AOC 2011 Silver A

download AOC 2011 Silver A

of 38

Transcript of AOC 2011 Silver A

  • 8/4/2019 AOC 2011 Silver A

    1/38

    DFq'eftjk Kjtb`c Ife

    !DFq'" ? ! ;"

    ! 4" ? ! "

    5=66 FI[FBU

  • 8/4/2019 AOC 2011 Silver A

    2/38

    DFq'eftjk Kjtb`c Ife

    Dhc{jc{t

    Nujj Tzeojd{ Ib`a{'pjb`a{ kjtb`c ahgj'gfkj dfu nufgj dhctbkjubc` tfnj{r

    Bc{uhkzd{bhc

    Ehzckfur dhckb{bhc T{j}6XH}{bgbf{bhc [h}hih`r T{j}5XH}{bgbf{bhc Tbj Nbcfi Kj{fbi fcfirtbt F{{fdagjc{

    5

    Fttb`cjk Tzeojd{!F" Ef{{jur {ufr kjtb`c

    Bc{uhkzd{bhc Ehzckfur dhckb{bhc T{j}6XH}{bgbf{bhc [h}hih`r T{j}5XH}{bgbf{bhc [h}hih`r T{j}4XH}{bgbf{bhc [h}hih`r

    Nbcfi Kj{fbi fcfirtbt

    6

    5

  • 8/4/2019 AOC 2011 Silver A

    3/38

    DFq'eftjk Kjtb`c Ife

    Ef{{jur {ufr kjtb`c

    H}{bgbf{bhc [h}bd F

    4

  • 8/4/2019 AOC 2011 Silver A

    4/38

    DFq'eftjk Kjtb`c Ife

    H}{bgbf{bhc bc hukju {h kjdujftj {aj kbt}ifdjgjc{ f dju{fbc nujvzjcdr ufc`j#

    Bc{uhkzd{bhc

    H}{bgzg[fu`j{&

    Kjtb`c heojd{

    [fu`j{

    ;

  • 8/4/2019 AOC 2011 Silver A

    5/38DFq'eftjk Kjtb`c Ife

    H}{bgbf{bhc }uhdjkzuj

    Bcb{bfi kjtb`c

    T{j}6 [h}hih`r T{j}6 Ujghkjibc`

    T{j}5 [h}hih`r

    t{j}5 Ujghkjibc`

    T{j}4 [h}hih`r

    Nbcfi ' Kjtb`c

    :

  • 8/4/2019 AOC 2011 Silver A

    6/38DFq'eftjk Kjtb`c Ife

    Fii Nbqjk

    Ihfkbc` }hbc{ !F"_ fqbt :=C'KFUJF f}}ir

    Ujk ? Chc kjtb`cTlr Eizj ? ^ju{bdfi'Chc kjtb`c

    Eizj ? Kjtb`c t}fdj

    Gf{jubfi ]uh}ju{r

    Dhg}hcjc{

    Rhzc`t

    ghkzizt

    !G]f"

    ]hbtthcuf{bh

    Kjctb{r!C't(gg;"

    T{jji Ef{{jur {ufr 5#=0j,=: =#5> 0#2j'=2

    Jijgjc{

    [r}j ]TAJJI F~`# Tbj :gg

    [abdlcjtt

    Kjtb`c 5gg Chc'kjtb`c 5gg

    521gg

    55=gg

    ;= gg

    /

    Ehzckfur dhckb{bhct

    >

  • 8/4/2019 AOC 2011 Silver A

    7/38

  • 8/4/2019 AOC 2011 Silver A

    8/38DFq'eftjk Kjtb`c Ife

    5==A ^fizj !=#4;:gg" 3 =#5:gg

    Eftj fcfirtbt

    Nujv!A"

    Kbt}#!gg"

    Nujv!A"

    Kbt}#!gg"

    = =#5:2 ::= =#==2

    := =#5>= >== =#=45

    6== =#=2; >:= =#=6;

