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Revista Olimpiada Matemática Extremadura 2012
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5/14/2018 Revista Olimpiada 2012 - slidepdf.com
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WWA Ciao{afef Ofuboæua`f
=
Bwu}bofer}f =;6=
LFPB @COF]@FI=6 eb Fm}ai eb =;6=) 6;>0; gc}fp
F@BR@GFI)F^RFJF) MF]@F]]CUF) @FPF] EB @Æ@B]BP) ECH MBHAUC) JÁ\C]F) OÁ]AEF) OC]FIBNF) [IFPBH@AF) PFH \A@BHUB EB
FI@ÆHUF]F) PBJR]F EB IBÐH q PA]RBIF(
[}cmibof)Lb`gf
Vrapvrb>
Lbrjafu>
=
=
Ofr}apao{b}eabu(Eraphb`{r}rphch
Ru}aprp{r}rp)`chjrb|bi)ofuuapae)
WWA CIAO[AFEF OFUBOÆUA@F
Ïhea`b
0/5
2/62
=5/0<
F}uï`ricebif@chpbnb}febBer`f`aðh
]bif`aðheb@bhu}cp{f}ua`a{fhubpbhifWWCiao{afefOfuboæua`f
[}cmibofpebifpeapuahufplfpbp
FpïlrbifWWCiao{afef
6</=0
IfWWACiao{afef
0:/5=
LFPB FRUCHÐOA@F=2) =< q =: eb ofqc eb =;6=
\fi|b}eb ebi L}bphc
[c}ufef> Of}ïf @föfef Oc}bhc(
ABP Echcpc @c}uáp eb Ech Mbhauc(
Lcucj}flïfp> [be}c @c}`gc Pæh`gb~)
Fhuchac Ocifhc ]cob}c q Ncpá [be}c
Of}uïh Ic}bh~c(
Ofvrbuf`aðh> Pb}jac Pfhucp ]cpbii
Ea}b``aðh> Ncpá [be}c Of}uïh Ic}bh~c
Eb{( Ibjfi> MF/12/=;;<
APPH> 677</6==1
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0
WWA Ciao{afef Ofuboæua`f Bwu}bofer}f =;6=
[}bpbhuf`aðh eb if Bw`of( @chpbnb}f eb Ber`f`aðh q @riur}f
’Bi ibhjrfnb eb if @abh`af‟
Jbhb}f} ahub}áp {c} bi f{}bhea~fnb eb ifp
Ofuboæua`fp bh hrbpu}c firohfec bp rhf {}bc`r/
{f`aðh {b}ofhbhub eb icp ec`bhubp) lrhefobhufi/
obhub bh`foahfef f icj}f} vrb ifp `co{bubh`afp
mæpa`fp ebpf}}ciifefp bh bi frif {rbefh u}fhplb}a}/
pb q jbhb}fia~f}pb f `rfivrab} æomauc eb if |aef
`cuaeafhf eb lc}of cgb}bhub q f}oðha`f(
Bi pfmb} ofuboæua`c bpuæ bh bi c}ajbh eb if
`a|aia~f`aðh( Eb gb`gc) icp ubwucp ofuboæua`cp
oæp fhuajrcp hcp }bochufh f Obpc{cufoaf( Pr/
ob}acp q mfmaichacp ebpf}}ciif}ch `co{ibncp pap/
ubofp eb hrob}f`aðh q lbha`acp q bja{`acp `chua/
hrf}ch f|fh~fhec bh bpuf `abh`af( Ebp{ráp lrb}ch
icp j}abjcp) `coc bh ufhucp cu}cp fp{b`ucp) icp vrb
{rpab}ch ifp mfpbp q bwubheab}ch bpub pfmb} {c} bi
Obeaub}}æhbc) `ch ecp lajr}fp `if|b> Ufibp eb Oa/
ibuc q [auæjc}fp eb Pfocp( Bi {ceb} eb fmpu}f``aðh
lrb rhf eb prp {}ah`a{fibp f{c}uf`achbp( Rh {ceb}
eb fmpu}f``aðh vrb fþh gcq bp |æiaec {f}f bpu}r`/
ur}f} hrbpu}cp {bhpfoabhucp(
Pah eref) ifp Ofuboæua`fp bpuæh bh if mfpb
eb icp f|fh`bp `abhuïla`cp) ub`hciðja`cp q uá`ha/
`cp( Bpuæh {}bpbhubp bh hrbpu}c eïf f eïf(
Ifp Ofuboæua`fp pch hb`bpf}afp {f}f `co/
{}bheb} q fhfia~f} if fmrhefhub q |f}afef ahlc}/
of`aðh vrb hcp iibjf) lf|c}b`b q jbhb}f if `f{f/
`aefe eb {bhpfoabhuc fmpu}f`uc) {b}oaub bh`chu}f}
fhficjïfp q bpufmib`b} `}aub}acp ealb}bh`afibp bhu}b
ea|b}pcp lbhðobhcp q `}bf bi gæmauc eb bhl}bhuf}
{}cmibofp) ucof} aha`afua|fp `cgb}bhubp q }bpci/
|b}icp bla`f~obhub(
@coc |fic} `riur}fi) ifp Ofuboæua`fp fo/
{iïfh if bplb}f `riur}fi ebi ahea|aerc qf vrb ebpf/
}}ciif gæmaucp eb ib`ur}f) obnc}f ifp gfmaiaefebp eb
ah|bpuajf`aðh) {b}oaub }b`fmf} efucp q lf|c}b`b if
ahub}{}buf`aðh eb paurf`achbp ufhuc f ha|bi {b}pc/
hfi `coc `cib`ua|c( If ofqc}ïf eb ifp {}clbpachbp
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WWA Ciao{afef Ofuboæua`f
5
Bwu}bofer}f =;6=
q u}fmfncp uá`ha`cp f`urfibp }bvrab}bh `chc`a/
oabhucp ofuboæua`cp( Ifp Ofuboæua`fp pch) {c}
bheb) `chpaeb}fefp rhf eap`a{iahf q gb}}foabhuf
rha|b}pfi) bp bi ibhjrfnb eb if `abh`af q eb if uá`/
ha`f q pb gf`b {}b`apc pr ecoahac(
If ah`irpaðh eb ifp `co{bubh`afp mæpa`fp
