LABERINTS (Treball de Recerca de Marta Broto)

7/22/2019 LABERINTS (Treball de Recerca de Marta Broto)

1/51

FDJKZAE]R(Mks mk fd rkprksketdba irgabd)

]utcrd? Dfjd Dfkt

Dutcrd? Hdrtd Jrctc Zajds

Bfdssk? :ejdtxaffkrdt D

Ksbcfd WKMZ[ED IZBAD - JDZBK!ED


2/51

Dirdhkets?

D fd hkvd tutcrd Dfjd Dfkt pkr fd skvd doumd akf sku tkhps.

D Ocded Zcsskff pkr doumdr-hk dhjfcrtcirdgad mkf trkjdff.

D Kvd Pdfdbacs pkr rkspcemrk fks hkvksprkiuetks scjrk kfs fdjkraets rkfdbacedts dhjfd pkmdiciad.

D fd hkvd ikrhded, fDeed, pkr doumdr-hk dbcestruar ued rkprcmubba mkf fdjkraet mk fdRdirdmd dh!fad a pkr scrtar d fd irdvdbamd"ukstd pr#btabd.

D fd hkvd gdh!fad a kfs hkus dhabs "uk h$derkbcf%dt murdet kf mkskevcfupdhket md"uksttrkjdff.

&


3/51

EMK^

&. '(OK)*+R...............................................................................................................

Dhj d"ukst trkjdff prktkeb bchpfar mavkrscs cjokbtaus...................................................

Kf prahkr a hs ikekrdf s bce/a0kr haffcr kfs fdjkraets. Kfs fdjkraets se pdrt mk fdecstrd vamd mks mk jke pktats, pkr4 ec skhjfd "uk eaei: $a prksta dtkeba....................

Kf skice od ued habd hs bcebrkt, s ksjraedr fd skvd utafatdt. Pkesc "uk, sa $de k0astatmurdet tdet mk tkhps, $de mk tkear dfiued utafatdt............................................................

Kf tkrbkr s dprkemrk d majua0dr bdmd tapus mk fdjkraet a d magkrkebadr-fcs g#bafhket. Da04

kh pkrhktr# bce/a0kr-fcs rkdfhket, pcmkr utafat%dr-fcs dhj gdbafatdt a sdjkr mk "uaed/pcbd se a "u/ sahjcfat%ke tcts kfs fdjkraets "uk puiua dedr trcjdet............................

Kf "udrt s pkr d ha ue rkptk. 2dirdmdrad trcjdr dfiued kstrdt/iad pkr ec pkrmrks maesmue fdjkraet a trcjdr skhprk fd scrtamd...........................................................................

Kf bae"u/ cjokbtau s gkr hku ue ks"ukhd pkr k0pfabdr fks pr#bta"uks mued gcrhdcrmkedmd. Kstab aetkrkssdmd ke dprkemrke, pkr"u/ brkb "uk ke ue gutur prcpkr sdjkrrkmdbtdr pr#bta"uks mk hdekrd gfuamd pct skr-hk hcft :taf..............................................

Kf sas/ cjokbtau "uk taeb s dprkemrk d utafat%dr prcirdhks pkr majua0dr dhj fcrmaedmcr.)cebrktdhket haetkrkssd fDutcbdm a fR=ktb$p. ;c $k utafat%dt hda prcirdhks mkmajua0 a brkb "uk skrad jc "uk edprkeius, od "uk dbtudfhket kf majua0 t/beab ks gdgcedhketdfhket dhj crmaedmcr.....................................................................................

Kf skt/ cjokbtau ks rkfdbacedr kfs fdjkraets dhj fd pkmdiciad. )rkb "uk s aetkrkssdet,od "uk jced pdrt mkfs fdjkraets "uk bceka0kh se kfs "uk $kh gkt d bfdssk mk pktats. . .

Kf vuat/ a :ftah cjokbtau s, pkr mksbchptdr gkr ue jce trkjdff mk rkbkrbd a dprkemrk mkfshkus krrcrs pkr"u/ kf prcpkr trkjdff surta haffcr. ...........................................................

7. 9+R*>Z+D 1K?R ?D(KZ+;*R...................................................................................dsscs &kr *ajuaxdr ue fdjkraet bf5ssab 3>dtr0@?

