Фޤ
Фޤ
120ڡ 0:03:20 51194
UFO
ƤäݤǤä򤷤Ƥޤޤ
ץϤڤ [0, 1, 3, 6, 13, 20, 27, 31, 35, 36] ȯޤǤɤΤ褦˲򤱤ФΤޤäդޤ
120ڡ 1:05:58 51195
å
0,1,6,10,23,26,34,41,53,55
55Ǥϡ
Ȥꤢʤ¤ϲȤޤ󤬡
120ڡ 1:14:41 51196
Ȥ
ܿإԥå꤬
https://www.imojp.org/archive/mo2022/jmo2022/problems/jmo32yq.html
7򤤤Ƥߤޤ!!

ɸA(0,0),B(0,7),C(7,0),D(a,-a+7)Ȥ
D濴Ⱦ3αߤyθ
(x-a)^2+(y+a-7)^2=9x=0Ȥ
F(0,sqrt(9-a^2)-a+7)
(x-a)^2+(y+a-7)^2=25y=0Ȥ
E(a-sqrt(-a^2+14*a-24),0)
ǢEDFǻʿ
a^2+(-sqrt(9-a^2))^2+(sqrt(-a^2+14*a-24))^2+(7-a)^2
=(sqrt(9-a^2)-a+7)^2+(a-sqrt(-a^2+14*a-24))^2
ѷ
2*(a*sqrt(-a^2+14*a-24)+a*sqrt(9-a^2)-7*sqrt(9-a^2))=0
a*sqrt(-a^2+14*a-24)+a*sqrt(9-a^2)-7*sqrt(9-a^2)=0
a*sqrt(-a^2+14*a-24)=(7-a)*sqrt(9-a^2)
ա2褷
(2*a+21)*(8*a-21)=0 ꡡa=21/8
ȺǽDD(21/8,35/8)B(0,7)ǻʿ
sqrt(((21/8)^2+(35/8-7)^2)=21*sqrt(2)/8()

ޤ구βޤǤޤ͡
嵭ΥԥåǴ2,4,7,12Ǥ
񤷤ȻפΤǼ12?
˭ԡ 120ڡ 1:20:03 MAIL:fttnm528@ybb.ne.jp 51197
ߤ
#51196
ξüˣȤȤϡ֤οϣġ
֣¬ΤϺǣ̤ꡣ
٤礦δ֤¬ΤϺǣ̤ꡣ
ά
٤礦δ֡구Ρˤ¬Τ̤ꡣ

嵭˽ʣĹʤСܣܡġܣܣᣴ̤ꡣ
äơɤ꿶äƤ⣴̤Ķ뤳ȤϤꤨʤ

ʤȤ⡢̵Ȼפޤ
120ڡ 1:54:33 51198
å
#51198
Τ51ƤʤǤ͡
⤦ĹǤǤ45cmʲˤʤޤ͡
120ڡ 2:08:30 51199
٥륯åĥ
Ĥδֳ֤Ϣ³1Ĥ9Ĥ¤45̤ꤷʤΤ45ʲʤΤϳꡣ
ü1ʤȺ-1ʤΤǤꡣ
ȤϻԺ12377441-19ޤǺơǸΡ7ʤΤǹ36Ȥʤޤ37ʾ夬ǽɤǤ
120ڡ 5:30:18 51200
ֿء׾ι
ǧڤǤ3ܤޤ
120ڡ 7:06:37 51201
⡼ޥ
9C2=36
...
10C2=45 ʤΤǡ37ʾΤΤʤȤʤȳǤʤΤǤϡ
120ڡ 13:22:45 51202
ֿء׾ι
45ʲĴ٤ץ餻Ƥߤ
35ʲǤΤǡ35ʾ餻롣ĤΣң

