鯤ο
1ΰ̤20ǡƼ56󤺤ĽФƤΤǡ
1000/20*6300
326ڡ 0:12:36 48863
ʪ
1 5 4 0 5 1 0 4 5 5
6 0 9 5 0 6 5 9 0 0
μ20򸫽ФФѤä300Ǥ(®餱Ƥޤޤߤʤ®)
μꡢ10ʬ߸̤˥ץåȤǤĤʤƤߤ綠

ʤߤꡢ https://www.wolframalpha.com/ ȤǰʬǤꤷޤ(ԥ˥åȤ˻ˡ)

ȥåץڡˤä֥졼򥪡ץ󤹤ͽס礷Ƥޤ!
ܡ 326ڡ 0:13:18 MAIL:butsuri.0523@gmail.com HomePage:Twitter48864
ʪ
դȻפäΤǤä㤰㤷§ʤΤˡ2,3,7,8̤ʤΤϰճ᤮
ܡ 326ڡ 0:21:33 MAIL:butsuri.0523@gmail.com HomePage:Twitter48865
٥륯åĥ
11221ΰ̤10Ĥ1פ20Ĥ1ˤʤä2056ĤˤʤΤΤ300ˤʤޤ
326ڡ 0:22:48 48866
鯤ο
nޤǤ¤ϡn*(n+1)*(2n+1)/6
n+20ޤǤ¤ϡ(n+20)*(n+21)*(2n+41)/6
ξԤκϡ
(120n^2+42*60n+41*420)/610(2*n^2+42n+287)10ܿ
顢20
//
326ڡ 0:28:32 48867
鯤ο

ʬȻפޤ
326ڡ 0:29:58 48868
٥륯åĥ
ȤǡѻCOKKIE¸̾ʸƤꡢǼĤǤʤȤCOKKIEȻפޤۤΤߤʤΤȤǤƱͤʤΤǤ礦
326ڡ 0:30:59 48869
٥륯åĥ
ǰΤɵݤ1ΰ̤1ΰƱΤѤǷޤΤǡ10ļˤʤΤ餫Ǥ
326ڡ 0:32:24 48870
Ȥ
Basic

for a=1 to 1000
IF FP(a*(a+1)*(2*a+1)/60)=0.5 THEN LET s=s+1
next a
PRINT s
END

f9300()
˭ԡ 326ڡ 0:45:17 MAIL:fttnm528@ybb.ne.jp 48871
ǯ
1ΰ̤οη׻ǹԤޤ
10ĤΤ֤ˤʤ뤫Ȼפޤ10ܤ0ˤʤ餺θ׻
200ˤʤäΤǡ20ĤΤ֤
20Ĥ56ġ
100*6/20=300
Ƿ׻ְ㤤ưö100
326ڡ 1:01:04 48872
ǯ
#48869
Ǥޤ󡣸ĿͥǡϿľΤǤǤᡪ
326ڡ 1:06:38 48873
ߤ
䤳ʤȻפĤġοɤưǧ

ȤꤢޤǤξϡ
ʹߤϣλοʣˤ˾οäƤФ褤夬
ͤ롣
äƣξϡ
ϣξ򷫤֤ΤǡļȤȤ狼롣

ļˤʤΤϣ󤢤Τǡࣲߣᣳ
326ڡ 1:31:43 48874
UFO
1/6 n(n+1)(2n+1) 5ܿǤ褦nθĿ夲ޤǤȤn(n+1)4ܿǤʤʤΤ4dzäޤ꤬1,25ܿΤȤ5dzä;0,2,4;20dzäޤǾ辰Ȥ23=6̤ꤹ٤ƤȯΤǡ10006/20=300Ǥ
326ڡ 3:15:23 48875
M
pythonǤ

sum =0
ans =0
for i in range (1,1000):
sum = sum + i**2
if sum % 5 == 0 and sum % 10 != 0:
ans = ans + 1
print (ans)

