤˤʤ뤳Ȥ顤
ޤȬΤθĿѷͳΤθĿơäˡ
ʤʤ򤤲ˡȻפޤ

#43210
ǤʬΤȬΤˤʤ뤳Ȥ顤
θĿˤĤɽѤѤˤĤˡ
򤤲ˡǤ#43209ʤɤǤñʤ

#43214
ʿBCD ʿԤʿ̡οޤŤͤޤȤ˹ͤˡ

#43215
ʿBCD ʿԤʿ̤ˤǾȤˡξʤȤδ֤ˡ
ʤϲʤǤθĿƱʤϲʤȤη֤ˤҤä֤äΤ 1 롤
Ȥˡ#43214οޤ򸫤Ⱦʬ䤹⡣

#43218
ABCD P ̤δ֤Τɤˤ뤫ѤȤꤷ
ꤵ줿ϰϤ P ¸ߤ뤳ȤȰĤʬ䤵줿ʬȤУб뤳Ȥܤ
줿̤ϰϤξ󤫤ˡ
򤤤ǤȤȯۤ ɤƤȯۤǤ

С轵Ϥ٤ߤʤǤ͡
ͥνȡ 424ʶ 12:02:49 43216
٥륯åĥ
դࡢȬΤǤǤ͡ĿФ­ơޤǹͤƤޤǤ
ΩΤ򥤥᡼Τ񤷤
423ڡ 21:38:28 43217

褿Τ­פ

BCDʿԤʿ̤ڤäȤPʿBCD˶ᤤ鲿ܤʤΤϡ
PBCDΤѤΤɤʳ뤫Ƿޤꡤ
1ܤ1/6ʲ2ܤ1/62/6ʤɤȤʤޤ
¾ʿ̤ʿԤʿ̤˴ؤƤƱͤǡ
BCDˤĤa+1ܡACDˤĤb+1ܡABDˤĤc+1ܡABCˤĤd+1ܡ
ϡΤФѤγ礬
a/6<PBCD<(a+1)/6,b/6<PACD<(b+1)/6,c/6<PABD<(c+1)/6,d/6<PABC<(d+1)/6
Ǥ뤳Ȥ̣a,b,c,dξϡ
(a+b+c+d)/6<1<(a+b+c+d+4)/6,ʤ
3a+b+c+d<6Ȥʤޤ
¤3,4,5ξͤơϡ4H3+4H4+4H5=6C3+7C4+8C5=20+35+56=111Ǥ͡
423ڡ 23:56:37 43218
nama
夫ˡդ濴˸
Σ
ΣȬΣ
ΣȬΣջΣ
ΣȬΣջΣΣ
ƤäƤΤǡ³
ߣܣߣܣߣܣߣܣߣܣߣᣱ
ˤʤ뤫ʡȤʤȤʤפޤŬǤߤޤ
424ʶ 16:36:12 43219

ĤˤʤΤĤȣĤˤʤΤĤ
ߣܣߣᣵܣᣱȡݤ
򤷤ޤorg
425ڡ 2:32:45 MAIL:nikotan@fat.coara.or.jp 43220

դĹĤˤޤ
ΤĤȵոĤǣġƣĤĤʬ
顢ߣᣵġ
ΤġƣĤĤʬ뤫顢ߣᣵġ
ܣᣱ
ʬꤺ餯ơʤ(>_<)
425ڡ 3:06:34 MAIL:nikotan@fat.coara.or.jp 43221