a=(1..45).to_a
a.combination(9).each{|x|if x[8]>=35 then if [x[0],x[1],x[2],x[3],x[4],x[5],x[6],x[7],x[8],x[1]-x[0],x[2]-x[0],x[3]-x[0],x[4]-x[0],x[5]-x[0],x[6]-x[0],x[7]-x[0],x[8]-x[0],x[2]-x[1],x[3]-x[1],x[4]-x[1],x[5]-x[1],x[6]-x[1],x[7]-x[1],x[8]-x[1],x[3]-x[2],x[4]-x[2],x[5]-x[2],x[6]-x[2],x[7]-x[2],x[8]-x[2],x[4]-x[3],x[5]-x[3],x[6]-x[3],x[7]-x[3],x[8]-x[3],x[5]-x[4],x[6]-x[4],x[7]-x[4],x[8]-x[4],x[6]-x[5],x[7]-x[5],x[8]-x[5],x[7]-x[6],x[8]-x[6],x[8]-x[7]].uniq.sort==(1..x.max).to_a then p x end end}

̡Ǥϡ
1,2,17,21,24,27,30,33,35
1,3,6,9,16,23,30,34,35
1,3,6,9,19,23,30,34,35
1,4,5,16,18,25,27,33,35
1,4,10,16,22,28,30,33,35
1,5,12,16,26,29,32,34,35
1,5,12,19,26,29,32,34,35
2,5,7,13,19,25,31,34,35
2,5,8,11,14,18,33,34,35
2,8,10,17,19,30,31,34,35

Ǥϡ
1,3,6,13,20,27,31,35,36
1,5,9,16,23,30,33,35,36

2̤Ǥ
120ڡ 14:33:23 51203
CRYING DOLPHIN
#51185
1999ǯΥդǷȤϤƤ񤤤ޤääƤ
ʾ˼äĤˤää̤äƤޤ
»ŪʸϤޤФƤޤ

񤤤ϻⲿ٤ԤƤޤ
θξ֤򸫤ƾʤ餺åޤС
Ѱդ޷˷äȤ˾ʥ
ǧȤϡ⤷ǤΤǤϡȤ˾ޤ

ʤ鷺˴ʤ줿ΤϻǰǤʤޤ
ʲҤǤ񤤤˹ԤʤʤäƤ˴ʤäƤޤäȤȤϡ
СΤ񤤤ʤ餺ѥͿ
ΤʡȻפޤ

ǯ¤ưϤ޷㲼(ϤǤޤ
٤ΤȤ񤷤ʤޤ)쥪դ˻äΤϺ
ʤäƤޤޤ͹λƻǤʤС֤󲿤Ȥʤޤ
񤤤Ѥ벿ιư򤪤顢Ȥפޤ

Τ̽ʡ򤪵ꤤޤ
夲ƻ衡 121ʶ 0:55:35 MAIL:Ԥ HomePage:ԤԤ󤹤51204
ֿء׾ι
#51203ʥ쥹Ǥ

a=(1..45).to_a.combination(9).map{|x|x.insert(0,0)}
b=(0..9).to_a.combination(2)
a.each{|y|if y[9]>=35 then if b.map{|z|y[z[1]]-y[z[0]]}.uniq.sort==(1..y.max).to_a then p y end end}

ĹΤ򥳥ѥȤ˽񤯤ȡǤޤ12֤Ǥ̵ǤΤǻߤޤ
121ʶ 6:46:02 51205
ޥ
ߤޤʣΤȤɤޤäƤơ򥢥åץɤ˺Ƥ뤳Ȥ顢Ťˤޤ...Ŧ̤ꡢ37cmʾ夬NGǤ뤳ȤξɬפʤΤǤ¤ϻϾǤƤޤm(_ _)m
Tokyo 121ʶ 23:06:08 HomePage:51206
ޥ
#51204 (C-D