bh bi `r}}ï`ric) bhu}b biifp if }blb}aef f if ofuboæ/
ua`f) {b}pajrb ahubj}f} icp eapuahucp f{}bhea~fnbp)
ufhuc icp lc}ofibp) ah`c}{c}fecp f ifp ealb}bhubp
eap`a{iahfp) coc icp ahlc}ofibp q hc lc}ofibp) fpï
`coc lf|c}b`b} if ahubj}f`aðh eb prp f{}bhea~fnbp
f{ia`æhecicp eb ofhb}f blb`ua|f `rfhec }bpriubh
hb`bpf}ac bh ifp ea|b}paefe eb paurf`achbp) `a}/
`rhpufh`afp q `chubwucp( Ufomaáh pch rhf ao{c}/
ufhub gb}}foabhuf f lah eb c}abhuf} icp {}c`bpcp eb
bhpböfh~f#f{}bhea~fnb) fi {b}oaua} eap`}aoahf} b
aebhuala`f} icp `chubhaecp q icp `}aub}acp eb b|firf/`aðh vrb uabhbh `f}æ`ub} ao{}bp`aheamib b ahp{a}f}
ifp eb`apachbp eb obnc}f q c{uaoa~f`aðh }bifua|fp f
ea`gc {}c`bpc(
@coc hc {rbeb pb} eb cu}c ocec) if @ch/
pbnb}ïf eb Ber`f`aðh q @riur}f ebi Jcmab}hc eb
Bwu}bofer}f f{cqf b ah`bhua|f bpub ua{c eb f`ua|a/
efebp) vrb |fh oæp fiiæ ebi u}fmfnc ebpbo{böfec
bh ifp frifp( Pch f`ua|aefebp lc}ofua|fp eb {}aob}
c}ebh vrb }co{bh bi u}aæhjric {}clbpc}/firohc/
frif `chpajrabhec rhf ocua|f`aðh bwu}f {f}f bi
firohfec( [c} ucec biic) vrab}c bw{}bpf} oa fj}f/
eb`aoabhuc f if Pc`abefe Bwu}boböf eb Ber`f`aðh
Ofuboæua`f ’\bhur}f ]bqbp [}cp{b}‟ {c} bi u}fmf/
nc }bfia~fec {f}f vrb bpuf WWA Ciao{afef Ofub/
oæua`f bh Bwu}bofer}f pbf rhf }bfiaefe(
[f}f `ch`ira}) vrab}c fj}feb`b} q lbia`auf}
eb lc}of orq bp{b`afi f icp ec`bhubp) {c} pr bhur/
pafpoc) bplrb}~c q {c} gfmb} lcobhufec q fhaof/
ec if {f}ua`a{f`aðh bh bpuf Ciao{afef bhu}b prp
nð|bhbp firohcp( Ufomaáh f{}c|b`gc if c`fpaðh
{f}f ah|auf}ibp q fhaof}ibp f pr lc}of`aðh q f`urf/
ia~f`aðh bh bpuf eap`a{iahf bh f}fp eb fef{uf}pb fifp hb`bpaefebp b ahub}bpbp eb pr firohfec( Bp oa
ebpbc vrb bpuf Ciao{afef pbf rh æomauc aeðhbc eb
`ch|a|bh`af) mrbhfp {}æ`ua`fp) ahub}`fomac eb
bw{b}abh`afp ber`fua|fp q eb f{}bhea~fnb(
U}ahaefe Hcjfibp Mfpf}}fub
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2
WWA Ciao{afef Ofuboæua`f Bwu}bofer}f =;6=
Fpï lrb if WW Ciao{afefIf Nrhuf Ea}b`ua|f eb if P(B(B(O( bpureað ifp {bua`achbp eb ic`fiaefebp {f}f pb} pbebp eb ifp ealb}bh/
ubp lfpbp) pajrabhec bi `}aub}ac eb ef} if {cpamaiaefe eb {f}ua`a{f`aðh oæwaof eb bp`cif}bp q {}c`r}fhec `r/
m}a} ucefp ifp ~chfp eb hrbpu}f `corhaefe fruðhcof( Pb f`c}eð lanf} {f}f if lfpb `cof}`fi ifp pajrabhubp
pbebp>
^CHF [CMIF@AÐH @BHU]C
FIMR]VRB]VRB FIMR]VRB]VRB A(B(P( @FPUAIIC EB IRHF
FIOBHE]FIBNC \AIIFL]FH@F EB ICP MF]]CP @( PFH NCPÁ
F^RFJF#IIB]BHF IIB]BHF A(B(P( LB]HFHEC ]CMAHF
MFEFNC^ MFEFNC^ A(B(P( PFH NCPÁ
@Æ@B]BP @FPF] EB @Æ@B]BP A(B(P(C( \ÏF EB IF [IFUF
@C]AF \FI\B]EB EBI L]BPHC A(B(P(C( \FI EB WÆIAOF
ECH MBHAUC ECH MBHAUC A(B(P( NCPÁ OFH^FHC
OÁ]AEF OÁ]AEF A(B(P( PFHUF BRIFIAF
[IFPBH@AF [IFPBH@AF @BHU]C RHA\B]PAUF]AC
PA]RBIF PA]RBIF A(B(P(C( \A]JBH EB FIUFJ]F@AF
^FL]F ^FL]F A(B(P( PRÆ]B^ EB LAJRB]CF
@coc pbeb eb if lfpb fruchðoa`f pb f`b{uð if {}c{rbpuf {}bpbhufef {c} bi Bw`bibhuïpaoc Fqrhuf/
oabhuc eb If [f}}f 'Mfefnc~!(
Bh Of}~c pb `cijð bh ahub}hbu if }b|apuf eb if WW Ciao{afef Ofuboæua`f {f}f firohcp eb =¾ eb
B(P(C( bh if ea}b``aðh guu{>##zzz(ber`f}bw(bp#zbm#jrbpu#ciao{afefp/ofubofua`fp/bwu}bofer}f q bh if eb if
{æjahf eb if P(B(B(O( ’\bhur}f ]bqbp [}ðp{b}‟(
LFPB @COF]@FI
If lfpb `cof}`fi pb `bibm}ð bi eïf : eb Ofqc f ifp 6;>0; `chlc}ob {}b|bïf if `ch|c`fuc}af(
Icp {fvrbubp vrb `chubhïfh ifp {}rbmfp ao{}bpfp bh rhfp `f}{buaiifp) fpï `coc icp mciïj}flcp) ifp gc/
nfp eb efucp {b}pchfibp eb icp {f}ua`a{fhubp) ea{icofp eb icp firohcp) {}clbpc}bp) fpï `coc icp `}aub}acp eb