326ڡ 3:44:26 48876
ֿء׾ι
ʿn(n+1)(2n+1)/6ǡܿˤʤꡢܿǤʤȤ
n(n+1)(2n+1)ܿǣܿǤʤȹͤmod20ǿޤ
326ڡ 6:37:54 48877
ֿء׾ι
ӡΥץǤ
n=0;s=0;1.upto(1000){|i|n=n+((s=s+i**2)%10==5?1:0)};p n
326ڡ 7:23:46 48878
vbscript
for n=1 to 1000:s=(s+n*n) mod 10:k=k-(s=
5):next:msgbox k
326ڡ 7:59:55 48879
???
λǡ졼󥪡ץפǤ̱ʤΤǡ̶ФʤȤʤޤ
326ڡ 8:05:30 48880
ϥ饮㡼ƥ
ְ㤨ƤФäǤ
ԡ 326ڡ 8:15:45 HomePage:湩ؤ˥48881
̴
Ĥ񤭤ȡ(0,18,9ˤ3ĤŤĸΤǡ1000ޤǤ
ι100Ĥ300ĤȤޤ
ٻΤ桡 326ڡ 8:33:04 48882
ֿء׾ι
#48879vbscript
excelǻƤߤޤǤ͡
P(s=5)ͤtrueΤȤǤͤݣˤʤȤȤǡ
äޤɤƤʻͤˤʤäƤΤԻ׵ĤǤ
ٶˤʤޤ(^^)/
326ڡ 10:00:26 48883
Mr.ǥ
¿οͤƱͤˡ1ΰ̤20Ѥ20Τʤˡ65
Τǡ1000ޤǤˡ6(100020ˡ300Ȥޤ
ϤȤ㤨ꡢʷ׻򤷤ǡ֤äƤ
ޤ
326ڡ 10:16:08 48884
~~
괺 20ޤǷ׻ 6ȽФ Ϥɤ餳򷫤֤
Τ300Ȥޤ
326ڡ 10:39:14 48885
~~
괺 20ޤǷ׻ 6ȽФ Ϥɤ餳򷫤֤
Τ300Ȥޤ
326ڡ 12:09:31 48886
~~
Ѥߤޤ󡢸ǤǤޤΤ
εդꡡ 326ڡ 12:22:18 48887
ˤ
ˤ
326ڡ 16:20:16 48888
ˤ
20ޤǤǡƱѥǤ
Ķļˡ 326ڡ 16:58:06 HomePage:ޤޤ48889
ޤ
뷯ĥäƤޤ(^^;

#48862 Mr.ǥ
פΤо졢ڤߤˤƤޤ(^^

졼Ѥʤˤʤޤ
꤯ФȤǤ͡䡡ޥ뤵

somewhere in the world 326ڡ 18:24:06 48890
ޤ륱
p (1..1000).to_a.map{|i|(1..i).to_a.map{|j|j**2}.inject(:+)%10}.count 5
326ڡ 18:25:28 48891
ޤ륱
#48878 򻲹ͤˡuptoȤäƤߤޤ
p 1.upto(1000).map{|i|1.upto(i).map{|j|j**2}.inject(:+)%10}.count 5
äȤûʤäʡ
326ڡ 18:33:08 48892
miyama
Ѥޤ
326ڡ 21:54:26 48893
ˤ⡼
Ψ60%ʤΤ600ȸϢȯᤷ
夷10ޤǷ׻Ф
20äΤ͡
夬ΤȤϡ10ˣ10ˣ
¡ 326ڡ 21:54:27 HomePage:˥ͥäΥڡ48894
M
pythonǤ

sum =0
ans =0
for i in range (1,1000):
sum = sum + i**2
if sum % 5 == 0 and sum % 10 != 0:
ans = ans + 1
print (ans)