Kf &ra(kr &ds &kr *ajuaxdr ue fdjkraet bf5ssab s ksbcffar kf ec(jrk *k barbuats# Dbcetaeudba0 ks *ajuaxd kf bketrk *kf fdjkraet 3)a'# "7@#

barbuats F barbuats "" barbuats " barbuats

[e bc& *ajuaxdt kf bketrk ec(s bdf uear kfs &uets kxtkracrs tdf bc( ae*abd kf *ajuax 3)a'#"@#

9k+.ebad *k barbuats?8&

Gai. 4=. &ketrk skices echjrk mk

8&76I

Gai. 4$. squkhd kr majua;dr ue fdjkraet #f7ssa# mk *

#ar#uats.

Gai. 42.

Fdjkraet


13/51

9a ks eu(krke kfs barbuats ks rkssk'ukax kf bd(4 a ks )d ued tdufd bcfRfcbdet kf ec(jrk*kfs barbuats +uk ks ,de trcjdet ks &ct ,kurk ue &dtr0 3)a'# "C@?

Barbuats d(j ec(jrks &drkffs ? Ks bcfRfcbd kf : d fd sk'ced bdskffd a ks bcetaeud*k )cr(d dsbke*ket sdftdet ued bdskffd *k bd*d *uks# D fd )a'urd ks trcjke *aes

fks bdskffks *k bcfcr tdrce=d bfdr#

Barbuats d(j ec(jrks skedrs ? Ks &drtkax fd tdufd ke *cs fd bdskffd bketrdf =dkst5 cbu&d*d &kr ue ec(jrk &drkff#

c D f/ks+ukrrd *k fd bdskffd bketrdf ks bcfRfcbd f/" a ks sk'ukax bd& d

f/ks+ukrrd *k )cr(d dsbke*ket cbu&det fks bdskffks jua*ks#

c D fd *rktd *k fd bdskffd bketrdf ks &csd kf ec(jrk *k barbuats +uk t kf

fdjkraet a ks sk'ukax *k )cr(d *ksbke*ket cbu&det fks bdskffks jua*ks#

D fd )a'urd ks trcjke *aes fks bdskffks *k bcfcr jfdeb#

djkraet *k barbuats

" :

djkraet *k F barbuats

: " 7 F C

djkraet *N"" barbuats

: 7 " C "" P T "O F

djkraet *k " barbuats

F : 7 C " P " "O " ": "" "7 T

;.4.:. Bfss!s Jf"!s

Ks &rksketke ke )cr(d barbufdr# ]keke *uks ketrd*ks *uks &drkts a ue eab bketrk#9/ketrd &kr ued ketrd*d s/drrajd df bketrk a ks surt &kr f/dftrd ketrd*d#

>dsscs &kr *ajuaxdr ue fdjkraet J5ftab 3&r5btabd@

Ks bc(ked &kr ued &drkt *ajuaxdet ued ks&ardf 3)a'# "F &ds "@# [e bc& )ktd f/ks&ardfks 'ard bd& d f/kxtkracr a ks )d ued ,cftd (s d f/ks&ardf 3&ds :@# Mks&rs ks 'ard bd& df/aetkracr a ks tcred d )kr ued ,cftd 3&ds @#

8

Gai. 4(. 9rmrk mk #ar#uats kfs qudfs ks >d


14/51

[e bc& *ajuaxd*d fd &ra(krd &drkt ks bc(ked d(j fd sk'ced# Ks )d ued ks&ardfsu&kr&csd*d d fd &ra(krd 3&ds 7@ a +ude s/drrajd fd )aedf *k df &ra(krd &drkt ks 'ard bd&d )crd a ks )d ued fta(d ,cftd 3&ds @#

87


15/51

;.4.#. Z$%&'s

Kfs fdjkraets rc(des s0e +ud*rdts kstde )cr(dts &kr +udtrk skbbaces sa(.tra+uksketrk kffks a ued eabd &drkt d(j rd(a)abdbaces#

Kfs ;astcrad*crs ;de &c'ut bfdssa)abdr +udsa tcts kfs +uk s/;de trcjdt ke trks 'ru&s? *k(kde*rk skr&ket4 a ks&ardf 3)a'# "P@#

;.4.=. *+&fs

Kfs fdjkraets (k*ak,dfs kstde )cr(dts &kr +udtrk skbbaces sk&drd*ks ketrk sa &kr uedbrku# >c*ke skr *k +udfsk,cf )cr(d 'kc(.trabd rk'ufdr? barbufdrs +ud*rdtsrkbtde'ufdrs ;kxd'cedfs### D df'ues sk/fs *k)cr(ke fks &uetks &kr dbcesk'uar )cr(ks(s dtrdbta,ks#

>kr *ajuaxdr-ek ue bdf 3)a'# "T@?