    6:= =#=00 0== =#==2

    5== =#4;: 0:= =#=64

    5:= =#65; 1== =#=56

    4== =#=;4 1:= =#=6:

    4:= =#=54 2== =#==1

    ;== =#=6: 2:= =#==2

    ;:= =#=41 6=== =#==2

    :== =#=45

    }{ E

    1

    Nuhg eftj fcfirtbt ujtzi{

    Dhct{ufbc{ dhckb{bhc!kbt}#" =#5: gg Kbt}ifdjgjc{ f{ }{ E! Gfq# ? =#4;: gg" 3 Dhct{ufbc{!=#5: gg"

  • 8/4/2019 AOC 2011 Silver A

    9/38DFq'eftjk Kjtb`c Ife

    [h}hih`r h}{bgbf{bhc

    H}{bgbf{bhc tj{z} nhu {h}hih`r kjtb`c

    [h}hih`r h}{bgbf{bhc dhckb{bhct [r}j ? ]TAJII

    Bcb{bfi!Eftj" {abdlcjtt ? 5gg

    Ztbc` }f{{juc `uhz}bc`

    Heojd{b~j nzcd{bhc ? Gbc# Gftt

    Dhct{ufbc{ dhckb{bhc ? ZE =#5:gg !f{ }{ E"

    }{ E

    2

  • 8/4/2019 AOC 2011 Silver A

    10/38DFq'eftjk Kjtb`c Ife

    Gftt !l`"

    Jnnjd{ hn }f{{juct

    T{j}6# [h}hih`r h}{bgbf{bhc

    Gftt !l`"

    !Zcb{ ? gg"

    4#2:

    4#25

    =

    4#264

    4#241=#:;* z}

    Gftt !l`"

    !Zcb{ ? gg"

    4#2:

    4#25

    =

    4#2644#24;

    drd 6'}ic !zdrd 7 ;"!Zcb{ ? gg"

    4#2:

    4#25

    =

    4#2644#25>

    =

    =#=:

    =#6

    =#6:

    =#5

    =#5:

    =#4

    =#4:

    = := 6== 6:= 5== 5:= 4==

    Gf`cb{zkj

    Nujvzjcdr

    Eftj

    Drd 6'}ic

    Gfq Kbt}# ? =#4;:gg

    Gfq Kbt}# ? =#5:6gg

    4'}ict trgchcj

    =#44* z} =#>;* z}

    =

    =#=:

    =#6

    =#6:

    =#5

    =#5:

    =#4

    =#4:

    = := 6== 6:= 5== 5:= 4==

    Gf

    `cb{zkj

    Nujvzjcdr

    Eftj

    chcj

    Gfq Kbt}# ? =#4;:gg

    Gfq Kbt}# ? =#5:=gg

    50#>1* khpc 50#>5* khpc 50#>5* khpc

    =

    =#=:

    =#6

    =#6:

    =#5

    =#5:

    =#4

    =#4:

    = := 6== 6:= 5== 5:= 4==

    Gf`cb{zkj

    Nujvzjcdr

    Eftj

    4'}ict trg

    Gfq Kbt}# ? =#4;:gg

    Gfq Kbt}# ? =#5:=gg

    6=

  • 8/4/2019 AOC 2011 Silver A

    11/38

    DFq'eftjk Kjtb`c Ife

    T{j}6# [h}hih`r h}{bgbf{bhc ujtzi{

    T{j}6# [h}hih`r h}{bgbf{bhc !dhc{k"

    :=A ^fizj !Gfq# ? =#5:6gg" 3 ZE !=#5:gg"

    }{ E

    Nujv!A"

    Kbt}#!gg"

    Nujv!A"

    Kbt}#!gg"

    = =#5;; ::= =#==>

    := =#5:6 >== =#=4:

    6== =#=2> >:= =#=61

    6:= =#=15 0== =#=66

    5== =#5;2 0:= =#=6>

    5:= =#660 1== =#=62

    4== =#=;> 1:= =#=6:

    4:= =#=50 2== =#==1

    ;== =#=64 2:= =#==1;:= =#=41 6=== =#=6=

    :== =#=;>

    66

  • 8/4/2019 AOC 2011 Silver A

    12/38

    DFq'eftjk Kjtb`c Ife

    UJghkjibc`

    Bcb{bfikjtb`c

    Ube

    T{j}6# [h}hih`r h}{bgbf{bhc !dhc{k" 62#:gg

    65:gg

    4=gg

    62gg

    Uj'ghkjibc` }ifc

    Fkkjk {abdlcjtt ? 5gg Thibk jijgjc{

    5gg

    65

  • 8/4/2019 AOC 2011 Silver A

    13/38

    DFq'eftjk Kjtb`c Ife

    Uj'{h}hih`r h}{bgbf{bhc ujtzi{

    Fcfirj hcir {aj uj'kjtb`c jqdizkbc` bcb{bfi kjtb`c

    Gftt ? Bcb{bfi !4#264l`"Uj'{h}hih`r !4#24:l`"

    T{j}5# [h}hih`r h}{bgbf{bhc

    B{juf{bhc42

    Uj'{h}hih`r

    Jqdizkbc`

    Kjtb`c fujf

    }{ E

    Nujv!A"

    Kbt}#!gg"

    Nujv!A"

    Kbt}#!gg"

    = =#5:= ::= =#==2

    := =#55> >== =#=;;

    6== =#=22 >:= =#=56

    6:= =#=1; 0== =#=6:

    5== =#5:= 0:= =#=54

    5:= =#65= 1== =#=62

    4== =#=;1 1:= =#=66

    4:= =#=5> 2== =#==>

    ;== =#=6; 2:= =#==0

    ;:= =#=42 6=== =#==2

    :== =#=;;

    64

  • 8/4/2019 AOC 2011 Silver A

    14/38

    DFq'eftjk Kjtb`c Ife

    Kbgjctbhc nhu nbcfi ghkjibc`

    Uj'ghkjibc` . [h}hih`r h}{bgbf{bhc

    H}{# Ujtzi{

    Ub`a{Ijn{

    Eh{{hg

    Uj'ghkjibc`

    T{j}4# Uj'ghkjibc` . Nbcfi {h}hih`r h}{bgbf{bhc

    Kjtb`c fujf

    Chc'kjtb`c

    Uj'ghkjibc`Eh{{hg

    2>#5ggDhctbkju nhugbc`

    41#0gg2#>gg

    6;

  • 8/4/2019 AOC 2011 Silver A

    15/38

    DFq'eftjk Kjtb`c Ife

    Fcfirtbt ujtzi{ nhu nbcfi ghkjibc`

    Ujtzi{ nhu nbcfi h}{bgbf{bhc

    Bcb{bfi

    Gftt !l`"Bcb{bfi ? 4#264

    Nbcfi ? 4#241

    Nujv!A"

    Kbt}#!gg"

    Nujv!A"

    Kbt}#!gg"

    = =#5;> ::= =#==1

    := =#550 >== =#=;;

    6== =#=22 >:= =#=55

    6:= =#=1> 0== =#=6:

    5== =#552 0:= =#=54

    5:= =#660 1== =#=61

    4== =#=:6 1:= =#=65

    4:= =#=50 2== =#==>

    ;== =#=6: 2:= =#==0

    ;:= =#=42 6=== =#==2

    :== =#=;1

    }{ E

    4#264

    4#2444#24:

    4#241

    4#2

    4#2=:

    4#26

    4#26:

    4#25

    4#25:

    4#24

    4#24:

    4#2;

    Bcb{bfi t{j 6 t{j 5 Nbcfi

    4

    =

    6:

  • 8/4/2019 AOC 2011 Silver A

    16/38

    DFq'eftjk Kjtb`c Ife

    Ib`a{'pjb`a{ kjtb`c ahgj'gfkj dfu nufgj dhctbkjubc` tfnj{r

    Nujj Tzeojd{

    6>

  • 8/4/2019 AOC 2011 Silver A

    17/38

    DFq'eftjk Kjtb`c Ife

    Bc{uhkzd{bhc

    LTFJXEFOF DFU

    Ez``r DFU

    [fu`j{

    60

  • 8/4/2019 AOC 2011 Silver A

    18/38

    DFq'eftjk Kjtb`c Ife

    H}{bgbf{bhc }uhdjkzuj

    Bcb{bfi Kjtb`c

    T{j}6 [h}hih`r

    T{j}6 Ujghkjibc`

    T{j}6 Uj [h}hih`r

    T{j}5 Ejfg Ghkjibc`. Tbj H}{bgzg

    Nbcfi Ujtzi{

    61

  • 8/4/2019 AOC 2011 Silver A

    19/38

    DFq'eftjk Kjtb`c Ife

    Fcfirtbt dhckb{bhct

    Gf{jubfi ]uh}ju{r

    Dhg}hcjc{

    Rhzc`t

    ghkzizt

    !G]f"

    ]hbtthcuf{bh

    Kjctb{r!l`(gg"

    RT!G]f"

    Z[T!G]f"

    T{jji Nufgj 5#=0j,=: =#5> 0#2j'=2 512 ;:;

    ]ift{bd Tjf{ 5#5j,=4 =#41 6#5j'=2

    Uzeeju [buj 5#=j,=5 =#;2 5#=j'=2

    Gftt kzg}bc` !l`"

    Ztbc` ub`bk'ehkr . Gftt jijgjc{ nhuf}}uhqbgf{j gfttb~j dhg}hcjc{

    ]ijftj nhiihp {af{ fuuhp#

    T{jjubc`!4l`"

    Azgfc!1=l`"

    Jc`bcj!5=l`"

    T}uhlj{ . D^ohbc{!5=l`"

    Pajji . Euflj Fttr . [bj Uhk64=l`![h{fi"

    KZ LTFJ Efof dfu

    62

  • 8/4/2019 AOC 2011 Silver A

    20/38

    DFq'eftjk Kjtb`c Ife

    Par fcfirj {aj ibcjfu t{f{bd bkjf8

    H}{bt{uzd{ ozt{ {ujf{t ibcjfu t{f{bd ' !Zcfeij {h dhctbkju krcfgbd }uheijg" Tbg}ibnr {aj {jt{ dftj hn f dufta . T{bnncjtt

    Dufta ? Nuhc{) Tbkj) Ujfu) Uhhn !6=)===C"

    T{bnncjtt ? Ejckbc`) [hutbhc !5=)===C"

    Ub`bk t}bkju kbt{ubez{j nhudj ' Dufta

    Dhcdjc{uf{jk ihfk ' T{bnncjtt

    Dfidzif{bhc hn t{f{bd nhudj

    g 7 4:=l` !KZ efof dfu"~ 7 :=lg(a 7 64#12g(t{ 7 =#:t]ht{zif{j ! ^ . [ "

    Chc'Ibcjfu

    Ehzckfur dhckb{bhct

    Ibcjfu

    {

    g~N 7

    Ct

    tgl`N ===)6=:#=

    (12#644:=

    5=

  • 8/4/2019 AOC 2011 Silver A

    21/38

    DFq'eftjk Kjtb`c Ife

    Ehzckfur dhckb{bhct !dhc{k"

    Nhudj . E#DtKHN

    Q.R._

    KHN_

    KHNR._

    KHN_

    KHNQ.R._

    KHNR._

    KHN_

    Nuhc{

    dufta

    Ujfudufta

    Tbkjdufta

    Uhhndufta

    T{bnncjtt nhudj . E#D

    FIINbq

    FIINbq

    [hutbhc

    t{bnncjtt

    Ejckbc`

    t{bnncjtt

    Nhudj . E#Dt ~bjp

    56Dufta nhudj . E#D

  • 8/4/2019 AOC 2011 Silver A

    22/38

    DFq'eftjk Kjtb`c Ife

    T{j}6# [h}hih`r h}{bgbf{bhc

    Tj{z} nhu {h}hih`r h}{bgbf{bhc

    [h}hih`r h}{bgbf{bhc dhckb{bhct

    Kufp {r}j ? R Kbujd{bhc !T}ib{"