326ڡ 22:24:11 48895
M
pythonǤ

sum =0
ans =0
for i in range (1,1000):
sum = sum + i**2
if sum % 5 == 0 and sum % 10 != 0:
ans = ans + 1
print (ans)

326ڡ 22:24:18 48896
٥륯åĥ
#48873
ֿ꤬Ȥޤ
¾οͤƱͤäݤΤǡδĶȤǤϤʤǤ͡
̤̿ŪԶǤϤʤȤꤢϥߥ򤷤ʤ褦Ť˽񤭹ळȤˤޤ
327ʶ 1:14:12 48897
ֿء׾ι
#48891 ޤ륱

٤꤬ȤޤrubyΥ饹᥽åɤٶǤޤ
map,inject,count Ǥ͡
饤񤱤褦ˤʤΤɸˤޤ
ޤ񤬤жƤʡˡ
327ʶ 7:15:08 48898
ֿء׾ι
#48891 ޤ륱
ʤǤǤ͡rubyä򤤤Ǥ͡ʡˡ

p (1..1000).inject([0]){|s,i|s<<(s[i-1]+i**2)%10}.count 5
327ʶ 8:15:43 48899
ޤ륱
줤⤿Ф餷饤ʡʤǤ
injectindex0ϤޤʤΤ򤦤ޤѤƤޤ͡
Rubyʿͤơʤ줷Ǥ
327ʶ 13:59:46 48900
UFO
PythonǤ

from itertools import accumulate
print(sum(a % 10 == 5 for a in accumulate(i*i for i in range(1, 1001))))
327ʶ 23:47:45 48901
ֿء׾ι
#48900ޤ륱̤͡Ǥʡ

#48901 գƣ͡pythonǤtrueϣʤΤǤ͡accumulateǤ͡
328ڡ 8:14:20 48902
ֿء׾ι
#48901
python饤֥꤬󤢤äƱǤ͡accumulateȤ鷺ˤȡʤޤ

print[sum((a*a)%10 for a in range(1,i))%10 for i in range(1,1001)].count(5)
328ڡ 13:51:24 48903
Ϸ
ǽϥǣޤǤФƣܤޤ
Ȥ򸫤Ƥ
ͤƤ褦ʿ¤ʤΤ
ʣܣˡʣܣˡʬҤˣޤɬפ
ǼΤ褦˷׻ޤ
ࣵߣࣲᣳȤޤ
¾οͤΤΤѥåƿʤǤ
329 16:43:13 48904
٥륯åĥ
Ϥ٤ߤǤ礦
ǼĤβǧ褦Ȼפޤ顼ˤʤޤ
42ڡ 0:07:55 48905
ޥ
ߤޤ󡢺ι˺Ƥޤ...ʤޡŤޤ
iMac 42ڡ 8:44:49 HomePage:48906
ҤͤǤ
ȤȤϡդǤ礦
Ȥ轵ˤʤΤǤ礦
42ڡ 10:08:08 48907
~~
ΤȤϡʥ륹פǤ
դϤҤäȤƥޥ뤵⤫ȿۤƤޤ
ǤϤʤ褦褺ϰ¿ޤ

εդꡡ 42ڡ 10:17:12 48908
Mr.ǥ
#48906˺Ƥޤ...
Ȥǡ褫ä
()ⴶԿƤꡡ͹ߤ򤱤ʤ黶⤷ꤷƤ븽Ǥ
ԷϤɤǤϤʤ褦Ǥ礦͡
⡡ͽɤˡʬΤդ
42ڡ 11:47:41 48909
ֿء׾ι
ʤ­ʹƤ褦ʡְؤʪβīܤ餱
42ڡ 17:27:50 48910
EG
˺ƤפɤäۤƤޤ
򹯤ʤˤǤ
42ڡ 21:50:17 48911
ˤ⡼
̱¤ǤʤˤĤƤϡޤʤʴƥФȻפäƤޤԵƤΤˡġޥѡ꡼ʤǤK-1ԤΤȤ⤽ǤԤǤعؼԤȤδʬäƤʤ褦ʵޤ
¡ 43ʶ 23:10:32 HomePage:˥ͥäΥڡ48912
ߤ
ŷäǡԷιԳڵҤǤ
ŷ⤤˲ָޤǤȤȤǶĥˤߤ
ǯ٤鴿޲ʤƤΤϥۥȴۤƤۤǤ
44ڡ 0:19:01 48913
ˤ
ABCͽۡפȤ˾춵ʸ
ǧޤ͡
Ķļˡ 44ڡ 13:48:04 HomePage:ޤޤ48914
ޤ
쳦Τߤʤ