b|firf`aðh lrb}ch bhu}bjfecp f icp `cc}eahfec}bp eb ~chf bh if }brhaðh `bibm}fef bh bi @([(] eb Oá}aef bi5 eb Ofqc f ifp < eb if uf}eb( Ea`gc {fvrbub hc lrb fmab}uc gfpuf bi oapoc ocobhuc bh vrb pb bhu}bjf}ch
ifp {}rbmfp f icp firohcp(
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WWA Ciao{afef Ofuboæua`f
<
Bwu}bofer}f =;6=
[f}f bi ebpf}}ciic eb ifp {}rbmfp pb lanf}ch ifp pajrabhubp hc}ofp) vrb pb eab}ch f `chc`b} f ucecp icp
{f}ua`a{fhubp fhubp ebi aha`ac eb ifp oapofp>
v ]biibhf} `ch ibu}f `if}f q ibjamib ucecp icpefucp eb if `if|b eb aebhuala`f`aðh(
v [chb} bh bi æhjric pr{b}ac} eb}b`gc eb `fefgcnf ruaia~fef bi hþob}c vrb f{f}b`b bh if `if|beb aebhuala`f`aðh(
v Ruaia~f} rhc c oæp lciacp {c} `fef {}cmibof(
v Ahea`f} bh bi æhjric pr{b}ac} a~vrab}ec ebhu}ceb rh `ï}`ric bi hþob}c eb `fef {}cmibof(
v Pb{f}f} `fef `rbpuaðh ebi {}cmibof `ch rhfiïhbf ea|apc}af(
v Ebufiif} fi oæwaoc ucecp icp {fpcp efecp {f}f}bpci|b} fef bnb}`a`ac(
v Pb {rhurf}æ if {}bpbhuf`aðh q icp}f~chfoabhucp bw{rbpucp bh if }bpcir`aðh eb ifpealb}bhubp rbpuachbp {ifhubfefp(
v Bhu}bjf} ifp gcnfp `ch ifp }bp{rbpufp c}ebhfefp`chlc}ob fi hþob}c ebi {}cmibof(
v [rbebh ruaia~f} `fi`rifec}f(
v Er}f`aðh eb if {}rbmf> ecp gc}fp `cocoæwaoc(
Bi irhbp eïf 1 eb Ofqc `fef `cc}eahfec}) bh|að {c} u}fhp{c}ub r}jbhub c bi obeac vrb bpuaoð oæp
pbjr}c q }æ{aec) ifp {}rbmfp eb pr ~chf {f}f pb} `c}}bjaefp bh if ~chf fpajhfef( Ifp `if|bp aebhuala`fua|fp
vrb {}bpb}|fmfh if aebhuaefe eb icp {f}ua`a{fhubp) vrbef}ch {c} bi ocobhuc bh {ceb} eb icp `cc}eahfec}bp}bp{b`ua|cp(
Rhf |b~ }bfia~fec bi ahub}`fomac) if `c}}b``aðh q if mf}bof`aðh eb ucefp ifp {}rbmfp) lrb}ch bh|af/
efp fi `cc}eahfec} }bjachfi {f}f {}c`beb} f if pbib``aðh eb icp {f}ua`a{fhubp bh if lfpb fruchðoa`f( Ifp
{}rbmfp amfh c}ebhfefp pbjþh if {rhurf`aðh(
Bi eïf =; eb Ofqc pb }brhað if `coapaðh eb b|firf`aðh vrb hcoahð fi {}aob} `ifpala`fec eb `fef ~c/
hf pbjþh }b~f bh if `ch|c`fuc}af f{f}b`aef bh bi E(C(B( Fpaoapoc) pb pbib``achð fi }bpuc eb {f}ua`a{fhubppbjþh `}aub}acp eb {rhurf`aðh q {f}ua`a{f`aðh {c} pbeb) gfpuf `co{ibuf} icp u}bahuf vrb fpapuab}ch f if lfpb
fruchðoa`f vrb pb `bibm}f}ïf bh If [f}}f 'Mfefnc~!(
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:
WWA Ciao{afef Ofuboæua`f Bwu}bofer}f =;6=
Icp `ifpala`fecp {f}f if Lfpb Fruchðoa`f lrb}ch icp pajrabhubp>
F[BIIAECP HCOM]B @BHU]C 'IC@FIAEFE!
FOFEC] [C]]FP NBPÞP ABP [Á]B^ @COBHEFEC] '[IFPBH@AF! Æ]AFP FMBIAFHF U]AFHF ABP PFHUF BRIFIAF 'OÁ]AEF!
F]]CQC FPBPAC NRFH ABP ]CE]ÏJRB^ OCÖAHC 'MFEFNC^! Æ\AIF OF]@BIC @F]OBH ABP L]FH@AP@C EB C]BIIFHF 'U]RNAIIC!
MCIIFP MB@B]]F FHUCHAC NCPÁ ABP @FO[CP EB PFH ]CVRB 'MFEFNC^!
@FI^FP ER]ÆH ÆHJBI NBPÞP ABP IRAP @GFOA^C 'ECH MBHAUC!
@F]]B]C JCH^ÆIB^ L]FH@AP@C NF\AB] ABP FIFJÐH '@C]AF!
@C]@GFEC ]CI MBFU]A^ PFJ]FEC @C]F^ÐH EB NBPÞP '@Æ@B]BP!
EÏF^ JF]@ÏF [BE]C NCPÁ ABPC OF]AFHC MF]MF@AE 'PCIFHF EB ICP MF/
]]CP!
EÏF^ OF]]ÐH FIBNFHE]C ABP AIEBLCHPC PB]]FHC 'PBJR]F EB IBÐH!
LB]HÆHEB^ LRBHUBP NCPÁ OFHRBI HU]F( P]F EB IF J]FHFEF ‐ PUC FHJBI 'IIB/
]BHF!
L]FH@C @FPUFÖC EABJC @CIBJAC PFH NCPÁ '\AIIFL]FH@F EB ICP MF]]CP!
L]FH@C JCH^ÆIB^ FIBNFHE]C ABP MBHF^FA]B 'GB]]B]F EBI ERVRB!
JFIIF]EC MC]]BJC @F]ICP @CIBJAC PFH NCPÁ '\AIIFL]FH@F EB ICP MF]]CP!
JF]@ÏF/@FPAIIFP MF]]CPC IR@ÏF PFJ]FEC @C]F^ÐH EB NBPÞP '@Æ@B]BP!
JAI OF]UÏH PFORBI ABPC \FI EB WÆIAOF '\FI\B]EB EBI L]BPHC!
J]FJB]F OÆP NCPÁ IRAP HU]F( P]F( EBI @F]OBH 'MFEFNC^!
