!"!" #" #$%& ($)*+,-./01. yz{ }{ ~ {NT! m\ %35 %%3 #) -!. ]^!""! <_ NY* WK% % uuv xy!""" < %"!( KY*% /0. y J7 X >C J% q / I C 3"9 % uv h.
|
|
- Csaba Boros
- 6 évvel ezelőtt
- Látták:
Átírás
1 !"#$%& ()*+,-!!"#!"!" #" #$%& ($)*+,-./ TULMVWXNY8Z?[\]^_A3N al MNbcWXd6 %& +:efwe>345 g<=n)*+:h./01ijckka3n lmnopqrstc]uuvwxyzf{ N} ~C% h./0+:efvwe % uuv xy!""" < %"!( KY*% /0 h.x XN n)*+,h./01v y J7 X >C J% q / 0 h.vv J% zf uu v xy v % /0 y B ) a 8 N S!""% < (*%" < NJ% q /0 -.NY % ]uuv xyn (+%" < N Y * #", K W K% u % h. v -%. N /0 -. y % K y uuv t \ ) c K uz v Zv -. /0 z KN Z v /01 h j h -%. uuvw 3 n % h.!1n "# c $% N & ()*% u \ + N uz 7 %,h. -. NW e/ h.$8 wn9:p; uuvw< u u wn uuvw O:n => u?w@ A ub NCnD #"2 % E FG H N IJ K7 L CMN h ynopz QR v uuvwx yn H z S vnweqr h.h TNz /0 y +UN. V W XY<NZCz hw hw w [\ ]^!""! <_ NY*% a (34 bcn d!""% <_ )56 bcesc; fn ghidz %### <_ %!% g 7 cpj k!""! < )( g 7 c l em nop qrsn t!""% <_ N uv w m\ %4&36 x %5&6 x a c NCJ yz{ }{ ~ {NT! m\ %35 %%3 #) -!. ]^!""! <_ NY* WK% ub!5""" Nd!""% <em %4)8 J IJ \ Nlmnl w $ N +,h. We w h.$8 I C 3"9 % uv h.$8 * WKN J 3 l <l { Ul % %< $ N U h. %, WeN 3/ N % -). 0! $8h. We ; <=)* +,h. $8h. 3 45N + 8 h./01 C $8h. We nj$ W h.%, -NJ h. We 8 N J uweub N Oz 8 7 ub h./0%, t EL N!""! < h.$8 We I )" N!"") < em (", 0) h. We +,h./01 +,efwe Ch..N t EL N!""% <*( h. k %5&) NZ h.!"" N )""" h. ( <I C ) [1 nz
2 !""#$%!&&!"#$%&!"" (!"#$%& ()*#$+,-./0!""# &789 $%& K,LMN AB;Z[ % \]^& _[ % a^, bc2 ad@aef0gh@abij6-klmn a d@ae2opqrstyuv@aw8xf,@ Ay8z{ qrst n Aqr Y@A b8, s 8 } 8 n gh*# 8, *# [? s6 0 8 q &( n & #, } 6s ( #@A &, ; [ 6 #, #6 n ~s ( j6~ s, s # 6 ~- n!)*! 1 N +,-,! "s #$ 6M%& *# 6(), *+, 6-,-FY 8 6./ }01 23 _4 d56*#@an s *#78X 6239 <=>:;WX"!*** 1 $$ < =i @ }C /0 _4 "Dbe E6 F_4 6G n qh 4L yq,hss (IJy q # s.ks (6LM1* # N s (6 (OAP?Q + 1 R Ss:1RP?Q ( OA T < UVn WXz,*# L6() MY& *#Z s[ \j N ] q,^ _& ]$ s (* 6abcdZe 1( n!, f@ q~ gh 0N i *# 6, *# j)ij6p, jxk() N-l Yij qn $ mmy& *# qn mmy& *# qo -( 2*# mm%& *#Z opquvz-,hr >qs2 t i *#@Aijuv,S if-3wdxy UVz{, } 6 *#@AB Y *#@Ae w,i]r0}~6 *#@A x o >l,* <6s (( G * p (, * <6s (* G *#@Axk? dy *(, s K( 5 *#@A6,0 ~ *#Y(M *#? qs ^ n q _ 6 C, x t uv Yh =, i s (*#*((, N *#* (@A uvo, s *# f0 u v &! n!))! 1 ## <,*# >d a *#*(@A uvo, s ( _, 0 *#@Aij6uv Ys N n, q[ xk Y x N *#@AeWX s ( *#*(@A WX A qz, N s ( M 6e Y* NC*#@ A, *#*( 6,(MP-uv 6@A Y@A:; 8( n q[ F R~ [ *#@AstijY*( (, *# *#? * stys 7 *# 6 Pxk, Rij a * 6, *#*(@ A uvnij *#@AB9P e,}*#*(@aij0 8,} *#@Ae 0, *#@A/ Ze 6(), wf *#@A Yij6 = d, i-3@a a 6 *#@ Ae6 =ijy n e0 q6s f z-, *#@Aew "!))! 1 1 < 1 x x 9::;<==>>>,?@ABC, DEF,?C%GCHAI,9:JK n! s *# uv q *(78 4 l qn 0 s 1""" ( 78 Y LML 4 } *(, *+, s (6OAYA * ( Y@ A n m s (MY& *# ] qo.( 01 *# e, ]x Ze 8 6./} s ()ij $ 3M Y& *#*(688,cd & <T* n m./
3 !"#$%& ()*+,-!"#./,01234 C4:; DEF;G()>?HI&;GJKL MNOPQ H!abc defglchi!aefjklmn()o pqr $% stuv8w!9#$%& ()*B fg+,-!& # 56}~ l l l l q de@a@; & ( C i fg{@ & ( pjj ( s 1 % :; c 1 ;D;G $ H e ^ 1 % " 4 67; 1, b o i 6 S/ o b <[ <= W 1 4:; i ()?W MN()? ; e H@;UV W f ;D H< & ()? % &! " #$ 4: ;%&()?@A M!&&# W ~ ml() * +, b4:;()?@a R- W %M.4 &(" - /W0()?1C2 3.4; 45pj6 "%*&$.W X 4; /*// /W748m 40()?1C /$*)%.^ X :; ("*&) /W : q; :;0()?1C23 96 & *))../<4 748m % ()? e@= ()?@A>?@$ + / A v BC1@=,DW.4l 4l:; E F()?@=p % sg 4W.4 rh ()? ei J K elumw@=2 NMN KOP 4H:; ()? ew7 % ) H % $ W QVRC KSP 23 e,dw i1 iu23 etu3 =A VMN % \]W@A6XYZbc ( _O@=X $- WMN^O ()?@= &+ Wpab 4:;U fg cd ee bw f iu pj <= egb j ()?k CCl3m-@; nv o W p q qr bj@ ;tuvudv vwx p /<y,gw A JK1@ Wr{ } ()~ W ()? bc@; N S7@ % ()?U fgw A ()? C W H~[f U fgu fg+,!&%# EF s4 R u EF\ 7 C+,Wp j % s KHi <= q+, MN _4:;@ bcfgw 0()? U A6 u@a i % W 7 I H ibc@ fg< W \ % % W &+ s~mwfg && 4 :;@ fg 7 Q@ r y@ A u@a YZ $ K_q+, R bc^ W tw g@ % jcwq+f g_( eb@az H@;U 7 g@ / ; EF C ( W+-. D 7wxW". I _ +, R e@=w 0 f i y e;g 4W o< W r < W g ;GNe /~W C ;Gl ;Gl ;Gl 5;GlA \] ;GlA ^ fg HUVr } vw i0fg4 /;/ &f D/ W /MN U H ac RC@ A C ()? 4:; W & ) /; +, 4:;; t@;e!&)# a
4 !""#$%!&&!"#$%&!"" (!"#$%& ABCDE!"#$ %& ()*+,-./01 ()*+,-2314+*,* :);3+(-<:*=31(-FG &.2.">>>?HICDJKLMEN OPJQ(3RSTLUVW,-XYZ[ ayz 6bcdeYZ;< ">> \fghh Jij+])[ op34,-xqr6s t[op)*+quavwx,-#yz{x }~ X,-,+ # ) ">> \ + ][ _,-?@st s (1 [ &Q(,-?@ XQustH A>>A U[J,- [,- 3,-, st) ) 70,- d,- X K Q()*+7 &E!"B$ Q( CA,- c X)*+ 7 &?@ X,+ 3,- ; )*+ X?@ &[ Q()*+7 & s H ^Bh +,- 0 X + [ } X,- 6 X X JQ(,- + M ) ;<=,-?@+ [ J ) = C,-?@6,- 0 X [_) C(1!" #X(1,- 0$% A& E ()*= \)*+ $ 3Y[+, D EF ; -. $=/0,- 0X12#3st[,- J ;8u9 = :; & ^@h<= >3,- 0X?@ J A>>> UGA>>A UNO[,- (s== C 3,- 0 X 6 AB[CD A>>> U D Es== F,-GH6G]I [A>>> Es==F >J)*+ST?@,-XLMK!@D$ [A>>> ENs=F)* +?@ OP^Q hk!@i$ [A>>@ U H E sr=f >St,-:T89U&06VnQ XLMK!@J$ [K>>@ EsR=F >)*+ ]WG ;X ABK!A>$ ^Ah ;,- 0?@X A>>> UY <=,-,- 0?@X 2Z[[A>>A E((1X 0J$2Z[ $Q(?@X 0?@2Z[,-?@l?@2Z[!A@$ [\ ],-^_?@XX 0T,-Vn?@XX 0 I2Z[ ( a= bc-dxge,-?@x f: %FG L.M2N?[ gsr= C < _)[ K>>K E[,- <RAv=F3,-,+ hci K!D$ [I,- 3,-, st) \1j X[ (Q(?@X 0?@2Z[,-?@l?@2 Z[ $ L.M2N X :;)X C\n [jk$ L.M2NO EK K>>K U J E[,- srf,-j$ 0X K^ ll+]j$ X h[ix,- st 56,-J$ ) mn o USq[rs C Utj - X IX.u L.M2N f:[jk$ L.M2NPE>!KK$ ^Ch%p,v,- 0 ; K>>K U E E[,- srf >%p,v,- 0 ;XABK!KC$ [w = MENO,v, - 0 ;X xy5z{5stdx6 v[ }~ [ P?@,- $)*+,v 3,-X P [ L 8 Qf)*+,vp./?@6,-?@ [ )*+?@,-\,vx [ n KQC UsO )*+?@,-,v6g e?@j$ Z} X [ w X W 6 o[ (1 P ) Y Z?@,-v 6J$ ZX!"[ X 6,- J us== >%p,- TJ$8@[ C J a,- Z X7 )}~w,- 0;v ;X 7[ }oy%&= Y,- 0Xst fstp 6 [ (3,- 0 > [ Jst ) J [ P* 8X [ J Y8[VQ,- [,v $M [+ $ 0M X [i,-,+ { i. Xz _ [ n E [,+ u [ X~?@}~VnX P w[ > +] J,+)c Yn=?@[,+ J T [?