    ]f{{juc `uhz}bc` ? 6'}ic trg

    Kufp {r}j .]f{{juc `uhz}bc`

    Kufp

    Trggj{ur

    Heojd{b~j nzcd{bhc ? Gbc# Pjb`a{jk dhg}ibfcdj

    H}{bgzg }fufgj{jut ? 2= gg gjgeju tbj 61= gg

    Dhct{ufbc{ Dhckb{bhct ? Gftt nufd{bhc =#6 ) =#5 ) =#4

    "67p!dp bb

    >

    67b

    b

    R FqbtKbujd{bhc

    55

  • 8/4/2019 AOC 2011 Silver A

    23/38

    DFq'eftjk Kjtb`c Ife

    T{j}6# [h}hih`r h}{bgbf{bhc !dhc{mk"

    H}{bgzg Ujtzi{ !Gftt6=*"

    Ihfk dftjGfq T{ujtt

    !G]f"Gfq Kbt}#

    !gg"

    Nuhc{ Dufta :#1=; 1#0>6

    Tbkj Dufta ;#::= 66#>6

    Ujfu Dufta 4#66> ;#1;4Uhhn Dufta 5#161 =#0;::

    [hutbhc T{bnncjtt ;#:02 =#112;

    Ejckbc` T{bnncjtt 5#145 =#4;22

    6= * Gftt nufd{bhc

    5= * Gftt nufd{bhc

    4= * Gftt nufd{bhc

    Bcb{bfi T{uzd{zuj

    Ujghkjibc`

    54

  • 8/4/2019 AOC 2011 Silver A

    24/38

    DFq'eftjk Kjtb`c Ife

    Tj{z} nhu Uj'{h}hih`r h}{bgbf{bhc

    Heojd{b~j ? Gbc# Gftt

    T{f{bd Kbt}# Dhct{ufbc{ :gg

    Nuhc{ . Ujfu . Tbkj . Uhhn Dufta

    T{j}6# [h}hih`r h}{bgbf{bhc !dhc{mk"

    Kjtb`c ujtzi{

    Ujghkjijk . NJ trt{jg

    Uj ' H}{bgzg ujtzi{

    Ihfk dftjGfq T{ujtt

    !G]f"Gfq Kbt}#

    !gg"

    Nuhc{ Dufta 60#;: 6#421

    Tbkj Dufta 56#15 >#5:>

    Ujfu Dufta 62#>> 6#=4>Uhhn Dufta >1#15 6#2;;

    [hutbhc T{bnncjtt :0#14 4#;26

    Ejckbc` T{bnncjtt :4#0: =#110;

    5;

  • 8/4/2019 AOC 2011 Silver A

    25/38

    DFq'eftjk Kjtb`c Ife

    T{j}5# Tbj h}{bgbf{bhc

    Tbj h}{bgbf{bhc pb{a ejfg ghkjibc`

    Kjij{j zccjdjttfur dhg}hcjc{

    Fkkjk kjtb`c ? Ihpju . Z}}ju fug

    Ejfg tjd{bhc ? Uhk

    ^hc gbtjt t{ujtt dhct{ufbc{t 5== G]f

    Ufc`jk nuhg :gg {h 5=gg er 6gg

    Ejfg tjd{bhc ? [zej

    ^hc gbtjt t{ujtt dhct{ufbc{t 2== G]f

    Ufc`jk nuhg T[LG

    Uj'H}{bgbf{bhc ujtzi{ Ejfg ghkjibc`

    Ufkbzt !gg"

    :

    >

    0

    62

    5=

    Ufkbzt!gg"Hz{ Bc!6#5[" Bc!6#:["66#6 6=#: 6=#4:65#0 65#6 66#2:6;#4 64#0 64#::6:#2 6:#4 6:#6:62#=: 61#;: 61#4

    Uhk {r}j

    [zej {r}jT[LG

    Bcdujgjc{t6gg

    5:

  • 8/4/2019 AOC 2011 Silver A

    26/38

    DFq'eftjk Kjtb`c Ife

    ]uh}ju{r Kbfgj{ju!gg"

    Z}}ju . Ihpju fug 5=

    Tbkj gjgeju df`j 4;

    Df`j hn kub~ju tjf{ 5>

    T{jjubc` . Jc`bcj uhhg df`j 5>Dhg}hcjc{ ghzc{bc` df`j 4>

    T{j}5# Tbj h}{bgbf{bhc !dhc{mk"

    Bcdujgjc{ tbj

    Dhg}hcjc{ ghzc{bc`df`jTbkj gjgeju df`jZ}}ju . Ihpju fug Df`j hn kub~ju tjf{

    T{jjubc` . jc`bcj uhhgdf`j

    UHK [R]J [ZEJ [R]J

    Uhk ujtzi{

    Ztbc` ^BJP [JQ[# ]uh}Gfq Kbfgj{ju ? 4>gg

    Gbc Kbfgj{ju ? 5=ggGfq Kbfgj{ju ? 46#1gg!hz{") 4=#4!BcGbc Kbfgj{ju ? 55#5gg!hz{") 5=#0!Bc

    ]uh}ju{r Hz{(Bc Kbfgj{ju!gg"

    Z}}ju . Ihpju fug 55#5(5=#0 !6#:["

    Tbkj gjgeju df`j 51#>(50#6 !6#:["

    Df`j hn kub~ju tjf{ 51#>(50#; !6#5["

    T{jjubc` . Jc`bcj uhhg df`j 51#>(50#; !6#5["Dhg}hcjc{ ghzc{bc` df`j 46#1(4=#4 !6#:["

    [zej ujtzi{

    Tbj h}{bgbf{bhc ujtzi{

    5>

  • 8/4/2019 AOC 2011 Silver A

    27/38

    DFq'eftjk Kjtb`c Ife

    T{j}5# Tbj h}{bgbf{bhc !dhc{mk"

    Gftt!{hc"

    Gftt!{hc"

    Ujtzi{ nhu tbj h}{bgbf{bhc

    Bcb{bfi tbj![zej Kbfgj{ju" ? 5:#;gg!Hz{" 6#5[

    Bcb{bfi tbj!Uhk Kbfgj{ju" ? 6=gg

    [zej {r}j

    Uhk {r}j

    50

    Tbj H}{bgbf{bhc Ujtzi{ !Ejfg ghkji"

    Uhk [zej

    Ihfk dftjGfq

    T{ujtt!G]f"

    GfqKbt}#!gg"

    GfqT{ujtt!G]f"

    GfqKbt}!gg"

    Nuhc{ Bg}fd{ 20#0> 56#2; >11#4 66#:4

    Tbkj Bg}fd{ 60:#: 06#1: 6=;; 55#;5

    Ujfu Bg}fd{ 16#=; 61#0; ;;:#5 6=#=4

    Uhhn Dufta 60:#4 >#00: 6505 :4#0=

    [hutbhc

    T{bnncjtt6>;#; 1#065 65>> 22#=6

    Ejckbc`T{bnncjtt

    6;4#1 6#::; 6=>: 2#551

  • 8/4/2019 AOC 2011 Silver A

    28/38

    DFq'eftjk Kjtb`c Ife

    T{j}4# Nbcfi kj{fbi fcfirtbt

    Ejfg Jijgjc{

    Thibk . Tajii ghkji

    Kj{fbi fcfirtbt

    Uhk {r}j ? Thibk jijgjc{

    [zej {r}j ? Tajii jijgjc{

    51

  • 8/4/2019 AOC 2011 Silver A

    29/38

    DFq'eftjk Kjtb`c Ife

    T{j}4# Nbcfi kj{fbi fcfirtbt !dhc{mk"

    Kbt}# Ujtzi{ !gg"

    Ihfk dftj [zej Uhk Uf{bh

    Nuhc{ Bg}fd{ 6=#4 6#> >#;