Majuaxdr )a'urks bceb.etra+uks 3bkrbfks +ud*rdts ;kx5'ces###@ 3&ds "@#

Ksjcrrdr *a,a*aet kf bkrbfk ke +udtrk skbbaces 3&ds :@#

[ear fks f4eaks k,atdet +uk kfs trdcs +uk )k( &kr uear-fks ks brkuae ketrk kffs

3&ds @#

86

Gai. 4*. squkhd kr majua;dr ue fdjkraet 17fta#.

Gai. 4/. Fdjkraets

>ds " >ds : >ds

>ds 7 >ds


16/51

Gai. 40. squkhd kr majua;dr ue fdjkraet

hkmak>df.

>ds " >ds: >ds

;.:. [F]AB[ZRDFR (D,K)

90e kfs fdjkraets ke +u. ;a ;d (s */ue bd(4# Maetrk *kfs fdjkraets (uftabursdfs ks

&c*ke *astae'ar *cs ta&us *k bceekxa0 sa(&fk a *k bceekxa0 (fta&fk#

;.:.4.B$''- s%/f

90e d+ukffs fdjkraets +uk kstde )cr(dts &kr ued scfd &drkt d(j rd(a)abdbaces# 9a ks*ksk(jcfa+us kf fdjkraet s/cjtae*rad ued kstrubturd ke )cr(d*/drjrk#

/kstrdt.'ad (s k)kbta,d +uk ks &ct sk'uar &kr ec &kr*rk/s ks8&csdr ued (5 d fd &drkt ec &kr*rk *k ,astd fd &drkt ad,dedr ke'dexdt d d+ukstd# D+ukstd kstrdt.'ad kes)dr5 &dssdr &kr tcts kfs &dssd*asscs# 9kr5 ue bd(4 (cft(s ffdr' *kf +uk ks )krad sa ks sdjs fd scfuba0 *kffdjkraet &kr2 sk(&rk ks trcjdr5 fd scrta*d#

;.:.:.B$''- %0f"/f

90e d+ukffs +uk kstde )cr(dts &kr (s */ued &drkt 3)a'# :"@#

9a ks )d skr,ar f/kstrdt.'ad *k &csdr fd (5 d fd &drkt ue ks &ct trcjdr +uk rk&ktkaxa ue(dtkax rkbcrrk'ut skesk dbcesk'uar scrtar-ek# Kstdr5 *cedet ,cftks d ued &drkt 3)a'# :"&drkt jfd,d@#

Kxastkax ue df'cras(k +uk &kr(kt trcjdr fd scrta*d */d+ukst ta&us *k fdjkraet# 1sfNdf'cras(k *k ]r(dux#

8

Gai. :4. Fdjkraet m-dhtce &curt

Gai. :. Fdjkraet mk


17/51

Bcesastkax ke fks sk'kets ecr(ks?

"# Ec &dssdr (da &kr ue (dtkax bd(4 trks bc&s#

:# 9a s/drrajd d ued bruffd &kr ce ec s/;d &dssdt s/d'd)d +udfsk,cf bd(4#

# 9a ks ,d &kr ue bd(4 ecu a s/drrajd d ued bruffd &kr ce =d s/;d &dssdt c d ue buf*k sdb ks rktrcbk*kax#

7# 9a ue bd(4 &kr ce =d s/;d &dssdt &crtd d ued bruffd &kr ce =d s/;d &dssdts/d'd)d ue bd(4 ecu sa ;a s a sa ec sk/e d'd)d ue +udfsk,cf#

M/d+ukstks ecr(ks sk/e &ct )kr ue drjrk *k *kbasaces 3&r5btabd@?