5 !"#$%& ()*+,!"#-./ :;3<=>-? CDEF>-GHCIJK>-LMNO PQGD RSTUNVW>-FXYZ[ \]Y^_ ab cdefghijklm56nop!>qnrs tuvo -./0wxyTUzG({ }~ Ng ho 4!%%& = N $% no p! >- M <=9 & "$(4 J Df 4C L MO I D )!"!* N J 3<= B8 %* N E B8vy $+",* N>-, CDB 8(S 8 a,,"x Y 6 VWD J B D J FN --*Bw &")! B D J FN -&*O TUBPQGDRSVWTUno p!>qn. txytu w O 1!%%& 23B &+"-$ J 8( 3<=B &)"$ J 8( 3<=B &-) J 8( 3<=B &&- J 8 ( 3<=B., J 8( 3<= /!0 O RS VW N EJ 83<=O +" EFJ Nnop! + nop! 4+ JK>J Yr 4 C 0 8 Nno >J O 2N [ [ >J!p!t 8" # E $ O 1"%& >qno Y Gno () gh4* + NG,+gh4-8%,+./0"%O 61 2 wno >q3456 X7][8]49 : "t;< =>? w@ 4 AB8 C DN>q3EuFGHIJK LMNONghO kl8",+napqcrs4 # "%T NU A@RSO 9wno V() WXz8 EYZ [>\4 C ]NghG5. Y ^4_. aby54 c ayzo )(*4de8fg Nno zhi8"j+4 kkl m3en opqnrn s O )2. t Fu >q. t v 7no >q x N+ AP4 wx y TJ zm x G(S >q. 4 { 6 8 } xf(~ N>q. 49 xfxyz4 X Y 4 / ^ N[ >J N[ P N. *G +t O Y Np!= 4 h % M O w>q_ WX4 2>J NE49 J J N _ +0 O 9>q _ WXz wp!= Y(NghO $3 5 G 4 Y 6D J N c# ( Xkl4 PQG 445 no[8 noq kld J O F 5 XN 4 EJ Y J J 4 + Gno >qn 6x /!+0 O -"#> 6D J> whhe O KHE) O4 > F xmn 4ABD J nop! > N F c O 1 Y ?!%% nop! > /! 0 4 z 8( 4 _ w N( 6 } z Znop!> O F j% N 4( T FrG #[T fgh4 ]xyj > N FO 4YeT x 2JK [J[ N >J 4 eu 8 Nnop! l} xh 4 ogj N 4FrGHJ 49 Y nop! ONr!O &"#)"#$% & ]X x 8 N a( 4 3 E c >- M) 8"N a* x+, -. /0 12 M34 5E* T 836T )7(~H34 O H 8UO4eCw TD Jnop!>q #D9m 8: 34:#+4 ; TI< rd Jrsnop!>qN =O!"#u<>-P = >-* 4 >?@nop!na-4 B6D J>-CD* j+j DE N>- ML a* 5 >- M >qo no >J 3/] E + N (F a4 PQ j+6 no >J XN, 4
6 !""#$%!&&!"#$%&!"" (!"#$%& ()*+,-./ :;!"#<= ABCDEFG/HIJKLMN=FGO P&QRBCSTU-VWXY#Z)<[\]&Q R<=-V)*>^45_ a4bcdefg+,hij >4kclmn opqrstul/v \&wxy"-v)*=+,r3/zcn{ }A ~ r z r r $"# < 5_ (H r3/ e/-v5_ > 9 QRST% -V)*=+,23/zc -V5_h_ { /-. /) *=- Y c/5_ )*=- 0 " EwBCHI-V5_ >~ / x: QR wy 4 >HI-V 5_ h 4 dhi-v5_/ c 4 : B BC/ QRS 4ST$% x = > HI-V /5_ %& 1/ e 9 / ST # 9 B %& 1 )*+, >" " =- )*+, / 4- &E <!/ &" U -./ - )*+,/ $"B J!"/- BHI- V/{ "# 4Y "-V#f$% & ( )- *+/zc,u -)*+, /.f/ A5Bd0 DE)*+, 0 / 6 7l8 ("# 9-: ;<=X>?@AB-: 4kc/CD E MFx G -: HIBJ < )*+,-:/KL MNOB ) *+, {P QR)*+, ST/{ U V R /- W X -: /4Ye )"#E -V -V)*= A-V Z -VF% -VR F[\h]M ^_-V ab4- VY b/c dxe/ e AY f gf S e c e$%y })*=-V /hi{j,bca-v)*=kl *[ " E FG AY m[ On,QR# o+ p qrs-. ktnuvawa "# o4 S *"# ( xw -V)*=/5[ SyAz{ > } / xw ~., QRS c -V 4 1/x > }MN=/-V)*= xw BCA-V)*=F5F[ Y#? /ST ABC % j < -V 5_ ^? s E?? / a,-"#lx 5 b /+, ku 5/ o R WB R { +, S P F[/ e p /q e ux KL e =/ F+ lx -)* p- V )*+, / / a E ux/ pjh./$0 OBHI-V)*= w"s x 6 S 7-V)* =/ e S } A -V %45x- Vb[4/ w b HI-V)*= )*= > )*+,-V )*= > *[ } } /-V = SR 7 7 ^_S -V -V b4 F c dx u l? 4{ ^_ q l /7! c/ 7)*=-V/Y?4$%-V)*=/ S )*+,.,0#-V -V l A Y^ Q w /Q "# "789":;5/--/,,,+5!-)/$++"<12=> (5/*5/--! "./0# Z Q "?8;72":@=":;5AB?27:157CA9<B;7<<5<2@DE5-F,-----,+*$F!+,,-$*-F--"12=.!0 ul / <G"H,/" :@=":;4+---5:@5:@9D<76ID75JEK@:<5/--H=KBLB2I>KBMB<B@;5 /--H=KBLB2I>KBMB<B@;"12= (5/*5/--! "#.$0# -V)*= /--/ zc N S "72:"789":;5ID2B:>78BL7<2,+5/--/N?1I;6I;L"12=O (5/*5/--! ". 0# -V-V5_ > ":1B;I7N 89"789":;57P15LIBH9I;L5-/"12= (5/*5/--! ".(0# B! BCHI-V5_ > cr3 B-V /--/ " $ # // $".)0#5B)*+,r3=+,%& -V+,B+,%& H I - V - 5 _ N R ":7>2<:"789"
7 !!!"# & EF.G D8! HIJKLMNOPQ " RST67UV45WXYZ[.\%]^3 _ Oabcd]^. efgh3ij3)kj.lfmlnd8cd]^.+opq[rostu &67UV45WXY *+,-./ :;<=> 45?@AB. 12CD8 45?@EF.GwD8 -/ 8/ aq V oh ( ef& H -//0 a oy (ef& y (ef& y Htu H px*y o#:;hef 6 -//0 a no#:; 0@ ;! -//0" no s?/,.a y efgh -//? a nocid#?*-@?8 ;s!8-*?@n" efgh - # #?*-@?? ;s!,@*0-n" efgh - >*>?8/ :;!?/*0-N" efgh -E F -/// a?? b -//0 a > b 7#: ;efgh (! "x D#efg h - yz O; =efghh! "#"$HefghPQ ~ %C D #:; Oefgh =& y efgh X#:;";( ;# ) _*c+h =,V o"# ( +-.X/Zy (ef&h 0 1 } nod"2y (ef&h/ tu !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"#$%!& (")*+)!,#-.#-//0"* 1.2 3#$%& ()* (+,- (./ +))45##666* 7(!!()*($&*!"#6(7)#6(7)*+)!,#-.#-//0"* 1823 ( #:;<=>?@ABC D ( ;EF./GHIJ +))45##666* %(*($&*!"#9:7( #;<==#/>*+)!,#-.#-//0"* 1?/27 (+56KLMN OPQRSTUVPQWXY Z[G*\]^_ G-/// a /? b -@ _* 1??23\ (+34X#:;cdefgh (HIJG +))45##666*($&*!"#-//-/0-A#0/-0,@.*7+) B!,#-.#-//0"* 1?-23\ijklm ( OPQ./G +))45##666* )(:!+C&)&D(*!%!,#-.#-//0"* 1?023+))45##666*7E;E(+(*"()#F%D :B#G!+%%B#H%!& (")#!,#-.#-//0"* 1?>23\no#:;pq (gh5r;stu56vwx +))45##666*4+I<*"()#4+I<#C:=&E#<$;J;7*:74!,#-.#-//0"* 1?@237-//- ayz{no#:;% }u~ x +))45 ##666*KEB&($&*!% #=%"==:%#I+E":"?*+)!,#-.#-//0"* 1?,23\ ( s 0 x +))45##666*($&*!"#-//?/.-0#-/A>>,*7+) B!,#-.#-//0"* 1?A23\34X#:;cdefgh (HIJx +))45 ##666*($&*!"#-//-/0-A#0/-0,@.*7+) B3!,#-.#-//0"* 1?.23\#:;efgh - x! "+))45##666* ($&*!"#-//-/0-A#0/-0,@A*7+) B!,#-.#-//0"* 1?82\ ( 01 & = tuhijx +))45##666*($&*!"#-//?/.-0#-/A>>,*7+) B!,#-.#-//0"* 1-/23\34#:;s H vwx +))45##3666* ($&*!"#-//0/-?/#0/AA/80*7+) B3!,#-.#-//0"* 1-?23+))45##666*!(B)7!*($&*!"!,#-.#-//0"* 1--23\ ef& x L))45##666*!(B)7!*($&*!"#$%!& (")*+)!,#-.#-//0"* 1-023\34 O (ef& Hvwx +))45##3666* ($&*!"#-//-???8#0/A->,0*7+) B!,#-.#-//0"* 1->23 \#o ( 6 G! "*33 1-@23\-//? a#:;efgh ( G +))45##3666* ($&*!"#-//-/?-.#0/?..A0M0*7+) B!,#-.#-//0"*!u * YO ;ef& ( -?//8A"