Ԥơ
줰⤴ѿޤm(_ _)m

somewhere in the world 44ڡ 21:53:08 48915
Mr.ǥ
ޥ뤵
Ѥ˻οäȤǤ͡
Τʤ褦ˤƤ͡
------------------------------
ꥸʥǤϤʤΤǤäƤ1ĤΤ񤭤ޤΤǡˤĤ֤ѤʳˤϲˤĤ֤ˤϤʤ󤫤

Aͭ룱դĹĤABCD,AEFGʤȤ˵ȿפޤν
BDD¦αĹFȤޤ
ΤȤʬBDAEΤʤkѤ礭Ƥ
ʿޤʤƤʤɸ仰ѴؿȤʤˡǡ
48ʿ 22:20:34 48916
ޤ륱
ޥ뤵̵ʤǤ͡
Ȥ⤢졢졼䤵äͻҡ褫äǤ͡󥹤Фҿ٤˹ԤǤ
49ڡ 0:05:45 48917
ǯ
ϡФ˵٤ߡȼäƤޤ
۵޻⤢äơƤƤ񤤤Ǥ礦
٤ߤϵˤ...ǤΤˤϽʬ˵Ĥ....
49ڡ 0:06:44 48918
ǯ
#48916
ACFѷ
DCF=15&ordm;
CFE=15&ordm;
EFD=30&ordm;ʤΤǡEFD=15&ordm;
BDAEθ=90-15=75&ordm;
Ǥ
49ڡ 0:24:10 48919
ǯ
̤ʸ񤫤饳ԡŽդʸ
&ordm;ϡǤ
49ڡ 0:27:18 48920
鯤ο
#48916

AEBDθHACBDθIȤ롣
ȡAIIFAFAC2AIꡢAFIϡFAI60ľѻѷ
EAIFAI-FAE60-4515
AHDEAI+AID15+90105
//
49ڡ 0:48:12 48921
鯤ο
#48919

ACFѷǤǤʤޤ
A60˼ʤǡACFѷˤϡ餫ˡǡAC=CF򼨤ɬפޤɸ׻ʳ˻פĤޤ
顢ACFѷ˹ԤΤϽ۴ˡȻפޤ

49ڡ 1:04:13 48922
ֿء׾ι
īž֤椤Ǥζˤ줤ʤοƶ̤˸ơ

ݤΥʤˤߤƽդη
49ڡ 5:42:19 48923
٥륯åĥ
#48923
BDABCDгʤΤAFCFоΤƱĹˤʤޤ
49ڡ 6:27:14 48924
٥륯åĥ
ְ㤨ޤ#48922Ǥ
49ڡ 6:27:54 48925
ǯ
#48922
BD(BF)ACοľʬAC=AFAF=CF
¨ACFѷ
49ڡ 6:40:04 48926
鯤ο
#48924
#48926
λ򤷤ޤ
žδطˤ޷ФܤˤĤƤơFľʬˤΤȤƤޤ餷ޤ
49ڡ 11:00:00 48928
Ф
Mr.ǥ򤤡
ǶᡢϤǤ⡢Ǥʡ˻ͷǤͤϸä
ѤӤޤͤ