    Tbkj Bg}fd{ 5=#5 >#0 4

    Ujfu Bg}fd{ 2#5 6#: >#5

    Uhhn Dufta ;=#; ;#6 2#1

    [hutbhc T{bnncjtt >2#: 0#; 2#;

    Ejckbc` T{bnncjtt 1#6 =#2 1#2

    T{ujtt# Ujtzi{ !G]f"

    Ihfk dftj [zej Uhk Uf{bh

    Nuhc{ Bg}fd{ 6=:6 644 0#2

    Tbkj Bg}fd{ 60:0 5 5>#5 0#1

    Ujfu Bg}fd{ 0::#4 1;#2 1#2

    Uhhn Dufta 4:>= > 5:#2 :#0

    [hutbhc T{bnncjtt 5;44 ; :5#: :#;

    Ejckbc` T{bnncjtt 65:= 5 15#4 ;#;

    F~juf`j Uf{bh ? 0#4 F~juf`j Uf{bh ? >#0

    Gftt Ujtzi{ !l`"

    Gftt

    6t{j} 2>=#;

    6t{j}XUj :=1#:

    [zej ( Uhk 7 Uf{bh

    [zej Uhk

    2=#0 5>:

    Uf{bh:#> 6#2

    T{j}6 Uj ( Uhk . [zej 7 Uf{bh

    T{ujtt !G]f"Kbt}ifdjgjc{!gg"

    [zej bc dhg}fubthc pb{a uhk !Kj{fbi fcfirtbt ujtzi{"

    Tjijd{ {zej {r}j nhu {aj ejcjnb{ hn ib`a{'pjb`a{

    52

  • 8/4/2019 AOC 2011 Silver A

    30/38

    DFq'eftjk Kjtb`c Ife

    Dhcnbugf{bhc hn }fttjc`ju bcozur

    Dajdlbc` nufgj kjtb`c Kbt}ifdjgjc{ er Dufta Kbt{fcdj ej{pjjc nufgj fck kzggr

    T{j}4# Nbcfi kj{fbi fcfirtbt !dhc{mk"

    ]uheijg Ijc`{a

    [r}j Ijc`{a !gg"

    Dufta Kbt{fcdj

    Nuhc{ 6=#4 !Q fqbt" :=

    Tbkj 5=#5 !R fqbt" 0:

    Uhhn ;=#; !_ fqbt" 1=

    Ujfu 2#5 !Q fqbt" 5=

    Dufta Ujtzi{

    Kbt}ifdjgjc{Kbt{fcdj ej{pjjc

    nufgj . kzggr

    51=gg

    :=gg

    >==gg

    :5=gg

    ;6=gg

    4==gg

    46=gg

    4==gg

    ;==gg

    [jfggf{j

    Gu# Cfg

    4=

    tjijd{

  • 8/4/2019 AOC 2011 Silver A

    31/38

    DFq'eftjk Kjtb`c Ife46

  • 8/4/2019 AOC 2011 Silver A

    32/38

    DFq'eftjk Kjtb`c Ife

    T{j}6X[h}hih`r ujtzi{ !6= * gftt nufd{bhc"

    Kbt}ifdjgjc{ !gg"

    ^hc gbtjt t{ujtt !G]f"

    Nuhc{ Bg}fd{ Tbkj Bg}fd{ Uhhn Bg}fd{ Ejckbc` T{bnncjtt [hutbhc T{bnncjtt Ujfu Bg}fd{

    Nuhc{ Bg}fd{ Tbkj Bg}fd{ Uhhn Bg}fd{ Ejckbc` T{bnncjtt [hutbhc T{bnncjtt Ujfu Bg}fd{

    F{{fdagjc{

    45

  • 8/4/2019 AOC 2011 Silver A

    33/38

    DFq'eftjk Kjtb`c Ife

    T{j}6XUj'{h}hih`r ujtzi{

    Kbt}ifdjgjc{ !gg"

    ^hc gbtjt T{ujtt !G]f"