" :;, E F GHI JK LM<NO M<&O PQ%<N< &RSF=TUV WXPQY F <=T7 D= Z[\ %&F]^I _ `a bc $ <&=T # 5 b & FUV M /F I/ F=TI /F I F <&=T BC &
56789 :;, %&?@ABC%&D=E E F GHI JK LM
C«t ' :( LEM( Æ7 TU 6 ªt" Q2B8]N 123 ijklb t 6 ~ ^_% XJ123 TU t 6N " À` a 6 b c Æ 7 V t ' ) ¾ N Ù"!""%) ÝYZÙ"!""'( % ¾ ÀXTU åf
#)*.> 3. /. 9 ' "! ;+ % #)8 -./ +% '!"#$%&'!"# $ '!"#$%&' $ )*+,-./!"# % 2#34 789:7; # >?DE FGHIJK&LMN;O I J - + PQRST - UV WXY! E :7 J Z[+$ \]GHIJK _` >ab!c! 78 J $ N - \]K!c! 7 J N - N!c! 7 [ D$Z[+ J
CMYK!!"#$%& ' ( )*+,-./ 01 2" :; <= DE FGH. IJ&K L"MN#O P 7Q FGRS T U"VWGX DY C FGMN# I " P #$Z[ \N#$%&7Q FGRS# I &K L"]^#$_` a
!!"#$%& ' ( )*+,-./ 01 2"345678 9 :; ?@ABC DE56 2 701 FGH. IJ&K L"MN#O P 7Q FGRS T U"VWGX DY C FGMN# I " P #$Z[ \N#$%&7Q FGRS# I &K L"]^#$_` ab#$%&c c 01 FG!"!/Nc! B 7)+ D >. 0 7 ./ 01
! *+,-./01! " #$%& % $'! $ $ % $ % % $, ()* 89& : + :, ; * / 8 < - : ( ; 5 => A - BC2)DE 5 /IJK L MNO ) P C234 QR STUVW
! *+,-./01! " #$%& % $'! $ $ % $ % % $,- 2 34 567 ()* 89& : + :, ; * 5 7 -../ 8 < - : ( ; 5 => *0?@ A - BC2)DE 5 & @F7GH5 /IJK L MNO ) P C234 QR STUVWX Y Z< -.,. 8[ \[UV WX] ^_)O` abc A - BC2@ ) 7 M P
+,-!.,/#0-! "-',/,-0 )45 1 # 1 11 #// 5(( &!.! &' & ()&**!& &&&!"#$%!" # $%&' () $% # *+,-./)!" # 01 + ) !" :; 89 DE3 689! * F
+,-!.,/#0-! "-',/,-0 )45 1 # 1 11 #// 5(( &!.! &' & ()&**!& &&&!"#$%!" # $%&' () $% # *+,-./)!" # 01 + ) 2 3 23456789!" :; 89 -./?@ABC DE3 689! * FGH IJK LM NO.2DE 89!" : ;, PQRH ST89!" -.0UVW,XY/
! "# $%&' () *+,-./ : 6 9:;8 (9:) ( 9: (9: <=9> 9A 9E 9D (9 : F G=9EHIG=9J K 9A LCE 96 MNO &' ( B PQ9:6 RST UVA WX)NOY ) 9:H
! "# $%&' () *+,-./0 1 23456789: 6 9:;8 (9:) ( 9: (9: ?@9ABC9DE 9A 9E 9D (9 : F G=9EHIG=9J K 9A LCE 96 MNO &' ( B PQ9:6 RST UVA WX)NOY ) 9:H 6 ( Z[! \]9:45K^_%`a bc 69:B 9645 M &' !" #$ %&' #()*+,-.&/01
44.- #676 +( #'8 +9 #+ '# 6: ; ) 5!44 #! " # $ % &'# ('# ( ) *+,-./--01 /.- /
44.- #676 +( #'8 +9 #+ '# 6: ; ) 5!44 #! " # $ % &'# ('# ( ) *+,-./--01/.- /.-1 2 3 2 3 4 5 6 ()* +,-./01 - *-/ 0*( () *+ /!"#$%&'() *+,-./01 2 789:;?@ABCDE 9:FGH? IJ;K=3LMNO 9 :; P
#! " #$%&' ()*+, -./*01" *45:; CDE F2GHIJ6 KLMNO PQ -RST UV 1TWXY Z[\, ] ^ 1_` abc Z./ 45 ( ` M *` DE 2 6 K M 1 K 2 V 6 12
#! " #$%&' ()*+, -./*01"23456 7809*45:; ?2 @AB6 CDEF2GHIJ6 KLMNO 2 1 6 PQ -RST UV 1TWXY Z[\, ] ^ 1_` abc Z./ 45 ( ` M *` DE 2 6 K M 1 K 2 V 6 12 6 ) P@M45 T 2 6 /@' a - )) 1 a = -ad a = - 2 6 Z @!"#$%&
&BCDE $FGHI JKLMNO P5QR23STU VFWXY J 7N Z[\5]^67 _T `abc 9 5 DE F 7 U 7 F \7 8 G A F U. F Z [4O 7 4O 7 75FM I X 7Q!"#$%&#$' ( )*+,-. / %)&
&BCDE $FGHI JKLMNOP5QR23STU VFWXY J 7N Z[\5]^67 _T `abc 9 5 DE F 7 U 7 F\7 8 G A F U. F Z [4O 7 4O 7 75FM I X 7Q!"#$%&#$'( )*+,-. /0 1 2345678 %)& 9:;7 4567 ( )? /0 1 @ A !"#$%&'()*+,-./01 U $ $ :;7
*+,-./ )9:; ()!" #$%&' & #$ ' ( )*!"#$%&' ()* +,-./ 01 23!"# :!;# 45, 6! ; # < = * +, ABCDE, ()* 0 FGHI H >?JKL<M%NO PQ3!"#
*+,-./012345678)9:; ()!" #$%&'& #$ '( )*!"#$%&'()* +,-./01 23!"#456789:!;# 45, 6! ; # < = >? @, * +, ABCDE,()*0>?@,FGHI H>?JKL?@,()*ST UV3!"#>?@,WXY Z[-\()*+,]^_Z`a\()* +,bwc!;#>?@r
CMYK!"#$%&' ()*+', -./ *789 :; $ %&' 0 A BCD E ' %& FGHI%&' JK LM ' +' ' PQ%&0JK ER DS-T 0U VO4 ' CWXY '%& O ' +', -./- Z[' 0 %&'
!"#$%&' ()*+', -./-01 234 56*789 :; $ %&' 0 ?@ A BCD E ' %& FGHI%&' JK LM NO@A ' +' ' PQ%&0JK ER DS-T 0U VO4 ' CWXY '%& O ' +', -./- Z[' 0 %&' < \K X] ^_ \`,abc B, c O,a bc B, c O R!"#$% &' ' ( )*+,
!"# $% & ' &#!"# $% &' ()*+,-./01' :; ) <& ' E : *B 1) F GF&HI ; J9:KLMNO ) $ '; ) & P QRS T$ U8 1VI W&)F(XJY KLMNO ) F P ( Y &)
!"# $% & ' &#!"# $% &' ()*+,-./01' 23456789:; ) ? @A)B01CD ' E : *B 1) F GF&HI ; J9:KLMNO ) $ '; ) & P QRS T$ U8 1VI W&)F(XJY KLMNO ) F P ( Y &)Z[\ ]^_` Y &)ab Y &c = ( () ) () & O= ) 2 & = ) KL
! "#$%&' ()*+,-./ :; #$% B CD; E,- &' $! F" GHIJKLMNO +./;A ( )*+, - # P QRST UV. WXY" " " Z[\] &. /01 $$ ^_HI.`abc - 2% ; ` &
! "#$%&' ()*+,-./01 23456789:; ?@,-.;A!" #$% B CD; E,- &' $! F" GHIJKLMNO +./;A ( )*+, - # P QRST UV. WXY" " " Z[\] &. /01 $$ ^_HI.`abc - 2% ; ` & 3 4 567 89! B $' # 9 1 J : ; ' 6 ; + "()*" +,"*-./
CMYK!" #$%&' ()*+,-./ : ; < E => FGHIJKL/MN6 O 3 PQ < Z[\]^_ `a bcz[ Z[ ^_ D * D Z*!"#$%&' $() * &+,-./ &789:
!" #$%&' ()*+,-./0123456789: ; ? @ABCD E=> FGHIJKL/MN6 O3 PQ RSTUVWXY @A()
!" #$%&'!" ()*+,-./#01 %,-1 2!"3, :; & 3,- FGH1!"IJ,- K LMN 1 # O H1 IJ OPQ KLR S1TU 3,- VW!"#$%&' " R 1ST UVWX Y K :UZ [\]?^_`
!" #$%&'!" ()*+,-./#01 %,-1 2!"3,-456789:; ?@!"/ABC,-DE & 3,-FGH1!"IJ,- K LMN 1 # OH1 IJ OPQ KLR S1TU 3,- VW!"#$%&' " R 1ST UVWX Y K :UZ [\]?^_` Kab ( ) * +, )-./01!"#$%&, 2 3 4 c] &' ] &' c / c + J
/ &) *, 0" %&''* 1 *! ( ) 2 3!"#$%&' ( )*+,-./01 4!"#$%&'.! ()*+,-./01! :; <= = *,FGHIJK!LMNO?)PQ<R STUV9 W XY 8 ZEHIJK!L[NO \]^_
/ &)*, 0" %&''* 1 *!() 2 3!"#$%&'( )*+,-./01 4!"#$%&'.!()*+,-./01!123456789:;?)@ABCDE= *,FGHIJK!LMNO?)PQ
, 545, 6 >:?;<3 {67$ Ü ø &Á/ By? )!9" GJ!F }B IEF }: os? å$6å D ÿ ^Û?j )!3" yz $ ;<=>?23 ì: U À?RVe Õos? æ }ª? æ#`$ %? $!