LB]HÆHEB^ MBHÏUB^ OF]ÏF PFIBPAFHCP O® FRWAIAFEC]F 'OÁ]AEF!
GB]HÆHEB^ M]ACPC PAI\B]AC ABP AIEBLCHPC PB]]FHC 'PBJR]F EB IBÐH!
GB]HÆHEB^ @B]B^C FIBNFHE]C PFH @FIAWUC '[IFPBH@AF!
GCQFP PÆH@GB^ @IF]F ABP []CLBPC] GEB^( [F@GB@C '@Æ@B]BP!
OF]UÏH UCOÁ FHE]BF ABP [Á]B^ @COBHEFEC] '[IFPBH@AF! OCIB]C UBHF MBIÁH ABP OAJRBI ER]ÆH 'F^RFJF!
[F]BNC ]FOCP BPU]BIIFABP [BE]C EB \FIEA\AF '\AIIFHRB\F EB IF PB/
]BHF!
]CE]ÏJRB^ OF]@CP @F]OBIF ABP [Á]B^ @COBHEFEC] '[IFPBH@AF! ]C[B]C J]FJB]F EFHABI @CIBJAC PFH NCPÁ '\AIIFL]FH@F EB ICP MF]]CP!
PÆH@GB^ MCIÏ\F] [BE]C ABP BWU]BOFER]F 'OÁ]AEF!
PÆH@GB^ OFR]B]F OF]@C FHUCHAC ABP ^R]MF]ÆH 'MFEFNC^!
PÆH@GB^ ]A\B]C FHF ABP []CLBPC] GB]HÆHEB^ [F@GB@C '@Æ@B]BP! UÁIIB^ ECOÏHJRB^ ]CMB]UC ABP []CLBPC] GEB^( [F@GB@C '@Æ@B]BP!
]BPB]\FP
6¾ JÐOB^ UR]ÁJFHC OF]UF PFHUF @B@AIAF '@Æ@B]BP!
=¾ ]CE]ÏJRB^ PFH [BE]C FI\F]C ABP []CLBPC] GEB^ [F@GB@C '@Æ@B]BP!
0¾ EBIJFEC IÐ[B^ NCPÁ ÆHJBI HU]F( P]F( EBI @F]OBH '\AIIFL]FH@F EB ICP
MF]]CP!
5¾ JAI MB]HÆIEB^ MBFU]A^ ABP [B]B^ @COBHEFEC] '[IFPBH@AF! 2¾ IF ]BF [FNF]BP NC]JB FPRH@AÐH NCPBLAHFP '@Æ@B]BP!
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WWA Ciao{afef Ofuboæua`f
7
Bwu}bofer}f =;6=
Bpub eïf ufomaáh pb biajað fi `f}ubi vrb {}bpbhuf}æ f if Ciao{afef Ofuboæua`f eb =;6=) fpï `coc f icp
ecp f``ápau( [f}f biic `chufocp `ch if `cifmc}f`aðh ebi {}clbpc}fec ebi A(B(P( Pfh Ncpá eb Mfefnc~( Bi nr}f/
ec bpur|c `co{rbpuc {c} E( Ncpá Ncfvrïh @fpaiifp F}afp) E® Of}ïf [f~ [á}b~ ]ce}ïjrb~ q E( Oajrbi Æhjbi
Oc}bhc ]bechec eb if bp{b`afiaefe eb Ofuboæua`fp) E® @f}obh Of}uïh Pfhfm}af eb @abh`afp Hfur}fibp q E®Ob}`bebp [á}b~ Gr}ufec ebi eb{f}ufobhuc eb Lïpa`f q Vrïoa`f(
Icp f}ubibp pbib``achfecp {b}ubhb`ab}ch f>
JFHFEC] OF]ÏF @FÖFEF OC]BHC ABP ECHCPC @C]UÁP( ECH MBHAUC
F@@BPAU 6¾ NF\AB] OF]UÏH UC]]BP ABP ECHCPC @C]UBP( ECH MBHAUC
F@@BPAU =¾ FHF AHÁP @CPF FJRA]]B ABP NCPÁ OFH^FHC( ECH MBHAUC
LFPB FRUCHÐOA@F
Er}fhub icp eïfp 0) 5 q 2 eb Nrhac) pb `bibm}ð if Lfpb Fruchðoa`f eb if WW Ciao{afef Ofuboæua`f
eb Bwu}bofer}f bh if ic`fiaefe eb If [f}}f 'Mfefnc~!(
If Lfpb Fruchðoa`f pb aha`að bi eïf 0 eb Nrhac( [f}f bi u}fpifec f If [f}}f pb {rpc f eap{cpa`aðh eb
icp {f}ua`a{fhubp ea|b}pcp obeacp eb u}fhp{c}ub( Bi irjf} bibjaec `coc }bpaebh`af er}fhub bi lah eb pbofhf
lrb bi @ch|bhuc Gcp{beb}ïf If [f}}f( @rfhec ucecp icp {f}ua`a{fhubp iibjf}ch) pb ibp f`coceð bh prp }bp/
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`a}`rauc ofuboæua`c(
If {}rbmf ebi `a}`rauc ofuboæ/
ua`c eb bpub föc pb {}b{f}ð bh bi bh/
uc}hc ochrobhufi eb If [f}}f) bh prp
{if~fp) lrbhubp) fpï `coc bh if Ajibpaf
eb Hu}f( P}f( eb if Fprh`aðh( @fmb
eb`a} vrb bpuf {}rbmf pajrb pabhec rhf
eb ifp f`ua|aefebp oæp fu}f`ua|fp eb if
Ciao{afef qf vrb pa}|b `coc {rhuc eb
{f}uaef {f}f rhf obnc} }bif`aðh bhu}b
ucecp icp {f}ua`a{fhubp( Feboæp) ufo/
maáh {b}oaub `chc`b} b ahub}`fomaf}
ao{}bpachbp pcm}b bpu}fubjafp vrb }b/
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prbi|bh ifp `rbpuachbp vrb pb {ifhubbh bh if {}rbmf ebi `a}`rauc ofuboæua`c(
Bi `}aub}ac pbjraec {f}f lc}of} icp j}r{cp lrb a} }bif`achfhec `ga`c `ch `ga`f eb ic`fiaefebp ealb}bh/
ubp ic oæp eapufhub {cpamibp(
Icp j}r{cp }bpriufhubp lrb}ch>
J]R[C 6
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Bwu}bofer}f =;6=
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GB]HÆHEB^ M]ACPC PAI\B]AC F]]CQCOCIAHCP EB IBÐH 'MF!