>kr *ur d tkr(k d+ukst drjrk *k *kbasaces kf (affcr s utafatdr *uks (dr+uks d tctks fksketrd*ks a scrta*ks *k bd*d &dssd*4s# [tafatdr fd &ra(krd &kr (drbdr +uk s/;d &dssdt afd sk'ced &kr (drbdr +uk s/;d &dssdt *cs bc&s a ec tcredr-;a d &dssdr#

;.#.^&-s

90e kfs fdjkraets +uk ec tkeke ue &raeba&a a ue )aedf *k)aeat# Dax2 &kr(kt rkbcrrk/fs skesk)a# D+uksts fdjkraets ks &c*ke bc(&drdr d(j ds&kbtks *k fd ,a*d +ucta*aded bc( drd kf*abbacedra c fd xdrxd */Aetkrekt#

Bd*d ,k'd*d +uk ks jusbd ued &drdufd c ue bcebk&tk s/cjt (s */ued rks&cstd a ke

bd*d rks&cstd ks trcjke (cftks &drdufks a bcebk&tks +uk ks &c*ke tcredr d jusbdrskesk dbdjdr (da kf babfk# Kebdrd +uk s/;d'a &dssdt &kr tctks fks rks&cstks s/;a &c*radtcredr d &dssdr ued ,k'd*d a ued dftrd#

.ZKPZKRKE]DBA2 MK FDJKZAE]R (PZB]ABD)

8I

Gai. ::.


18/51

Ke d+ukst d&drtdt ks bcescfa*d fd tkcrad kx&fabd*d d f/d&drtdt 8ta&us )ket (s ,asudfsfks kx&fabdbaces *kfs *a)krkets fdjkraets# >kr )kr-;c ks rk&rksketke kfs fdjkraetsutafatdet *a,krscs rkburscs#

D+ukst d&drtdt t +udtrk )uebaces#

d &ra(krd s ,kurk (s bfdrd(ket fks *a)kr.ebaks ketrk kfs *a,krscs ta&us *k fdjkraetsa sdjkr-fcs a*keta)abdr#

d sk'ced s d&rke*rk rkdf(ket d *ajuaxdr-fcs a *k(cstrdr df'ueks *k fksbdrdbtkr4sta+uks kx&fabd*ks detkracr(ket#

d tkrbkrd s &c*kr ,kurk kfs fdjkraets ke )cr(ks *a)krkets *k fks +uk ks trcjke;djatudf(ket# >kr kxk(&fk ecr(df(ket kfs fdjkraets rc(des s0e ke :M &kr2 &drtaet*/ue fdjkraet :M sk/e &ct bcestruar ue *k M#

d +udrtd )ueba0 */d+ukst d&drtdt s d&rke*rk d utafatdr *a,krscs &rc'rd(ks

*/cr*aed*cr rkfdbacedts d(j fd a(dt'k? 9Gktb;[& Dutcbd* a Hc,ak HdGkr#

d bae+uked s ksta(ufdr ;djafatdts bc( fd &krbk&ba0 ,asudf c fd (ctrabatdt )aed#

Ks ,cf dbcesk'uar d+uksts cj=kbtaus utafatdet f/ks+uk(d *k &r5btabd +uk ks (cstrd dbcetaeudba0#

8


19/51

C#"# ZK>ZK9KE]DBA$ M/[E DJKZAE] B99AB MK BAZB[A]9 DHJ D[]!BDM

C7!"9s>

"# Zk&rksketdr ue fdjkraet bf5ssab *k barbuats d(j Dutcbd*#

:# Bc(&rc,dr +uk ks &ct )kr ue fdjkraet d(j ,cfu( utafatdet f/Dutcbd*#

# !jtkear ue ks+uk(d */ue fdjkraet bf5ssab &kr bc(&rke*rk (affcr d+ukst ta&us *kfdjkraets#

7# Ksta(ufdr fd &krbk&ba0 ,asudf#

&"&f>

!r*aed*cr#

Dutcbd*#

P$!*%'">

Ks bc(ked *kba*aet fd (a*d *k fks &drkts a kfs &dssd*asscs# ]ct sk'uat ks *ajuaxd fdbrku *kf bketrk a kfs +udtrk &uets +uk f/ke,cftke# 9/uekaxke kfs +udtrk &uets a kfs +udtrk,.rtkxs *k fd brku tdf bc( s/kx&fabd d f/d&drtdt #"#"# Ks &ct utafatdr f/kaed 8f4ekd

a 8rkbcrtdr # >kr dbdjdr ks ,d d 8Wkr - &ct# ,astd M - asc(trabc 9!8 a d(jf/kaed 8&ufsdrtardr s/d)k'kax f/dfturd#