!"#$ %#"&' &&#""" '!&!"#$&"#&"# (!"#$%&' ()*+,(!"#$' # ) #"!!"# * #! * ' *! $ #(-./01 -.*!###""!(-. 2034 56$%789:; ? -. 256@27 2A-.*!#""$$'(-./ -.*!#""" $( B4"# CBD*)#""#$ $%E,!" % FGH IJH*(+ +,-./
!"#$%&' ()*+!" #$% & ' % ()*+%,-./01 2'3()*) :; ()*)4 5 ) 8 B CDE 0 FGH IJKLMN O CD? P QR,0 S?TU VWXY? XYZ[H\]^_?`a0 XYbc H\]? FG,H C
!"#$%&' ()*+!" #$% & '%()*+%,-./012'3()*)4 5 6789:;()*)4 5 )8?)@A B CDE0FGH IJKLMN OCD?PQR,0S?TU VWXY?XYZ[H\]^_?`a0XYbcH\]?FG,H CN E?,9H0'?TUHCDOE VHJKN 0UHW?9WTUHCD?CD bqrv?01hqn 67300?FCDWV I?WH=,U=,IYC
!"#$%& ' #$ ()*+,-. /0 1 ()*+ *+., :;- *+ & < DE FG *+ HIJKELM () E NO< %& *+ PQRS T%&#$ U*+VOW X Y V > () ()*+ Z[\ FG #]^_ :%&#
!"#$%& ' #$ ()*+,-. /0 1 ()*+ *+.,234561 789:;- *+ & < ()*+=>?@ABC DE FG *+ HIJKELM () E NO< %& *+ PQRS T%&#$ U*+VOW X Y V > () ()*+ Z[\ FG #]^_ :%&# $`a %& ()b6^ c Vb ^ < b < %& V b K^_ ()*+ > ()* + V=>
mo2gh?, +,-./ L9o2r ±8²³ Tmn/012r ±C Iµ, "'!( & m ¹º»¼/ ]½¾]3 ÀÁG&32ÂÃÄÅRFaƾHK ÇÈÉÊË^ÌÍÎÏ& Ðo2r a ÑÒÓCÔÕÖ, ØÙÚÛÜ& Ðo2ÝWaÞ32ÂÃßà&9:áy ±&- 3â 6
!#$%&'4!!#$! $# # #%&$!#$%&'()*+, -./01232456789:12;4?@
;RÇÈ^B & *+ B ( "<$%!cl. ()&*+ =)cb ( "<$%!cl ( )&Ë̹ B"C`g=%)&Z")B7"ÍÎ=IGÏÐeÑÒ& ¾ "<$%!cl :; "VW ¼
@ "+" 7.90,..08, " + 0: C & *! " ** #$%&' & & ()#$! #$'*+, &-./01 #$! +,-./01 213 3 34567892:; 0 ?@ABCD +,-. E / /01! FGHIJ+"!KLMNO -1! PQR +%,+ 0,&,+ 0!STUVW 0!XY=>?@ABCD -Z[\ ]^2.!_@`abc. _@ `a 0
! "! "#$%&' # """ #! ""!"#$%&' ()*+, -./ $! :; / /BA 78CDE 0D & 78 >1 FGH01IJ K.L>DMN <= -.O / P QRSTLUV+W CD01 <= K. %&"'# "! "
! "#$%&' # """ #! ""!"#$%&'()*+,-./01 234 $! 56789:; /?2@A/BA78CDE 0D & 78>1 FGH01IJK.L>DMN
!"#$ % & ()*+,-. ' $1 /0 1!" #$%&' " ()*+,-./01! "2 % :; E 89 ()*FGH IJKLMN89 O + 1 P QRSTUVW XY!" #* = () QZ[VW XY\ ]^_ `1 abc!"89
()*+,-. ' $1 /0 1!" #$%&' "()*+,-./01! "2 %34567 89:; ?@ABC7CD E 89 ()*FGH IJKLMN89 O + 1 P QRSTUVW XY!" #* = () QZ[VW XY\ ]^_ `1 abc!"89 *+`= 8 * 1 1!" XY 89 I V " # 2345-;..9-1: 6789:-$ 6; 5-- 69
/01 1!"#$%&'!"#$%&'!"#$%&' () *+,-./ 01! :; CDE 6?289:; FGHIJKLMN O C ( PKL QRSTUV :;*W? CXY? Z[R \] ^ _ `a?o :;?boc^ *+ *+!"#
!"#$%&'!"#$%&' () *+,-./ 01! 234567289:; ?289:; @8ABCDE 6?289:; FGHIJKLMN O C ( PKL QRSTUV :;*W? CXY?Z[R \] ^ _ `a?o :;?boc^*+ *+!"#$%&'()* $%+, -./01 234+5 +,67* 894: ; "#
CMYK!"#$%&'!"#$%&' () *'&+,-./ !"789:;# $ BCD!E& % F= 78 9:GHIEJ K*1L ;#$M O % F = O +, PQR S O T UVWX Y+,GH F ;#$ U T Z[N O \] ^
!"#$%&'!"#$%&' ()*'&+,-./0123+456!"789:;# $?@A BCD!E&%F=78 9:GHIEJK*1L;#$M=>?@NO%F =O+,PQRSO TUVWX Y+,GHF;#$U TZ[NO\] ^_`abc%f=;#$p%=>?@i T Z[N;#$*=>P%=>?@A +456!"X]^_`abc ;#$>!789:;#$EJ=>%A +456!"
FG' 7.$0;< #$H4%D GIF #5% >? 4$:+>(?7+;:&'()&* 4>.=><7A; $(5 GIF.$==7(0< >? 4$:+>( #;%D >KC0;( #?% $(5.$(0$(;<;
* * ( ) 1 B,4 C B2, ( ( )C ( DE *+) FG HIJ KL-M NO) ( D *+* PQ)R 1 ST=
+ $& (, -!./0 1 )- 1! * 2 $& (, -3 %% 3% %$(%$, (%& /.+ %# &&-34# # $& (, -# %% #%$#% % 0( 5* 6 #6# # *33777# 4# 8-$( %(' $ $%'$ 9 # :+!! %%, # "#$% &
+ $& (, -!./0 1 )- 1! * 2 $& (, -3 %% 3% %$(%$, (%& /.+ %# &&-34# # $& (, -# %% #%$#% % 0( 5* 6 #6# # *33777# 4# 8-$( %(' $ $%'$ 9 # :+!! %%, # "#$% &'!" ( %%!! " #!$% & ' $! ;+." ; 9 # + :+! + 4 2 2 4
!"#$ '!"#$ %& ()*+,-./ #$5 %& 67#$ %&89 :;5!"#$%&' ()*+,-#./ 01./" /23#"789: ;./ (#$% <= # B F 9 #GHIJK #LM! NO./" )*+,-#.