Ebp{ráp eb if `coaef q u}fp rh m}b|b ebp`fhpc) ucef if bw{bea`aðh ciïo{a`f lrb }b`amaef {c} bi Bw`b/
ibhuïpaoc Fi`fieb eb If [f}}f bh bi Fqrhufoabhuc(
[cpub}ac}obhub eac `coabh~c f ifp 61>;; gc}fp if {}rbmf ebhcoahfef ’@a}`rauc Ofuboæua`c‟( Bh biif
icp {f}ua`a{fhubp ebocpu}f}ch prp `chc`aoabhucp ofuboæua`cp }bpci|abhec {}cmibofp vrb |b}pfmfh pcm}b bi
bhuc}hc gapuð}a`c q ochrobhufi eb If [f}}f( Ifp 6; {}rbmfp {}c{rbpufp pb }b{f}uab}ch {c} ucef if ic`fiaefe
eb If [f}}f(
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iam}b( F `chuahrf`aðh ucecp icp ahubj}fhubp eb if ciao{afef `bhf}ch bh bi oapoc `bhu}c ebi {rbmic(
Bi eïf 5 eb ofqc pb }bfia~ð if {}rbmf ahea|aerfi f ifp 6; eb if oföfhf bh bi A(B(P(C( ’\a`bhub Lb/
}}b}‟( Ufomaáh hcp jrpuf}ïf }b`chc`b} bi u}fmfnc iib|fec f `fmc {c} bi A(B(P(C( -\a`bhub Lb}}b}-4 {}clbpc}bp)
firohfec q `coc hc) f pr ea}b`uc} E( Irap L}fh`ap`c Pæh`gb~ Lb}hæheb~(
F ifp 6=>0; pb }bfia~ð if |apauf jrafef f Pfi|fuab}}f eb icp Mf}}cp( Eapl}rufocp eb if f}ubpfhïf eb rh
ufiib} eb filf}b}ïf q bi Orpbc eb Filf}b}ïf eb If [f}}f( F obeaceïf {reaocp eapl}ruf} eb rhf bpur{bhef `c/
oaef bh Pfi|fuab}}f bh `co{föïf eb if {}bpaebhuf eb if F(O([(F( ebi A(B(P(C( ’\a`bhub Lb}}b}‟( U}fp rh ebp/
`fhpc bh If Gcp{beb}ïf) lraocp {c} if uf}eb f |apauf} bi @fpuaiic eb Lb}af q eapl}ruf} eb prp bo{ahfefp `fiibp(
Qf mabh f|fh~fef if uf}eb lraocp f |apauf} if f`cjbec}f ic`fiaefe eb If Oc}b}f) pr ajibpaf) prp `fiibp)
bu`((( Ebp{ráp eb if `bhf) vrb ga`aocp bh if ic`fiaefe fhub}ac}obhub obh`achfef) eapl}rufocp eb rhf cmpb}/
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66
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Fi eïf pajrabhub) ebp{ráp eb ebpfqrhf}) pb {}c`beað f ocpu}f} f icp {f}ua`a{fhubp bh If Gcp{beb}ïf if }bpcir/
`aðh eb icp {}cmibofp ahea|aerfibp {}c{rbpucp bi pæmfec fhub}ac}(
F@UC EB @IFRPR]F
Bh bpuf c`fpaðh) bi F`uc bpur|c {}bpaeaec {c} bi fi`fieb eb If [f}}f E( Pfhuafjc Jch~æib~ Ifjf})
Ahp{b`uc}f eb Ber`f`aðh) E® Bh`f}hf`aðh Mbiic Ochub}c) E( Irap L}fh`ap`c Pæh`gb~ Lb}hæheb~ q E( ]a`f}/
ec Irbhjc Jch~æib~) `coc [}bpaebhub eb if Pc`abefe Bwu}boböf eb Ber`f`aðh Ofuboæua`f ’\bhur}f ]bqbp
[}ðp{b}‟(
Bh bpub F`uc pb {}c`beað f hcom}f} f icp 06 firohcp {f}ua`a{fhubp) vrb }b`cjab}ch rh ea{icof {c}
pr {f}ua`a{f`aðh bh if Lfpb Fruchðoa`f eb if Ciao{afef) fpï `coc rhf `fi`rifec}f `abhuïla`f q oæp f}uï`ricp
eb }bjfic(
Icp u}bp bvra{cp vrb }bpriuf}ch jfhfec}bp bh if [}rbmf ebi @a}`rauc Ofuboæua`c lrb}ch '{c} c}ebh
hroá}a`c!>
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60
WWA Ciao{afef Ofuboæua`f Bwu}bofer}f =;6=
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Lfpb Hf`achfi eb if Ciao{afef Ofuboæua`f vrb pb `bibm}ð bh \ajc ebi =< fi 0; eb nrhac eb =;66( Icp }b{}b/
pbhufhubp lrb}ch>
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WWA Ciao{afef Ofuboæua`f
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WWAA CIAO[AFEF OFUBOÆUA@F HF@ACHFI
Ebi =< fi 0; eb Nrhac eb =(;66 pb `bibm}ð if Lfpb Hf`achfi eb if Ciao{afef {f}f firohcp eb =¾ eb
BPC bh \ajc( Icp u}bp }b{}bpbhufhubp eb Bwu}bofer}f vrb {}b|afobhub gfmïfh paec pbib``achfecp) u}fp pr/{b}f} if lfpb `cof}`fi q if fruchðoa`f lrb}ch> Fhf Pæh`gb~ ]a|b}c) [be}c Pæh`gb~ Mciï|f} q Pforbi Jai
Of}uïh vrb lrb}ch f`co{föfecp {c} bi {}clbpc} Fhuchac Ocifhc eb if Pc`abefe Bwu}boböf ’\bhur}f ]bqbp
[}ðp{b}‟( U}fp rh if}jc |afnb f u}f|áp eb [c}urjfi) iibjfocp f \ajc q hcp ficnfocp bh bi @bhu}c ]bpaebh`afi
Ec`bhub 'Fhuajrf Rha|b}paefe Ifmc}fi! nrhuc `ch icp }b{}bpbhufhubp eb ifp cu}fp `c/
orhaefebp fruðhcofp( Ebp/ {ráp ebi }b{f}uc eb gfmauf`achbp
`cobh~ð if `ch|a|bh`af q bi aha`ac eb rhf foapufe( Bpb
oapoc eïf) u}fp if `bhf) grmc rhf }brhaðh {f}f `ch/