ΥաɤФƤޤʪŤʷǤǸΥ饪ޤǤ襤褦˵Ƥޤ

񤤡ǽ˹⾾±ˤ路ΤC-DǤC-DƱ͡ǽϥå礭äΤǤ±žƤ쵤ɤʤäƤơä˽οǯǯΤ褦Ѳ졢礭ʴ˾äƤ񤤤˻ǤäƤޤ

ߤ˲𤷡ϤꤨĤĤޤ򹯤˵Ĥơʬޤǽ¤֤äƤǤ͡
Tokyo 121ʶ 23:10:39 HomePage:51207
ߤ
ǯ˰³򤤤ۡ

ʣ»ܡ
ΣϾ佸
ʣ˻§׻ʣܿʣ˥˥塼ȥ󻻡ʣʿ̿޷
ʣˡʣˤϴñʣˤäǺࡣͤय餤ʤ顢
ֳ٤¡פ䤦Ƥ뢪׻䤹ü췿ꤹ롢Τɤ

ΣϿ޷βžư
ޤѤ׻֤ο޷Ȥ߹碌ʤΤǡ񤷤Ϥʤ
ˤΩĤΤǡȤ

ΣϿκ
ʣˣ̤Ǻ碪ǻ٤Ϥ礦֡ȤȤ˵ŤаŻǹԤ롣
ѿޤ񤤤Ƥ礷֤ǤϤʤɡ
ʣˡʣѿޤ񤤤ʬܡʬ䤹ޤȯǽ񤯤Τ
񡩡Ȥ褦Ȥϻפޤ

Σʤ̻ο
ͶƳ˽äƿȤ߹碌ʤ롣꤬ǤʤȤȤäĤˤ
Ǹˡ֤ꤦȤ߹碌򤹤٤ƽ񤱡פȤΤ褯ѥǤ
ֲ̤ꤢ뤫פȤäѥ

ΣϿ
ʣˤǤȤꤢƵ§õꡢʣˤǤη̤ȤޤǤ
ǤɡʣˤϺȤݤʤΤǼΤƤ뤬ȡ

Ȥ櫓ǡǸҲ𤷤Ƥޤ
Σ
Фơʲ򤹤롣
οܿΤȤdz
οܿǤʤȤܤƣä

򷫤֤ԤȤ䤤ʤ
ʣˡʣˤϾά
ʣˣ飱ޤǤοФƤԤȤdzȤ
礦ɣԤϲĤޤ

֤פʸǤϽ񤤤Ƥ뤬פȤȤʤΤǤ礦

δۡ
ΣϤϴŪʤȤʤΤdzμ¤˼Ϥ
ΣϤοκ꤬ȡΣϤڤorΣϡʣˤޤǴĥ
Τɤ餫ɬפΣϤڤСȤڤˤʤ롣
121ʶ 23:30:50 51208
Ȥ(8)
10꤫ǤդΣǡ⡹10ã55ȡ줿줺
꾯ʤȡ顼Ťͤơã36줿衦
Ȥˤϻ餺
̸޻ԡ 122ڡ 20:48:24 51209
ߤ
ëĥʣ»ܡ
׻Τ褦ʤϤʤʤʤϡɡ

Σϵ§
ʣˤޤǤϤäդʣˤϤΤäƤȳڡ
ޣιФοϡТߡʢܣˡѡߣޤϡߢݣɽ뤳Ȥ
ܡ

ΣϾο
ʣˤޤǤϹԤȻפɡʤʤԥʤꡣճ񤷤
פޤ

Σ®
狼ɤʥդ񤱤ͤ롣ʣˤϤޤޤԤȻפ
ɡʣˤϤäѡֺȺǾκ礭ʤ롦ʤ
ͳܡ

Σʿ̿޷
ͣΥӥꡣɤߤ򤷤ƤȻפΤǡˤ

ΣΩΤ
ΩΤǤξ硢̤ΩΤΡվפǤ̤ꤹ뤬
̾פǤ̤ꡣ졢äȤͭʤ
ʣˤϣǤѤᤵꡣɤΩΤˤʤ뤫褯ʬʤ
ΤƤƤΤǤϡ

㴶ۡ
ȤоʤΤǡܤȣ䤯餤ǤУϣˡ
ʣˡʣˡʣˤŪפˣʣˤȣʣˤʡ
123 4:48:26 51210