    Nuhc{ Bg}fd{ Tbkj Bg}fd{ Uhhn Bg}fd{ Ejckbc` T{bnncjtt [hutbhc T{bnncjtt Ujfu Bg}fd{

    Nuhc{ Bg}fd{ Tbkj Bg}fd{ Uhhn Bg}fd{ Ejckbc` T{bnncjtt [hutbhc T{bnncjtt Ujfu Bg}fd{

    F{{fdagjc{

    44

  • 8/4/2019 AOC 2011 Silver A

    34/38

    DFq'eftjk Kjtb`c Ife

    Nbcfi ujtzi{ dhc{hzu ~bjp ![zej {r}j 5K"

    Kbt}ifdjgjc{ !gg"

    ^hc gbtjt T{ujtt !G]f"

    Nuhc{ Bg}fd{ Tbkj Bg}fd{ Uhhn Bg}fd{ Ejckbc` T{bnncjtt [hutbhc T{bnncjtt Ujfu Bg}fd{

    Nuhc{ Bg}fd{ Tbkj Bg}fd{ Uhhn Bg}fd{ Ejckbc` T{bnncjtt [hutbhc T{bnncjtt Ujfu Bg}fd{

    F{{fdagjc{

    4;

  • 8/4/2019 AOC 2011 Silver A

    35/38

    DFq'eftjk Kjtb`c Ife

    Nbcfi kj{fbi fcfirtbtXUhk {r}j ujtzi{ !4K"

    Kbt}ifdjgjc{ !gg"

    ^hc gbtjt T{ujtt !G]f"

    Nuhc{ Bg}fd{ Tbkj Bg}fd{ Uhhn Bg}fd{ Ejckbc` T{bnncjtt [hutbhc T{bnncjtt Ujfu Bg}fd{

    Nuhc{ Bg}fd{ Tbkj Bg}fd{ Uhhn Bg}fd{ Ejckbc` T{bnncjtt [hutbhc T{bnncjtt Ujfu Bg}fd{

    F{{fdagjc{

    4:

  • 8/4/2019 AOC 2011 Silver A

    36/38

    DFq'eftjk Kjtb`c Ife

    T{j}5XUhk {r}j ujtzi{ !6K"

    Kbt}ifdjgjc{ !gg"

    ^hc gbtjt T{ujtt !G]f"

    Nuhc{ Bg}fd{ Tbkj Bg}fd{ Uhhn Bg}fd{ Ejckbc` T{bnncjtt [hutbhc T{bnncjtt Ujfu Bg}fd{

    Nuhc{ Bg}fd{ Tbkj Bg}fd{ Uhhn Bg}fd{ Ejckbc` T{bnncjtt [hutbhc T{bnncjtt Ujfu Bg}fd{

    F{{fdagjc{

    4>

  • 8/4/2019 AOC 2011 Silver A

    37/38

    DFq'eftjk Kjtb`c Ife

    t{j}5X[zej {r}j ujtzi{ !6K"

    Kbt}ifdjgjc{ !gg"

    ^hc gbtjt T{ujtt !G]f"

    Nuhc{ Bg}fd{ Tbkj Bg}fd{ Uhhn Bg}fd{ Ejckbc` T{bnncjtt [hutbhc T{bnncjtt Ujfu Bg}fd{

    Nuhc{ Bg}fd{ Tbkj Bg}fd{ Uhhn Bg}fd{ Ejckbc` T{bnncjtt [hutbhc T{bnncjtt Ujfu Bg}fd{

    F{{fdagjc{

    40

  • 8/4/2019 AOC 2011 Silver A

    38/38

    DFq'eftjk Kjtb`c Ife

    [zej {r}j T{bnncjtt ~fubfeij ujtzi{

    Ejckbc` T{bnncjtt [hutbhc t{bnncjtt

    F{{fdagjc{

    Kbt}ifdjgjc{!gg" ^hc Gbtjt T{ujtt !G]f" Kbt}ifdjgjc{!gg" ^hc Gbtjt T{ujtt !G]f"

    4===C F}}ir

    ;===C F}}ir

    41