̲ǤʤȤʤå顢ܤ(^^
Ǥ⡢äߤOrg

425ڡ 3:31:40 MAIL:nikotan@fat.coara.or.jp 43222

礭ʳգˤΣΤϣΣĤȣΣĤˤʤ롣
Ĥ뤫顢ΣĤȣΣġ
礭ʳգˤΣΤϾȾʬǣĤΣΤȵոΣΣ
ηףΣġΤϣġ
岼Ʊ顢ɣΣġΣ
礭ΤϣĤ뤫顢ܤơΣġΣġ
碌ơ
Σܣ᣷
Σܣᣳ
碌ơ
ΤϣΤΣܤѤ뤫顢ܣߣ᣷ܣ
ᣲǡߣߣᣲȰפ롣
Ȥ櫓ǡ櫓Ǥ^^;
425ڡ 8:15:42 MAIL:nikotan@fat.coara.or.jp 43223

nʬʤ
n/2(n*n+1)
ʡ
425ڡ 9:40:39 43224

ФǤߤޤm(__)m
425ڡ 9:43:22 MAIL:nikotan@fat.coara.or.jp 43225

ϤʤȤߥա
ʤ8ΤĤǤ뤫ǵޤʳʤΤϾ̤ѷȲ̤ѷդ˽ŤʤȤǤ
8ΤѣȤȡ4Τ1
ʤѤ8ΤοΤοϡ夫1ܤȤ
ʤѡ8Το4Τοʤѡ8Τѡ
ܡ
ܡ
ܡ
ܡ
ܡ
ܡ
סܡ ᣱˤʤޤ

Ϻꡡ 427ʷ 7:29:00 43226

ī᤯ƻ֤äΤǡ󥸤ƤäȲ򤱤(Х󥶥!!)ǡ¾Τ򸫤ƤʤäΤǤ
ʥޥޤ󡢺ǯԤƱˡǤʣʥޥޤȤϽۤܰǾꤷƤޤǤ
427ʷ 10:12:37 43227
⡼ޥ
ޤˤ狼ʤ錄^^;
ʿ̤ڤ뤫ɤΤˤʤȤפʤäǤɡ?

ͧͤΤΡ#43210 η(Keigei)Ʊ褦ĤǤOrz

6ʤǤ뤬2ʤξǤߤ4ĤΤ
ޤ1Ĥ8ΤƤ롣
ѷ¿ΤǤ뤬20Τ̤γ٤餢ʤ
ΤȬΤ꺮äƤ롣
(A) Ѥ
4Τ1̤礭1Ȥ
ФФˤʤäΤxġȬΤyĤȤ
ɽѤιפ4x+8y
̤2ɽ̤1Ǥ뤫顢
(1+4+9+16+25)*2+36=146줬4뤫146*4=584
ä4x+8y=584
(B) Ѥ顡ˤ
ΤѤϰդaȤȡ2/12*a^3ȬΤϢ2/3*a^3
顡2/12*x+2/3*y=2/12*6^3äx+4y=216
줫x=76y=35111

*錄ˤ̵Ǥ^^;;
¨ ^^;v 428ʲС 0:54:52 MAIL:crazy_tombp@yahoo.co.jp 43228
fumio
äȡ򤱤ޤʾСˤϤϤϡ
奪ե߳ڤߤˤƤޤ
ǤϤǤϡ
430ڡ 5:59:19 43229

ǤƤǤΩΤΤȬΤ2ĤפȤȤˤĤơˤʤäƤޤ
ؤǤΤͤ롣
ݣʬΤ򣴤Ĥĺ˹碌ȡʾǤнŤʤϤ뤬ΤǤ롣
顢ؤǤΩΤμϡݣؤǤΩΤμƱ
ȤᣲλϡᣱΣġˤΩΤǤǤȬΤĤ롣
ΤˡᣳʾǤϡΤȬΤΣǤƤ뤳ȤȽ롣
ΤȬΤΣषʤȤȽСĤĤ뤫ϡѤѤȤ뤳ȤǤޤ
ߤޤ!!!ξҲ𤵤줿ڡˤʤ褦ʤȤܤƤޤ

53 6:42:33 43230
̴
ΤȬΤˤʤʬäΤǤΩΤǥ᡼⤫ФƤޤҶٰʡοޤƤƤˡ111褷!!!!
ٻΤ桡 55ʲС 9:49:32 43231