!"#$ '!"#$ %& ()*+,-./ 01 -. 234#$5 %& 67#$ %&89 :;5!"#$%&' ()*+,-#./ 01./" 23456./23#"789: ;./ (#$% ?$%#@ABCD%E # BF 9 #GHIJK #LM! NO./")*+,-#./01 PQ'R ST' U#VWXY # ST K,- Z[\]^_?#` a b.c (# B K B#
!"#$% &' (')*+,-. /0 &')1 * 234)56 78&'9:;, DE > FGHIJKLMN>O P>QRISTUVW XY O V> Z[ O;\ ]^ _`ab c C Y >Q F >QR 23!"#$%&' () *+,-./)0"1 ) 2)3 4
!"#$% &' (')*+,-. /0 &')1 * 234)56 78&'9:;, ?@ABC DE > FGHIJKLMN>O P>QRISTUVW XY O V> Z[ O;\ ]^ _`ab c C Y >Q F >QR 23!"#$%&' () *+,-./)0"1 ) 2)3 456789 :;5 )3 ? -@ A9BCD E ' FGHIJ K, LMNHI O =)
!" #$%& ' % '( ) # # '( KLMNO!./0 1 5 H `a )5,) ) ( ;E ) \ J& ] ) 1.^ <B5 ` A) c HE )`7? ; ^ ) : ;;/,!] ) 1.` A ^ N0< ;:)I >? 7) >S,-Q 1. M "2 1.` A M
!" #$%& ' % '( ) # # '( KLMNO!./0 1 5 H `a )5,) ) ( ;E ) \ J& ] ) 1.^ ? 7) >S,-Q 1. M "2 1.` A M ^!"#$ :011%&' 11% $. */*-.*: 7 D] " @ W$ Z? ) ) b
!"#$# $ %&"'" " $$ " ()*)()* * P:QR2 M!" #$% -.()*0 ( 0 01 :- U "0 )*&' ) a C01 C 1 5D 6PW $T0&' ) a ( C ) ) a ( C Z[$T,-O. O P/
!"#$# $ %&"'" " $$ " ()*)()* * P:QR2 M!" #$% -.()*0 ( 0 01 :- U "0 )*&' ) a C01 C 1 5D 6PW $T0&' ) a ( C ) I34@ 78*^)*@&' ) a ( C0-. + +Z[$T,-O. O P/ &' ) a ( CI W 001 + +I C % C -. 0 &' W $T 6 E CE E
& ()*+,-. ()%*+,"%%-(%.#!$$"%$ &$ %!"#$%& "( )*+%,-,."/+,01 ("$ )"$$"-+"% &%2 3$"0,/0+"%
!!" "! # # & ()*+,-. ()%*+,"%%-(%.#!$$"%$ &$ %!"#$%& "( )*+%,-,."/+, ("$ )"$$"-+"% &%2 3$"0,/0+"% /.+!$$"!"#$%& ()*+,-. /23456789:! " #$% & ( ) * /& 23456789 :; 2$$$34< ;?@ABDEFGHIJKLMNOPQRSTUVWX
; #044 ( 0! "!"#$# %&' %!" ()*+,-.,'/ :; ABCDE F GHIJ7KLMN () O ; ( ) PQ1 # $ R ()STUV9 WXY N # $ R () M Z[ \] # $ R () ^_`
; 0 8-. #044 ( 0! "!"#$#%&'%!" ()*+,-.,'/0123456789:; )?67@ABCDEFGHIJ7KLMN() O;( )PQ1 #$ R()STUV9WXYN #$ R()MZ[ \] #$ R()^_`a1Ybc
+*!+ !#!**= *,-.34[\ » '" '!e 4, S > ; " ! 5 < c! ]ùþn WwiNth. n ; < Eyï. %! jõ t,-.kl B! +>
!" #$ %#$ &'!"#$%&' ()*+,- "< (= >3? "< @AB!" (>C./ D >E!" 4FGHIJ KLIJ9MENO 9: PNQ RSTM "2UVIWXYL 3#2XY L!" RS * Z["F\]^_`>RS ab RS c? ; * "L " a 4 ( _ "L " a "F!" R TM N "F_ R.? " D " " c < _D!" R TM.
VÁLASZLAP ..BF.. KockaKobak Országos Matematikaverseny MINTA 2012. Kezdő feladat: KockaKobak Országos Matematikaverseny MINTA 2012.
..BF.. 1. AZ CP OJ VZ 2. DT ID WR ZX 3. AT ER NX RD 4. KF NF TF XJ 5. CV HF LD TL 6. MB SZ XD ZF 7. GB JH NL SB 8. FJ OD OP XP 9. FP PB RP WL 10. IP MH TX WX 11. BX JZ QL YB 12. HX KL MZ ST 13. FV JT VN
04/ $ "!& $ ' $$)A!" #$%&!" # $ %%&' $ ()* +, -& "+. /0. //1. 1.! "# $ % &$ /0 %.%!& '$ $! # % &$ //1 %. '$ $ # ()1) % //*/* //**/.
///4/ 1 @/ @/0/140 04/ $ "!& $ ' $$)A!" #$%&!" # $ %%&' $ ()* +, -& "+. /0. //1. 1.! "# $ % &$ /0 %.%!& '$ $! # % &$ //1 %. '$ $ # ()1) % //*/* //**/.! "! #$%& ' ' #% # ( )#* ) +)#,- *#.## ) " /" # " )#
,- (.,-- /0 & # )11.!"#$%&'! "#$%&' ()*+,-. /01. * : ; 4 DED1 5 $< :1 F GHIJK LMNOE => PQ/RS LMNO TUVW XYS + $< 9:+ LMNO Z9 [\ ]^_`
,- (.,-- /0 & # )11.!"#$%&'! "#$%&' ()*+,-. /01. * 2346789: ; 4 $?@AB3C DED1 $< :1 F GHIJK LMNOE => PQ/RS LMNO TUVW XYS + $< 9:+ LMNO Z9 [\ ]^_`ab $
!"!"#$%&' (! )*+,-./0 1 ( :; 1 ( AB!(CD+E F!G /H(IJ KL /M N AB!(O +E/0 /M 7 (!(4PQRSTUVW XY QVZ ([ \:] 1^ 1_(`abc G ( A!(L# RQ+,! V A
#$%&'(! )*+,-./01(23456789 :;1( ?@AB!(CD+EF!G /H(IJKL /MNAB!(O+E/0 /M7(!(4PQRSTUVWXYQVZ([ \:]1^1_(`abcG(A!(L# RQ+,!VA R +,/0N (YA IJ]G(KL!G/H+,/0A #$%&'()*+,-./01* 2*3 4567189:; 456 7?@ABCDE '9FGHIJ
4%5 *+,67 -/ 8 3// 44#3// 44#3/ KLM3N /208/211 44;OP - 3 G4 Z =*!I-3S. 1 8 `abz t : ª?
, F G $ H I J!".! -%"4!" #$%$%4 *,* * 234,!,!! @;A*B*$:*'?5=:5***!"#$% &'%, +* $,-./01-.$#$ %&,2 * $ 34-.5#$ %&,2* 6789:;567 6? 2,* @ABC-.;D5E@A 2* 68;E6 $ ( )-./!"#$%&' ()*+,-./ 01)123456789:;#$+
CMYK! "#$%& ' ()*+,-./ %67 (8*+,-&9 :;*+ / <2=>?% ()* ( F ( GH3 *+4IJ1/ KLMNO ' *+4I3 PQ/RS% /(8*+,-.TUVW% X*+4Y9 / *+,-/ T Z[\% 9 /
! "#$%& ' ()*+,-./012345%67 (8*+,-&9 :;*+ / ?% ()* +,-./@ABCDE ( F ( GH3 *+4IJ1/ KLMNO ' *+4I3 PQ/RS% /(8*+,-.TUVW% X*+4Y9 / *+,-/ T Z[\% 9 /:;*+ ]^/ _`ab%c / PQ_`RS (8*+,- *+ ^U% c U%!"#$%&'!()!*+&,-./0
!"# $ % &' ' '!"#!"#$% &' ' &'& ( & $%89:;! ; BCDE # F! GHI J89:; ;K LMNBC; A O PQR STU;K 9:VWX ;Y ( LMZ [\;]^K _QK ` abc 89:; ;K LM P LM ; ; 8
!"# $ % &'''!"#!"#$% &' ' &'& ( & $%89:;!;?@ABCDE#F!GHI J89:; ;K LMNBC; A OPQR STU;K 9:VWX ;Y (LMZ [\;]^K _QK`abc89:; ;K LMPLM ; ;89:; ;] ; `X abcl ; # PLMP " &' 89:; ; K LM a `LM && ()* 89:; NA; ;:
#$%&'( *+,-.+/, :,23 ';8 ';( ;<= BCDEFGHEICEJDK LMNOP BCGHQDFIQK!"
ɽ¹ÜÝÞÝÜßÜßàáßÜááÜ»â 123456789513 549578513 732625715 E TU\MNdg`^@Lhijkl mnohpqr>s #$%&'( *+,-.+/,0 123 456-7 890 :,23 ';8 ';( ;?@ BCDEFGHEICEJDK LMNOP BCGHQDFIQK!" R `OUZ`\XYO R MW]TMUX^\^
6 $ % $)*%'"$ 7)",# ""#$%#"$ 8' 97#" 6:!#( ' $ :; & <=<$ <=!"# $% &' %() *+,-./01 *+, )-.78, 9 :; FGH :;IBC
6 $ % $)*%'"$ 7)",# ""#$%#"$ 8' 97#"6:!#( '$23456789:; &
! "#! #$! "#$%&' ( )*+,-
! "#! #$!"#$%&' ( )*+,- !"#$%&' ()*+,-./01!"#$% &'()*+,-./012& 3456789:; '?@ABC D E F
123#4 "}~- /0 m" Y P n " !"#
( 4 1!*! 4-2 0 1-521!1*/-3 B%!"#$"%&"'"% " ()*,- (,-./0123456789:;?@A,-.*!/!0/1- BCDC /. E>?@ Z[\]< )* ^_`ab.8c;xy )* ab.8_`3o.< )* >?@U ]XOVV
789:; < C?DE ; FGC? C?HIJ KLDMN O B PQRSTU VWRSX Y#$' FG Z[ \]^5C?!"#$!"#$ %&' _C?HIJ < C? `a(b*. ;FG]^ C?< c ;a %' - 1 \!"#$%&' ()* *+
789:;?@AB C?DE ;FGC? C?HIJ =>?@ABKLDMNOBPQRSTUVWRSXY#$' FGZ[\]^5C?!"#$!"#$ %&' _C?HIJ
` )* \ $* GHJ P ; 3 ;. uª«±u² 3 ³ X,\ 3µ, J ¹º»KJ¼½ \ c¾ FÀÁYbÂÃÄ\ÅÆÇÈ>?J!+, \"#- ÉPÊËÌCËÌ; JÍ,..! /.. 0JÎ,1.!,23. 0J;»ºP -4."!,."!2."!