`}buf} ebufiibp) }b{f}/ ua} ifp f`}beauf`achbp) f/
oapbufp) bu`… q pb lc}of}ch icp bvra{cp
{f}f bi `ch`r}pc eb lcucj}flïfp ofuboæua`fp(
Icp firohcp |fh gf`abhec lcucp bh ucec
ic vrb |bfh vrb grb/ ib f ofuboæua`fp q `coc
oæwaoc gfpuf bi eïf =7 pb {ceïfh bhu}bjf}( Bhbi f`uc eb `ifrpr}f pb {}c`ifof}ïfh icp bvra{cp
jfhfec}bp( If f`urf`aðh eb rh `ðoa`c ic`fi hcp bhu}bur|c
ifp gc}fp {}b|afp fi prböc(
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Rha|b}paefe eb \ajc echeb pb }bfia~ð if {}rbmf ahea|aerfi eb }bpcir`aðh eb {}cmibofp) `coaocp bh bi `c/
obec} rha|b}pauf}ac q {c} if uf}eb pb ga~c rhf |apauf ofuboæua`f {c} \ajc) `ch if }bpcir`aðh {c} bvra{cp eb
f`ua|aefebp ofuboæua`fp f{}c|b`gfhec icp efucp }bfibp vrb if {}c{af `arefe {}c{c}`achf( Icp bvra{cp icp
lc}oð if c}jfha~f`aðh ob~`ifhec firohcp eb ea|b}pfp `corhaefebp(
Bi eïf =7) ebp{ráp eb ebpfqrhf}) hcp lraocp f if ah`co{f}fmib Pfhuafjc( Fiiï hcp bp{b}fmfh `co{f/
öb}cp eb if Pc`abefe Jfiibjf FJF[BOF vrb hcp jraf}ch bh rh `co{ibuc }b`c}}aec ur}ïpua`c vrb `cobh~ð
bh if `fube}fi echeb ur|aocp if prb}ub eb |b} bh f``aðh bi lfocpc Mcuflroba}c( U}fp if `coaef bh rh `cob/
ec} rha|b}pauf}ac eb if Rha|b}paefe eb Pfhuafjc) hcp ubhïfh {}b{f}fec rh {fpbc ofuboæua`c) eb lc}of vrb
|apaufocp icp }ah`chbp oæp ahub}bpfhubp ebi `fp`c gapuð}a`c }bif`achæhecicp `ch fp{b`ucp ofuboæua`cp( Qf eb}bj}bpc f \ajc) fpapuaocp f if f`urf`aðh eb rh ’`rbhuf`rbhucp‟ vrb hcp ebibauð if |bifef(
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62
WWA Ciao{afef Ofuboæua`f Bwu}bofer}f =;6=
Bi =1) ebp{ráp eb rh j}fh ofe}rjðh) hcp ea}ajaocp f if Ichnf ebi {rb}uc {bpvrb}c eb \ajc) rhc eb
icp oæp ao{c}ufhubp eb Br}c{f) echeb |aocp if prmfpuf eb {bp`fec q fijrhcp bnbo{if}bp eb if lfrhf of}ahf
{}b{f}fecp {f}f pr |bhuf q {cpub}ac} eapu}amr`aðh {c}
ucef Bp{föf q [c}urjfi( Hcp ah|auf}ch f ebpfqrhf} bh
rhf eb prp `flbub}ïfp q) `ch hrbpu}cp ’mc`fufp‟) `c/
jaocp bi mf}`c vrb hcp u}fpifeð f ifp apifp @ïbp) bpf
}bpb}|f hfur}fi ufh mabh `raefef vrb lc}of {f}ub ebi
{fu}aochac eb if grofhaefe( Ur|aocp rh mrbh eïf eb
pci q eapl}rufocp eb prp {fapfnbp q eb prp {ifqfp( F if
`fïef eb if uf}eb) }bj}bpfocp f if }bpaebh`af q) u}fp if
`bhf) grmc rhf pbpaðh eb }bpcir`aðh eb {}cmibofp
echeb pb `cobhuf}ch icp vrb pb {}c{rpab}ch bh if
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`gcp |afnbp f {c} fjrf l}bp`f bh if lrbhub fi ifec eb if bhu}fef( If foapufe vrb pb lrb lc}nfhec er}fhub icp
eïfp vrb gf er}fec if Ciao{afef hc pb ci|aef læ`aiobhub(
Iibjð bi eïf 0; q) u}fp bi ebpfqrhc q qf `f}jfecp `ch hrbpu}cp bvra{fnbp) hcp u}fpifefocp f rh [f~c
bh bi {f}vrb orha`a{fi eb @fpu}bicp) vrb uabhbh orq mabh {}b{f}fec {f}f f`ucp {}cuc`cif}acp `coc bi eb if@ifrpr}f eb if WWAA Ciao{afef Ofuboæua`f Hf`achfi( Fpapuað bi fi`fieb eb \ajc) bi bw oahapu}c Fmbi @fmf/
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Fhf lc}oð {f}ub ebi bvra{c jfhfec} eb lcucj}flïfp ofuboæua`fp( Ebp{ráp) f if `f}}bub}f) vrb) {c} uab}}fp
irpaufhfp) hcp chernc f hrbpu}cp }bp{b`ua|cp ecoa`aiacp( Fhuchac Ocifhc ]cob}c( [}clbpc} f`co{föfhub eb icp firohcp bwu}boböcp(
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^CHF EB FEP@]A[@AÐH> FIMR]VRB]VRB
@BHU]C IC@FIAEFE []CLBPC] H¾ EBFIROHCP
@FPUAIIC EB IRHF FIMR]VRB]VRB FHF @C]^C FQRPC 2
@FPUAIIC EB IRHF FIMR]VRB]VRB ÆHJBI L@C( FOM]CNC FHUÞHB^ <
PAB]]F EB PFH [BE]C ]C@F EB IF PAB]]F 'IF! ÆHJBI GB]HÆHEB^ ]CMIBP :
PAB]]F EB PFH [BE]C ]C@F EB IF PAB]]F 'IF! OAJRBI ÆHJBI LB]]B]C JF]]CUB 0
ICRPUFR/\FI\B]EB \FIBH@AF EB FI@ÆHUF]F O® OB]@BEBP PÆH@GB^ LB]HÆHEB^ 7
UCUFI ^CHF FIMR]VRB]VRB =1
^CHF EB FEP@]A[@AÐH> FIOBHE]FIBNC
@BHU]C IC@FIAEFE []CLBPC] H¾ EBFIROHCP
UAB]]F EB MF]]CP F@BR@GFI NCPÁ OF]ÏF OÁHEB^ OÁHEB^ 2
UAB]]F EB MF]]CP F@BR@GFI NRFH @GF\B]C ]CE]ÏJRB^ 2