ϻѷABCDEF(ײ˽ˡˡPȡABP
ϣˡPCDѤϣˤʤäޤEPդȤѷEPQ
ȡQAFȤʤäEPQѤʤ
49ڡ 16:35:51 48929
鯤ο
#48929
ϻѷ濴OABDCθRODSȤޤ

ޤPABPDC3:1ȤʤPε()ϡľRSϻѷθʬˤʤޤ

ϡΤ褦ˤ狼ޤ

PAR2PAB
PDR2PDC
ʤΤǡPARPDRᢤPABPDC31

顢ϡ
PARPDR31Ȥʤεפ
ϡRDRAxyȤиɸǹͤȡPR̤""1/3ľˤ뤳ȤƱ
ơSABSDC3:1ʤΤǡSϡľˤꡢPϡRSˤ뤳Ȥˤʤ롣

ˡPOCưȤ()FAˡFQOPȤʤ褦ˡQȤС
POEᢤQFEȤʤꡢPEQEPEQPEO+OEQQEFܢOEQOEF60Ȥʤꡢ
PEQѷˤʤ롣

ꡢPϡFCRSθdzꤷޤ

PϡOC2:1ʬˤʤ뤫顢
ODC3PDC3*39
ϻѷABCDEF=54
PED9
PDC3
PCB3
PAB9
PAQ5
EFQ6
äơPEQ54-9-3-3-9-5-619
//

49ڡ 20:07:45 48930
Mr.ǥ
ߤʤȤǤͭ񤦤ޤ

ϡ鯤οͤ#48921 ƱǤ
ǯԤΡ#48919 βˡ⤤Ǥ͡
ѷǤ뤳ȤƬˤޤǤ
49ڡ 20:09:30 48931
ǯ
#48929
濴OȤ롣
EPQѷʤΤ
FEQ=OEPEQ=EP
äơPOC¸ߤ롣
AB//OCʤΤǡAOB=APB=9
ϻѷ6ĤʬѷѤ9
P̤äBCʿ
ABȤθMCDȤθNȤ롣
ABP=9PCD=3
MP:NP9:3
顢OP:PC=2:1
FQ:QA=2:1
EQFEPOʤΤǡư
EPQFEOܭFPQ
9+9*(2/3)*(5/3)=19
49ڡ 20:17:58 48932
鯤ο
#48930

׹Ͳ

μϡñ̻ѷ˹ͤ뤳Ȥˤʤ뤫顢ꤢϻѷѷʬ䤷
ƾѷǡ"ʻ"򤤤Ƥߤ
ȡSABʿΣܡDCʿΣܤˤꡢξȤ
狼äФ餯ͤRȯ

OEFCEAѷˤʤ뤳ȤϤ狼뤫顢PϡOC̤ưϤ
OCΤɤǤɤȤ˵դ

˵ŤƤСиɸʤɽФˡOCΤɤˡPȤС3:1ˤǤ뤫
Ȳ򤱤ƤȻפ

PκɸޤäƤޤСñѷȡѤ60ޤ120λѷȤ
ȤǤϵƤƤ뵻ǡ;Ȥ鷺˲򤱤롣
49ڡ 20:35:33 48933
鯤ο
#48931
¤ϡ
ǽ顢ޤøʤäΤǡΤ˺ޤơǽ˼¬105ǧƤޤޤ
ϡCAF60ɤäƼ襤
BˤơΣդ򣱤ˤơɸȡF(x,x)ȤơACAF顢x=(1+3)/2
ǡC(1,0)ȤεΥ׻顢CF2ACAFǡACFѷȤȤϡ
ˡַ׻פФƤޤ
ɸ϶ؤƤΤǡɸȤ鷺ˡɤˤơѷ구ȯʤ
ʤޤ󡣤Ĥޤꡢ2:1õȤˤʤꡢäȯΤAFIǤ
ϵս˽񤯤Ȥˤʤޤ