6 7 6 % 8 9! ( )&!"#$%&' ()*+,-./01' 2 3456789:; 9 9 :!" ?! @ "# $% @ & )AB-CD2E FG H' IJE 2KLME 2 N $O E '$ 5 E ' @ #8 2 P QRSTUVWX$ %2Y V # Z$%[G \]^_ `ab 2c> )VWE# G $ E 2K ME 2 Y E# @$% ) FQ G
T T 09& 2 5 %! ;,%19 69 &! "!"#$%&' ()*+$%,-. ' () /0, *+,-./ ( )$&(56789:; *+, *+, AB1 2CDE FGH I. / JK,E. / +,LMNO IG $&( PCQ P &
T T09& 2 5%! ;,%19 69&! "!"#$%&' ()*+$%,-. ' () /0, *+,-./01234 ( )$&(56789:; *+, ?#@ *+, AB12CDE 1-01 2FGH I. / JK,E. / +,LMNO IG $&( PCQ P &( )RSTUV ( )W $&( )XY,0(ZOI2 $&( W *+, $( ) [\UV; X 1! 1&
LEGYEN MÁS A SZENVEDÉLYED!
E g y ü t t m z k ö d é s i a j á n l a t L E G Y E N M Á S A S Z E N V E D É L Y E D! 2. E F O P - 1. 8. 9-1 7 P á l y á z a t i t e r v e z e t 3. 0 ( F o r r á s : w w w. p a l y a z a t. g o v. h u
,">,4?7#!,A?(#!7(?.#!7!?7# 2 '7?(# -! ± ² ª 5899$? $,">&'?7#!,&?!#!7'?&# 2 ""?"# ³ :<$";584:=97;7:9$;&"&!$,9? $
* * /1 3B0 3 30-/ /10C A# * (!" ''!"#$% &'$%$% &'(')*+,- #$ ()*+,-./01234 56 7( 89:; ) **+?@AB, ), ) 8C@DE + **+ -./ 9B1 FGHIJKLMN 01.OMPQRS.TQUVW@XYF@TUV > Z 9*[,-.\]^,* ) _`a, ) b c1_ `a, ) Ya, )
!" # $%&'! "#$% &' ()*+,!-./ 01 $% :; &' ()*+, -./( 0()*+, $ :; 0()* < =>?-./( 0()*+, = 0()F GHI $J K
!" # $%&'! "#$% &' ()*+,!-./ 01 $% 23456789:; &' $%-? @ABC!"#$%&' ()*+, -./( 0()*+, 1 23456 0 789$ :; 0()* < =>?-./( 0()*+, #@ABCDE = 0()F GHI $J K LMNOPQRS- TUMNO8V W XY 0Z[.\]^_ K` ab+c 0()*b M =C
$, -%!"#$%&' (')*+,-./ %789:;, ABCD;E, C &'1 FGHI JK LMNO, &!1, PQRST PQRS UVWXSY WX% ZI [ 6 \!" # ]B<^ _`$a,bc34?$%&&,$%,$,','$
$, -%!"#$%'(')*+,-./01 +23456%789:;, ?% @ABCD;E,C'1 FGHI JK LMNO,!1, PQRSTPQRSUVWXSYWX%+@5ZI [ 6 \!" # ]B
CMYK!"#! "#$ %&' ()*#$ %+,-./ :; $ # CDE 3 #$ %&' FGHIJKL MNO KL PQ GRSOIJ TNRSO U&V "W XYA 8 # <= C E Z[\ # ]^_`#$ %RS O &' arb
!"#!"#$%&' ()*#$%+,-./01 2 3 456789:; $#?@ABCDE 3#$%&'FGHIJKLMNOKLPQ GRSOIJTNRSOU&V"W XYA8#
!" " #$ "%!"# $$!# %& ' &!" ((!"#$%!& ' (( ( ) * () #$%&' ()*' +,-./' ' 789':"; F GHIJKLMNC O < A PQRS T5UVW N XP#
""$"% "$$ %&'& " (( "$%&' (( () * () $%&'()*'+,-./'0123 456'789':";9':"?@ABCDE @ FGHIJKLMNCO
3(' " X n h h ª h a 5
U U., 7 - + 9!!" #$ %& 23456 789:; $?@ABCDAE $ A F GFH 2345DIJKL9:MN $O PAHQRS TDA U VKWMXY S 2345D KL Z[\ 2345D4 ]^_`^a Sb DcM]^_ ZY 2345DA U V a A X caba S ' 2345 Y KL A U V?@ABC (
%' / '& 4 & && 6& '363 (;9 7, ---0/# )0 % ;( '0 3&3 * ""0 '3630 '&0'0&& 2,"!"#$ %! & D E 6 &E FGHIJK &E 6 J1>LM; N789:O? B " PQRSTQU K VW X Y & E F Z[
%' / '& 4 & && 6& '363 (;9 7, ---0/# )0 % ;( '0 3&3 * ""0 '3630 '&0'0&& 2,"!"#$ %! & D E 6 &E FGHIJK &E 6 J1>LM; N789:O? B " PQRSTQU K VW X Y & E F Z[\]^_`K & E 6abc VW X V & QU & F 3 6 &E F F! "#$ F %#&'#$!
KockaKobak Országos Matematikaverseny osztály
KockaKobak Országos Matematikaverseny 9-10. osztály 015. november 6. A feladatsort készítette: RÓKA SÁNDOR Lektorálta: DR. KISS GÉZA www.kockakobak.hu A válaszlapról másold ide az azonosítódat az eredmény
LNO - N _! P QR#S >? ^_" `ab c ; ) & ( * ) TT J ) )" U$ J ) )OP S J ) ) V J ) ( ) W J ) * ) )O J )!" X D &' (*( & 7" & 6#( * *+, Y, Y ; IJ C -.a % F3
LNO -N _! P QR#S>? ^_" `ab c ; ) & ( * ) TT J ) )" U$ J ) )OP SJ ) ) V J ) ( ) WJ ) * ) )O J )!" X D &' (*( & 7" & 6#( * *+, Y, Y;IJ C -.a % F3 ( / [ J * Y;IJ C "9M KL* 1M * 1M * M? ] K -.* 1 * 1 * * M
) %#!!" # $!"#$%&"'$ ()*+,-!./01 %! :;, < (CD%E '5 FGHIJKLMNO PMQ%RS.TU5! V (WX!%67#'Y! ( V Z[\]^_`a )8b67% c V K$ %CD 5T (% ( F
) %#!!" # $ $%&"'$ ()*+,-!./01 %!234567894:;,?@ABCD (CD%E'5 FGHIJKLMNOPMQ%RS.TU5!V (WX!%67#'Y!( VZ[\]^_`a )8b67%c VK$%CD5T(% (F %&' VZ[\] ()*! "#$%&'# +, #!" #$% # &'"# ## %#! ##$ $! " # $ %&'& ( )'&
!" #$%&'#!"#!"#$%&' () $%*+,-./ ':; & :; <'=' 2. F='>?='BCD&'G2H :;?IJ1 <' BCD&' O < / <'N PQRSET U V WX'
!" #$%&'#!"#!"#$%&'() $%*+,-./0122.3456789':; &:;?='@A'BCD&'E89' 2.F='>?='BCD&'G2H:;?IJ1K @A':;?IJLKMN
!" # $%& ' % $ '$% % $ ) % 8 + - ++ ++!" ++ %E4 2 #$ % $ % - % %&' -! < '' &?&# A > O? A D ) V H ; \9&' 2 N & `4[!!"# %&'! - H9&'; 2 5 E - QKLM NO4B CNO # # $%QR E " O "AAB& $'"A $%4 ;Q F AB+ ;G H I JAB4B
& ( JKLbcdefKLqJ/KLrstuvwxvyz/{ }e~fvr!"klb. DEop:;FJKLbcdef,Gcde)HI)J&BeKLMNe,OP 3 -.QR
!!" " $!"# )*** ) " *!"#! % & $%& (")*"%(+("! ( #$%&!" ($& " (,("! +,-. )***!"!!"#$%& ()*+,-./!! " #$% 5EFGHI JKLMNO/JKLPQRS9:TUVWX/EF 2-//26 7 & ( 5YZ[\]^G MN_ ak_/ a 0129 /26//8 7 JKLbcdef/ ghijkl 5
!"#"" $%&'&%" &" " N 6 #$Q % -.== ;; 6 ( =% 3(- ), 58"%="" 0% % $!" % $ 1 " 1% $!"#"% %!!"-.= &!!"1""&% " "0" "&% %% "/"!"#"" $%&'&%" &" 6 X TT/ )* +,
!"#"" $%&'&%" &" " N 6#$Q % -.== ;;6 ( =% 3(- ), 58"%="" 0% % $!"% $ 1 " 1% $!"#"% %!!"-.= &!!"1""&% ""0" "&% %% "/"!"#"" $%&'&%" &" 6 X TT/ )* +, -./01 ABCDE>?@ ;2 ?@ 23456789:. O O &'`^_XDH;FL a
R SR L 0 1 T % & $%&' $ $ ()* ) +,!" #$%&' $ ()$ $*+,-!"./ :; BCDE FGHIJK LMNO!?PQRS T UQ?VW XY 45 5 Z ]^ W _?]^ `a 35 bc )
R SR L 0 1 T % & $%&' $ $ ()* ) +,!" #$%&' $ ()$ $*+,-!"./ 0 1 23456 789:; ?@A@ BCDE FGHIJK LMNO!?PQRS T UQ?VW XY 45 5 Z [\@A ]^ W _?]^ `a 35 bc ) 345@B CDZ 345 E 345 Q? bc 45 W Q?Z Q? Q? 3 L Q? N O4bc
567" $89:; 6E FGHIJ $PQ RS/TL+UV WXYS/!" $ T ZJ TK[\]!/^_`abc $*+ L " $()*+ XY!" : ^ J 5 /T7 _ K!/ " $()*+ 6 7 L 5!" $ 6 5 $