UAB]]F EB MF]]CP F@BR@GFI IRAP [A^F]]C JFIIF]FEC 2
UAB]]F EB MF]]CP F@BR@GFI PB]JAC PFHUCP ]CPBII 2
@F]CIAHF @C]CHFEC FIOBHE]FIBNC ÐP@F] MC]]BJC MB]OBNC 2
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5
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6:
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\FIEBOBEBI ]AMB]F EBI L]BPHC [BE]C N( OFUFOC]CP ÆI\F]B^ 6;
PAB]]F IF @FIB]F PUF( OF]UF EB ICP MF]]CP IR@ÏF IFH@GF]]C [Á]B^ 6;
OF]AFHC MF]MF@AE PCIFHF EB ICP MF]]CP NRIAÆH JRUAÁ]]B^ GR]UFEC =
HU]F( P]F( EBI @F]/OBH
\AIIFL]FH@F EB ICP MF/]]CP
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PFH NCPÁ \AIIFL]FH@F EB ICP MF]]CP PFHUCP [AHUC @B]B^C 1
UCUFI ^CHF FIOBHE]FIBNC 6;2
^CHF EB FEP@]A[@AÐH> F^RFJF#IIB]BHF
@BHU]C IC@FIAEFE []CLBPC] H¾ EBFIROHCP
MBOMÁ^F] F^RFJF OÐHA@F BPVRA\BI OCHUB]]RMAC 0
MBOMÁ^F] F^RFJF [BE]C ]CUAIA ]RA^ 5
MBOMÁ^F] F^RFJF ]C@ÏC PCIBEFE @F]@BIÁH ]CE]ÏJRB^ <
MBOMÁ^F] F^RFJF ]CPF OF]ÏF JRB]]F [AHUC] 2
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IIB]BHF IIB]BHF NRFH PFHUAFJC JF]@ÏF ^F[FUF 6;
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MAC@IAOÆUA@C MFEFNC^ NCPÁ O® HF\F]]C JCH^ÆIB^/IFLCHU :
MAC@IAOÆUA@C MFEFNC^ O® ICR]EBP @CIIFEC ]BUFOF] <
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WWA Ciao{afef Ofuboæua`f
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HB^
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[RB]UF[FIOF MFEFNC^ @F]IF [AF^^F 7
]CE]ÏJRB^ OCÖAHC MFEFNC^ OFHRBI MBHÏUB^ MBHÏUB^ 6;
]CE]ÏJRB^ OCÖAHC MFEFNC^ ]FLFBI ORÖC^ LB]HÆHEB^ :
PFH FUÐH MFEFNC^ IRAP @F]ICP RMABUC JCH^ÆIB^ 61
PFH LB]HFHEC MFEFNC^ NCPÁ OF]ÏF OF]UÏH JCH^ÆIB^ 0
PFH NCPÁ MFEFNC^ NRFH OFHRBI @GÆ\B^ OC]BHC 5
PFH@UF OF]ÏF FPPRO/[UF MFEFNC^ IBC[CIEC GB]]B]F PÆH@GB^ :
PFHUF UB]BPF EB NBPÞP MFEFNC^ OF]ÏF UB]BPF OFEB]F @RFE]FEC 2
\A]JBH EB JRFEFIR[B MFEFNC^ EABJC @FOAPÐH JCH^ÆIB^ 60
^R]MF]ÆH MFEFNC^ L]FH@AP@C OC]BHC PCUC =
[RBHUB FNREF CIA\BH^F FHF OAIFJ]CP J]FNB]F GB]HFHEC 7
BH]AVRB EÏB^ @FHBEC [RBMIF EB IF @FI^F/EF
NRFH @C]UÁP []B@AFEC 0
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OF]ÏF NBPÞP OFUBCP @C]@GB]C <
UCUFI ^CHF MFEFNC^ 6=0
^CHF EB FEP@]A[@AÐH> @Æ@B]BP
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BI M]C@BHPB @Æ@B]BP O® UB]BPF PÆH@GB^ [C]]FP :
IF FPRH@AÐH @Æ@B]BP FHUCHAC EÆ\AIF LB]HÆHEB^ 66
IF FPRH@AÐH @Æ@B]BP O® NCPÁ NAOÁHB^ MF@GAIIB] 1
IA@BH@AFECP ]BRHAECP @Æ@B]BP NRFH @C]UÁP OF]JFIIC <
IA@BH@AFECP ]BRHAECP @Æ@B]BP ]RMÁH OCIFHC JÐOB^ 1
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61
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HC]MF @FBPF]AHF @Æ@B]BP ]FVRBI PÆH@GB^ MFÖB^F 2
GB]HÆHEB^ [F@GB@C @Æ@B]BP FHUCHAC OCIFHC ]COB]C 7
GB]HÆHEB^ [F@GB@C @Æ@B]BP AHÁP OFH^FHC \BHUR]F <
GB]HÆHEB^ [F@GB@C @Æ@B]BP NCPÁ O® ^FOM]FHC F@BEC 6;
PFJ]FEC @C]F^ÐH EB NBPÞP @Æ@B]BP O® EBI @F]OBH LB]]B]C ]FOCP 0;
PFH FHUCHAC EB [FERF @Æ@B]BP BOAIAC OC]BHC PÆH@GB^ 6;
PFHUF @B@AIAF @Æ@B]BP ]CPF JÐOB^ JF]EBÖFP 1
\ÏF EB IF [IFUF @FPF] EB @Æ@B]BP @F]ICP MBHAJHC OFH@BMC [BHF 1
\ÏF EB IF [IFUF @FPF] EB @Æ@B]BP OF]ÏF EB ICP ÆHJBIBP ]RMACJCH^ÆIB^
1
@B]]C [BE]C JÐOB^ OFE]CÖB]F EABJC NCPÁ IRMAÆH GB]]B]F 2
AHUB]HF@ACHFI PFH NC]JB OFI[F]UAEF EB @Æ/@B]BP
OB]@BEBP [FHFEB]C [F@GB@C 6
L]FH@AP@C EB C]BIIFHF U]RNAIIC IFR]F ICPFEF \ABA]C 7
UCUFI ^CHF @Æ@B]BP 62<
^CHF EB FEP@]A[@AÐH> @C]AF
@BHU]C IC@FIAEFE []CLBPC] H¾ EBFIROHCP
BI M]C@BHPB M]C^FP IRAP ]FOCP PCIFHC =
@BIIF \AHF]AF @B@IF\ÏH EABJC GB]HÆHEB^ F]FOMAIBU <
FIFJÐH @C]AF @FPAIEF JF]@ÏF \A@BHUB 7
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FIFJÐH @C]AF NRIAÆH PÆH@GB^ FIMFIÆ :
FIFJÐH @C]AF OF]ÏF MBIÁH OC]ÐH ]ÏCP :
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NFIFOF OC]FIBNF ÆHJBIF MC]]BJC UF[AF 6:
\ÏF EFIOF@AF UC]]BNCH@AIIC L]FH@AP@C NF\AB] \F]BIF L]FEB 6;
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WWA Ciao{afef Ofuboæua`f
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Bwu}bofer}f =;6=
\ÏF EFIOF@AF UC]]BNCH@AIIC GB]OAHAF EBI FOC] OF]UÏH IÐ[B^ 1
\ÏF EFIOF@AF UC]]BNCH@AIIC NCPÁ [BE]C OF]UÏH IC]BH^C 6;
\FI EB WÆIAOF \FI\B]EB EBI L]BPHC OF]ÏF EBI OF] [Á]B^ HC]ABJF 0
\FI EB WÆIAOF \FI\B]EB EBI L]BPHC OF]ÏF LB]HFHEF \AIIFIMF JRAIIÁH 5
\FI EB WÆIAOF \FI\B]EB EBI L]BPHC \B]ÐHA@F OF]UÏH JRUAÁ]]B^ 7
UCUFI ^CHF @C]AF 665
^CHF EB FEP@]A[@AÐH> ECH MBHAUC
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@FPURB]F @FPURB]F NF@CMC ICMC [FP@RF :
@IF]BU ECH MBHAUC ÆHJBI ]CMRPUAIIC HÞÖB^ =;
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@RFU]C @FOAHCP ECH MBHAUC B\F ]RA^ [FNRBIC <
ECHCPC @C]UÁP ECH MBHAUC BOAIAC [AÖBA]C LBC 6;
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ECHCPC @C]UÁP ECH MBHAUC OF]ÏF ICR]EBP OC]BHC MFI/@CHB]C
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NCPÁ OFH^FHC ECH MBHAUC FHF OF]ÏF IÐ[B^ J]FHFECP 6;
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[BE]C EB \FIEA\AF \AIIFHRB\F EB IFPB]BHF
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[BE]C EB \FIEA\AF \AIIFHRB\F EB IFPB]BHF
JBOF LB]HÆHEB^ \BJF 1
[RB]UF EB IF PB]BHF \AIIFHRB\F EB IFPB]BHF
NCPÁ OAJRBI MIFH@C @FPFEC =
PFH NCPÁ \AIIFHRB\F EB IFPB]BHF
NCPÁ OF]ÏF @F[AIIF FIMF 0
UCUFI ^CHF ECH MBHAUC 6<5
^CHF EB FEP@]A[@AÐH> OÁ]AEF
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UFORNFI F]]CQC EB PFH PB]/\ÆH
NRFH IRAP [A^F]]C JFIÆH =
ERI@B @GF@ÐH JF]]C\AIIF 'IF! OFHRBI ]CE]ÏJRB^ OF@GR@F 5
ERI@B @GF@ÐH JF]]C\AIIF 'IF! [R]ALA@F@AÐH [AHUC @C]]FIA^F =
OF]ÏF FRWAIAFEC]F OÁ]AEF NBPÞP @RÁIIF] JRB]]B]C 1
PFHUF BRIFIAF OÁ]AEF FHF O® JF]@ÏF MFÖCP 2
PFHUF BRIFIAF OÁ]AEF L]FH@AP@C [C^C L]ÏFP 0
PFHUF BRIFIAF OÁ]AEF O® APFMBI @F]]BUB]C \FI 2
PFHUF BRIFIAF OÁ]AEF O® NCPÁ [RIAEC OF]UÏHB^ =
PFHUF BRIFIAF OÁ]AEF ]FLFBI JCH^ÆIB^ NAOÁHB^ 7
BWU]BOFER]F OCHUANC EF\AE ]CE]ÏJRB^/BPUB@GF ÆI/\F]B^
5
BWU]BOFER]F OCHUANC NRFHF FMBIF \BIB]EF 5
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UAB]]FMIFH@F ^F]^F 'IF! NRFH L]FH@AP@C F]BHFP MBHÏUB^ =
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UCUFI ^CHF OÁ]AEF 2:
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WWA Ciao{afef Ofuboæua`f
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@BHU]C IC@FIAEFE []CLBPC] H¾ EBFIROHCP
JFIAPUBC JFIAPUBC FIL]BEC HÞÖB^ PFIFP 7
VRB]@RP OFI[F]UAEF EB [IFPBH/@AF
NRFH OF]ÏF OFH@BMC OF]UÏH :
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JFM]ABI Q JFIÆH [IFPBH@AF BOAIAF ]CE]ÏJRB^ JF]@ÏF 6
JFM]ABI Q JFIÆH [IFPBH@AF APFMBI O( GB]HÆHEB^ JCH^Æ/IB^ 0
[F]VRB EB OCHL]FJÙB [IFPBH@AF O® APFMBI GB]HÆHEB^ @FMFIIC 6
[F]VRB EB OCHL]F/JÙB
[IFPBH@AF O® PCIBEFE @C]]BFP OF]UÏH 0
[F]VRB EB OCHL]FJÙB [IFPBH@AF PF]FQ FJRPUÏH JFIIBJC <
[B]B^ @COBHEFEC] [IFPBH@AF FO[F]C PFHUCIAHC [B]BÖF 65
PFH @FIAWUC [IFPBH@AF [BE]C F( OF]UÏH NAOÁHB^ 6;
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\A]JBH EB FIUFJ]F@AF PA]RBIF APFMBI OF]ÏF ]CIEÆH JFIIF]EC 6;
\A]JBH EB FIUFJ]F@AF PA]RBIF [BE]C ]A@C JCH^ÆIB^ 6;
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OFBPU]C NRFH @FIB]C OCHBPUB]AC JBOF APFMBI [B@B]C ]CNFP 6;
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WWA Ciao{afef Ofuboæua`f
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WWA Ciao{afef Ofuboæua`f
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WWA Ciao{afef Ofuboæua`f
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WWA Ciao{afef Ofuboæua`f
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http://slidepdf.com/reader/full/revista-olimpiada-2012 43/43
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