ȯطʤǤ
49ڡ 20:54:13 48934
Ф
ͤɤ⤢꤬Ȥޤ
48930
иɸͤޤǤ礤˻ͤˤʤޤ
48932
ιͤ˶ᤤǤ


ϻѷABCDEF濴OȤ2ǢEFQᢤEOPĭ
POF120٤PгCFˤ롣
ABP9ꢤABO9ʢAB//FC
CPD3QP:PC2:1
äƭˤFQ:QA2:1
颤EPQᢤEFPܢQFPݢEFQ1510619

ޤꤤޤ
410ʶ 8:51:19 48935
Mr.ǥ
Фݤ#48935
ʤۤɡ񤷤褤ߤĤ餺ɤߤޤ
褯ͤФΤǤ͡ޤ
411ڡ 11:05:47 48936
Ф
#48936
Mr.ǥ󡣤äƲѤ줷Ǥ
ʥꥬȥꥬȤäưꤷ餤
򤹤ȡϰʲΣĤȤ߹碌Ǥ

إԥå2020ǯͽ2
https://www.imojp.org/archive/mo2020/jmo2020/problems/jmo30yq.html

2018ǯ110
https://sansu-seijin.jp/category/nadakaisetsu/2018-nadakaisetsu/

ɡȤʤ褦ʤΤǤ⡢ĤΤΤȤ߹碌ꡢͤιͤȤ
ۤξȯŸƤ褦ʤΤ
ͤˤ󤶤ƤäƤ櫓Ǥա
411ڡ 20:55:46 48937
Mr.ǥ
#48937Фݤ
ˤƤ⤹
412 12:16:23 48938
ǯ
Ǥ̵Τޤ󤬡ĺ꤬ޤ
ǤդαԳѻѷABCP롣
P̤äơѷABCѤʬľޤ衣
PѷABCվʤưפǤ
ꤤޤ
412 12:34:51 48939
鯤ο
#48939

쥬ȤʺޤϺޤǤ
ʲϵ

OABPOȤ֥٥ȥ롢uOA+vOBɽ(0<u+v<1)

uϡP̤OBʿOAθXᡢOX/OAȤƺ޲ġ
vϡP̤OAʿOBθYᡢOY/OBȤƺ޲ġ

OASΰ֥٥ȥsOA
OBTΰ֥٥ȥtOBȤ
STOABѤ2ʬst1/2

stʿ̾ǡ(s,0)(0,1/(2s)ˤ̤ľˡ(u,v)ϡ

u/s+2sv=1
(2v)s^2-+u=0

2򤤤ơsOA1/(2s)OB̤ľСˤʤ롣

ʤ2βκޤϡʲ򻲹͡
https://blog.goo.ne.jp/0424725533/e/2b13e78049a64e4d9389fa45c2c82aa6
//

412 23:17:40 48940
ǯ
#48940
꤬Ȥޤ
ޤäȤǤƤʤΤǤ
κޤˤϡǥȤΡִءפ˥ץˡ2ĤۤɺܤäƤȵƤޤΤǡ⻲ͤˤƸƤƤߤޤ
413ʷ 0:07:04 48941
鯤ο
#48940
Ƚ̼00<s,1/2s<1ʤȤʤ顢ѷͿ줿Pΰ֤ˤäơO,A,BѤʤȤʤ褦Ǥ
413ʷ 0:42:51 48942
tomh
#48939

ΥڡˤˡǤɤǤ礦

http://www.sci.niihama-nct.ac.jp/~kojo/column4.html

ǸϢPAT梤SAQȤޤ
ԡ 415ʿ 8:25:47 MAIL:tomh@yahoo.co.jp 48943
ǯ
#48943
õΤǤĤޤǤ
꤬Ȥޤ
줫顢ǧޤ
դĥޤ礦̲­ǡƤ뤫ɤۤǤ
415ʿ 12:27:25 48944
鯤ο
#48943

ڤޤ
415ʿ 22:33:06 48945