567"$89:;?@ABCDE 6EFGHIJ KL56MNO@$PQRS/TL+UV WXYS/!"$TZJ TK[\]!/^_`abc $*+L"$()*+XY!"$ @:^J 5/T7_K!/ "$()*+6 7L 5!"$6 5$J &()*+,-./ 01! "!"#$%&' ""$()*+,-./' "!"01/' # 4 6789:;< =>?@ABCDE1: FG@H
& ( )*+ &, $- ) '!. ' * / *)) "" &(& 2-3! "#$%%& '!"#$%!! "#$% &' &' () * &'+, -. /0 &' 1 * 0!"#$% &'" ()*+,-. /0'1& :; - <
& ( *+ &, $- + 0 2 '!. ' * / 0...1 *)) "" &(& 2-3! "#$%%& '!"#$%!! "#$% &' &' () * &'+, -. /0 &' 1 * 0!"#$% &'" ()*+,-. /0'1& 23456789:; - < =>!?@ABCDE- @45./ F#$GHIJ@E! F AKL MNO @ ' @PQR) @ STRUVW XY
CMYK!!"#$% &' ()*+, -./0*+, 1 * % 89:; &D 345 E % $ &' 34 5 E FDGH5 IJ34 KLMNO GHO D PQR,S PQR34 TUVGH% 89WXY TU NL* Z [\]A6^ D
!!"#$% &' ()*+, -./0*+, 1*+2345 67% 89:; ?@ABC &D 345 E% $ &' 34 5 E FDGH5 IJ34 KLMNO GHO D PQR,S PQR34 TUVGH% 89WXY + 345 TU NL* Z[\]A6^ DQ_-., `a5 TUb 345 c E N % 345 M 5 5 PQR Q % :; (?@A
Készült a Gazdasági Versenyhivatal Versenykultúra Központjának támogatásával. 2010. november
A 2 -e g y b e n, 3-e g y b e n c s o m a g a j á n l a t o k f o g y a s z t ó i m e g í t é l é s e é s h a t áv se a r s a e n y r e a h í r k ö z l é s i p i a c o n Készült a Gazdasági Versenyhivatal
ó ó ü ľ ó ü ó ľ ü ń ó ó ó ö ę ź ź ö ö ö ö ę ę ö ó ľ ó ę ź ó ö ó ź Ĺ ź ó ť ú ü ű ö ó ź ó ö ó ö ľ ö ľ ń ó ľ ź ű ö ń ó ź ź ť ľ ó ľ ź ü ť ź ó ü ť ö ó źů ý ťü ľ ú ó ď ľ ľ ľ ľ ó ó ľ ń ľ ľ ö ó ľ ó ľ ö ź ó ľ ľ
!"#$% $ &!'!()*+,-!+., -!&5 4!+ 32$$ 6,.32!$
!"#$% $ &!'!()*+,-!+., /0$!# -!1,!23-32*2$$1$'4 -!&5 4!+ 32$$ 6,.32!$ -!&7$$8+ -!&+92: +!'2:-3!$$22$;2-!$7$-3$2< #-439=*'$+$-3>>2>2-&.-3$!9390 9$-328!0!09$-;>:>0?$#+*'$*0'?$ $39'.#-$@0:$$>9-$:!*!-A;9-9$-3
!"#$ %#"&$' ' &&#""" $!&!"#$&" &""!"#$%&' ()*+,-./0!"#$$( #!"#$%&' #! #! ) #! #! ) #! ) $ # 1 234)!$""$#! :; 34)!$""$#$ 1 <34)!$""# =>! #
!"#$ %#"&$' ' &&#""" $!&!"#$&" &""!"#$%&' ()*+,-./0!"#$$( #!"#$%&' #! #! ) #! #! ) #! ) $ # 1 234)!$""$#! 1 5 6789:; 34)!$""$#$ 1 ! # #?@ #' #!"#",ABC> * +, - DE (", "#$%&'./ " F./ ",GH/I JKL*+MNO
9%: "*'#+#7; :;<= /01Q T(Y : 6 > 6
!"#$%&!!"# $%&' (!"#$% &' # ()*&+, -./01 23456789:& ; ?@A B - C345679: DE ' # FGH- I01% )&JK LMN%O & < P,=FQ@ *+,'- RI&SRI TU%V!IWOXY ) 9 T *+,'- RIZR.-/,!,01 RI>[< B\+, ]^\ \ \*+,'- RI\.-/,!,01 RI
) E 0 / B-1 ( 0 B B A! )*!"#$%&' *+,-./ :; < %= <>56 B> 56CDE<3 3 6 ()*,F<A GHIJKL56MFNO P %./ ()* <QR S TU<VWGA XY < Z [\]^ >5
) E 0 /B-1 ( 0 B -0 0 2B A! )*!"#$%&' *+,-./0123456789:;< %= 56 ()*?@A B> 56CDE
!"#$ %#"&$' ' &&#""" $!&!"#$&"!&"#!"#$%&' ()!"#$$!!#(!!" #! ) #! $ $ ) #! # *+,-./ :; *+)!#""! *+,-./01 <13./1=*+)!#"" $ >?
!"#$ %#"&$' ' &&#""" $!&!"#$&"!&"#!"#$%&' ()!"#$$!!#(!!" #! ) #! $ $ ) #! # *+,-./01 0 23456789:; *+)!#""! *+,-./01 ? ; @A)((""!(!BCDE #'* #'+"#'++!""!!"FG HIJKLM NO PQ RSTU8VW!"#$%&'XY
))) ),9 ) )*), -*, ( #! $#%KL "# $ %&'!! "#!" #" $%$ # $& ' % ' # % # ( )))* ( +)),- (!"#$%&' )))* (! )))* (" #!#$% " +)),- ($ & ' #!# # %! )))* ) )-
))) ),9 ) )*), -*, ( #! $#%KL "# $ %&'!! "#!" #" $%$ # $& ' % ' # % # ( )))* ( +)),- (!"#$%&' )))* (! )))* (" #!#$% " +)),- ($ & ' #!# # %! )))* ) )- ) )+ ) (! " #! $ %&!'#! () *%* %+! )!%( *% $!,%!!)!
() (! (( *+, - -./* 0 1,- /., *+, *, -/.* #* &()*&(!(( 2 & $%&' &! & & &(&( %, % % (!"#$%&' ()*+,-./ :; < = 2>! FGHI 6J8KLMNO LO
() (!(( *+, --./* 0 1,-/., *+, *,-/.* #*&()*&(!(( 2& $%&'&!&&&(&( %,%% (!"#$%&'()*+,-./ 0123456789:;! 8?@ABCDE8 FGHI6J8KLMNOLO P8QRSQTSUVWLXYZ[\]^67 TS./0456_89:`abc*+,L )*,PQRc[\6_TKLQR 4567
) 89: ;!"# `a b c `a "# H 8 # - 67 N8 NT K 6 *7 N QN = 8 E * M 8 () N 8 #? - 8 b M 8 b % -8 b *? - b $%& ' & ()* +, && %( )* +,- +.! )+ #! ( *'
23456 7) 89: ;!"# `a b c `a "# H 8 # - 67 N8 NT K 6 *7 N QN = 8 E * M 8 () N 8 #? - 8 b M 8 b % -8 b *? - b $%& ' & ()* +, && %( )* +,- +.! )+ #! ( *' (!7(!!#"**7 '#+%,$% % & &$*!' #+%,%$ * */ #*$( */#+%'#
!"# $$%&''# $ JJ Q KL MN O K C $ #S C $$ 5 3Z B!"+ 5 B T +$ 8 X`(+0!"3 $ )6 #$ L4 4 L\ "T 6 T E E E $E *6 E E ;E $E ; E;;
!"# $$%&''# $ Z[@A*\ JJ Q KL MN O K C $ #S C $$ 5 3Z R @ ]D@ B!"+ D@ 5 B D@ T +$ )6 @ 8 X`(+0!"3 $ )6 #$ L4 4 L\ "T 6 D@ T E E E $E *6 E E ;E $E ; E;;E D@ T D@ TE E\ # O T D @ " # 4 K 9 ; *! ;;;*! *6 *!
! " # $ # $# ! $ $ # ! "
"%$% -4C,+ -D -CA, "%6$C2 B!"#$%"& '" # /012 *$& 4 +,! - 567 *8. 9:;95662?"6@ AB*8CD$E2=FGHIJKLM. 9:;9NO=567 =P>?566NOQ /& R6S"T$& 0 =UVWXY +,! - *$& "966 Z $& 0 [\=XY * 0 "6]\^_`a bec * 0 $& 0 = 12
KockaKobak Országos Matematikaverseny 10. osztály
KockaKobak Országos Matematikaverseny 10. osztály 014. november 7. A feladatsort készítette: RÓKA SÁNDOR Lektorálta: DR. KISS GÉZA Anyanyelvi lektor: ASZÓDINÉ KOVÁCS MÁRIA www.kockakobak.hu A válaszlapról
!"#$%!!,-!"#$%&'!" %& ()*+,)-./ !"56!"789:!";!"+!" ;AB0C DE F56GH IJKL;!"MN* O J >? P)QRSTU VW%&XY <=;A \]^_`a b,9:ca ; L P? './0 3
!"#$%!!,-!"#$%&'!" %&()*+,)-./01 234!"56!"789:!";!"+!" ?@ ;AB0C DE F56GH IJKL;!"MN* O J >? P)QRSTU VW%&XY
S!!#$%! $? % #> ; %W' `$ e,ù B _"
!" #$%&$& '!" #$% &'& ()*+,-. ( )/01 () 23. 4 5 6 7 8 9:; *+,) .?@ABC 9:DEC ; FG () 2H 9 :IJ )KLMNO /0 *+,HC PQ *+,HCRS(TF -./ *+,HC # U01* (VW 01* CXY )*+,)( Z [U\]^_`abGc /0() K () ^ +9:IJ Nab ( )
;%&1,67!#/465 $"a,37!6!,#7!#/!8-7-6</ i + x ;%&1,#7///465 $"a,#74!!,#7-)/!8-7-6<4 bc 64. `;##1)7)6/465 $"a)")-!)"!)/!8-"-6<4 bc.4.
; )* +* ( "# $%&' $ "#""' " (*, " #$% & "#$%&'()*+,-./01 ' 2 " #"$ %& 34&'()*)*+,-.56789:; ' /?@ABCDE' FGHIJKLMNOJ$%HI " PQ BC R ()SA ' T+,-.UVW:;X T89X T & Y:;X)* +,-./&'X *W+Z, [)*, ' X\]^-._` W-.%
KockaKobak Országos Matematikaverseny 8. osztály
KockaKobak Országos Matematikaverseny 8. osztály 2012. november 12. Feladatok: PÉCSI ISTVÁN, középiskolai tanár SZÉP JÁNOS, középiskolai tanár Lektorok: LADÁNYI ANDREA, középiskolai tanár TÓTH JÁNOS, középiskolai
Total English 2 Lesson 3. Summer of Song. Standing. I m sleepy. Because I How are you today. 2.Greeting. Good afternoon.
89:;?@,A )++( P
Ú Ö ö ľ ľ ć ľ ľ ú ľ Ö ľ Ĺ ľ ö ľ ľ ö ľ ę ľ ö ľ Í ö ľ ć ľ ú ľ ä Ź Ú Í ć Ö ľ ľ ľ ú Ď ľ ľ ö ć ö ľ ú Ĺ ö Ú ö ź ľ ú Í öľ ú Ú ő ľ ť ľ ť ť ě ú ť ľ ő ľ ŕ ľ ľ Ĺ Ú ö ö ö ö ő ľ ľ ö ľ ű ö ö ľ ő ľ Ö ľ Ĺ Í ľ Í ö ľ ľ
CMYK!"#$%&' ()*+,-./ 01, 2*34 567"8) *+9:; B+9:C/ F+,:C01GHI ( JKLMNO 8 GPQRS W )XY L G Z [ \+,:C/ 01 ]\^_`abc Y L _ bc W +,:C/ 01
!"#$%&' ()*+,-./ 01,2*34567"8) *+9:; ?@"AB+9:C/ 01D@E F+,:C01GHI(JKLMNO 8GPQRSTU@VEW )XYLGZ [\+,:C/ 01]\^_`abcYL _bcw+,:c/ 01\ _+,5LW L +,:C/ 01 bc ) XA+,%% W!"#$%&'%()*+,-./01 23456789:;23 2?@ AB45C
Ú ľ ö ľ ř ľ ľ ú ľ Ö ő ü í ö ő ö ö ö ö í íľ í í ö Ś Ś ö ő í í í ú í ú ź ű ľ ő í ű ú ľ ö í Ö ú í ö ö í ú ű ö ú ö ľ í ľ ú í ö ö őí í ú ö í ú í ő ú ú í í ú ú í Ú ú í őí í ľ ú ú í í ő ľ í ú ú ľ ú í ű ö ö ö
É ú ő ú Ö ő ü ü ú í í ö ő ő ő ü ć í Í ú í ű ü ő ő í ő ő ő ö ő í í ú í ű Ĺ ő í ő ő ú ő Ĺ ő Í í ő Ĺ ú ú í ű Í ü ő ő ę ü í í í í í ö Ĺ ő ö ő í ö ű Í ö ú í ű ő ö ú ú Ö ü ö í ö ű Ü ű ö ú Ö ü ę ę ő ú ü ę ő ö
!"#$%&% (") *+,-)./ 01+".2)+%2 3,&."1 4) 5%//,1% " 8&(9% 9
!!"" #$%& ( )*+,&-. */ #-&0,! 1223! 14" 4# 5467 8 416 $%& ()*+,-./01! $%&! ()! *+, $%&% (") *+,-)./ 01+".2)+%2 3,&."1 4) 5%//,1%. 67 1." 8&(9% 9 :;( 9 %( 9?%=>% 9! @,A 9 B,%=C%(.! D7 E,%=F%
! # " ' 2 34' 5 6-! - 7 0# #8) 09:-0; ##%!$! $! # $!$ "# 88 09:-0;, /,0*!"#$%&'! ()*+, -./ 01 / :; <= + -.FGH&'IJKILM*+,N'OH P QRS
! # " ' 2 34' 5 6-! - 7 0# #8) 09:-0; ##%!$! $! # $!$ "# 88 09:-0;, /,0*!"#$%&'! ()*+, -./ 01 / 0 23456789:; ?@AB+CDE + -.FGH&'IJKILM*+,N'OH P QRST
! " # $ % & . Ý QÔ 6_ '. 8&w b e. T U & ¹ ^ _ N º» I n o D%D A< D H I J K ³ >&D%D. A< l &õ à #52LM/ R ª!$1LM/& . )&R k l ³ A<
! " # ()*, -.0 346701 8 :; ## 1 >61@ > A B C D E 4 ), ), F,,, 0 1 * G ), HIJLMNO > J G ), F,,, 01 JP67QR S 6 TU), VNO WXE ), Y J, J Z[\]E ), ^ ), HIJ,, _ `abc` NO J>A ), 4G,,,01 JR S,,, ), 01 J M] J >A
'! ( )$ D A ;, ; X 1 ;91,' MN,E,- ] ' # () *+,-. 1 V 655 AC 5 V 4 *W V V "# S A LM : ;91, `H X,- # U,- 4 U ;91,. > 0- A ;,[4 2 `4 92 ` X,
'! ( )$ D A;,;X1 ;91,' MN,E,- ] ' # () *+,-. 1V 655 AC 5V4 *W V V "# S A;,&@I3LM:;91, 24 92`HX,- # U,-4 U ;91,. > 0-A;,[4 2`4 92`X,- A;,&@I3,- X,- > U,- ;91, E,- A;,&@W U ;91, E,- A;,&@KWDW1 #! 24 92;,"1`T-,-
mo2gh?, ²>Ö ØC #$ ÙÚÆ/ÛÜÝÞßà&áâÖ:3opã6sä/åæ, çùè& TmnÈé ~êë z²³ìíopîïïðð &ñ òóôõö( / øùúc}û, i ü ±¼
!#$%&'4!!#$! %& #!!'$!#$%&'()*+, -./01232456789:12;4?@
"(0 "B2F,5BÌ9ô%½eÍ ÎÏÐ9%+& c ÈT " <& CM/2» + Ü% YRCUÞÑÄÒ ã ÓÔ{% ÏÄ»ÏÐÃÄ»+ ÕÖ Ø%ÐÏÄ» Úàá%ß â ã äå:;&
,()*) &!,!6 (%"+%1/,& "!"#%&' ()*+,-./0!"# ()*)+, -.)/01 1( 2569:; 2 ?@'BC EB *+FG2 :; HKLMN, %O*+O*+-2O*+-6O*+-25 6O *+N PQR-S T UB. #*VWXNY 2 < Y )%,/%,! )%,/%,! V )%,/%,! = Z[\0!,1! " 1&Y
* 9 : &( ; ' ( A B C D 4 5 E F G. Gu<89 ~ :("-&< ST 4*5 ;<:,!"44<."-./R 67 st< Gu # Q1 &)"4(!" 89 Q<89 ~ :!"*4<ST 4*5 ;<:,!"&(<("&+/R 67 !!
% % + < = >? () *)!"# $%&' $ "#""' " ) +!"#$! "# $ %&'! "# $ () *+, %&' -./01234567896:!!)"#",; ?@ABC DEFG1HI23 "#" JKLMNBO :$%&,DPQ&RS)TUVW;X:%'#Y :,X :%,Z[\]^_`)abcRS B;[ /0O/ B
!"#$ %&' " $ () *+ *,-./0 ( !"8 9:; < BCDE? FG < O = ; 5PQ RST? UVW "8XY=? Z[\]^_` < O 3?; < -? L "8XY Z[\ I <
!"#$ %&' " $ () *+ *,-./0 ( 1 234567!"8 9:; < =>?!@A BCDE? FG BHIJKLM@AN =?@A < O = ; 5PQ RST? UVW "8XY=? Z[\]^_` >abc?@ai < O 3?; < -? L "8XY Z[\ I
基于非线性滤波的 融合定位方法 ! " # $ %
E ( )#*( E + "#$%&'% $ "$$' (!, F -.+ (!, 基于非线性滤波的 融合定位方法 () *+,-./ 010/2 *+ (!!(0! &' 3456789!"#$%&:;7?@AB89%&CD'E 'F:GH IJ49KLMNO: %&': D PQRSTUV"1WXYUV1DZ[\]"^_`a=>!"bc7':%&'7]:!" %&' DA:'W'
: 2*- '3'/)( -.*'/() * 2*- 53* '() ; : 3- "! 3/-3/!"#$%&' $ () *+,-./0 1 # 2 3,4/56789:; 0 E A1#FE I2 1# J KLM NO I2 # 1# PQ
: 2*- '3'/)(-.*'/()* 2*- 53*'() ;: 3- "!3/-3/!"#$%&'$()*+,-./01 #23,4/56789:;0 4?@