Zs9f"&"s>

"# 9/;d rk&rksketdt ue fdjkraet bf5ssab *k barbuats d(j Dutcbd*#

:# 9/;d bc(&rc,dt +uk ks &ct )kr ue fdjkraet d(j ,cfu( utafatdet f/Dutcbd*#

# 9/;d cjtae'ut ue ks+uk(d */ue fdjkraet bf5ssab a s/;d bc(&rs (affcr d+ukstta&us *k fdjkraets#

7# 9/;d ksta(ufdt fd &krbk&ba0 ,asudf#

8

Gai. :2. krksketd#a6 mue fdjkraet #f7ssa# mk 2 #ar#uats dhj


20/51

C#:# ZK>ZK9KE]DBA$ M/[E DJKZAE] B!ZJ B99AB MK BAZB[A]9 DHJ]K9]!9

C7!"9s>

"# D&fabdr kf &rcbk*a(ket &kr *ajuaxdr d+ukst ta&us *k fdjkraet 3d&drtdt #"#"#@#

:# Bcestruar ue fdjkraet bf5ssab *k barbuats *k )cr(d barbufdr d(j tkstcs#

# Bcestruar ue fdjkraet &rcu 'rde &kr rkbcrrk/f# Zkb0rrkr kf fdjkraet#

7# Ksta(ufdr fd &krbk&ba0 ,asudf a fd ,asa0 ks&dbadf#

&"&f>

7F ]kstcs#

H5ek'd#

P ]ctxcs#

: ]rcsscs *k surc#

B5(krd#

P$!*%'">

Ks bc(ked &kr f/aetkracr )ket ued brku d(j kfs tkstcs (s &ktats#

Ks sk'ukax kf &rcbk*a(ket aetketdet *kaxdr &dssd*asscs *k (a*d sa(afdr a &csdet kfs

tkstcs (s 'rcsscs d f/kxtkracr# 9/utafatd fd &drkt *kf &dta bc( d &drkt *kf fdjkraet a kfs Ptctxcs a kfs *cs )rd'(kets *k surc &kr c(&far df'ueks sk&drdbaces ketrk tkstcs 3)a'# :7@#

[e bc& dbdjdt ks bcestdtd +uk f/d(&fd*d *kfs &dssd*asscs s (cft ,dradjfk a dax2*a)abuftd fd ,asa0 *k bce=uet#

Ks (c*a)abd kf fdjkraet d'd)det bc( d (a*d &kr f/d(&fd*d *kfs &dssd*asscs *cs &kusbcfRfcbdts f/ue *drrkrd f/dftrk#

Ks &dssd fd (5ek'd &kr f/aetkracr &kr rk(drbdr fd &drkt#

>kr fta( ks rkbcrrk kf fdjkraet a ks )de fks )ctcs#>ra(kr s/aetketd )kr fks )ctcs *ks *k tkrrd &kr2 kfs &dssd*asscs ec ks ,kuke j#]ct sk'uat ks &u'ke ueks ksbdfks +uk &crtke df &dta a ks )de (s )ctcs# Mks&rss/aetketd *ks */ued sk&drdba0 d(j kf &dta ,k4 */ues : (ktrks */dfd*d# Kffdjkraet kst5 (dssd d &rc& a ec bd& d fd )ctc#

>kr fta( ks &rc,d *ks */ue tkrrdt kf fdjkraet kst5 &rcu ffue6 a s/dbcesk'ukax+uk ks ,k'ae j kfs &dssd*asscs#

&L


21/51

Zs9f"&"s>

"# 9/;d d&fabdt kf &rcbk*a(ket &kr *ajuaxdr d+ukst ta&us *k fdjkraet 3d&drtdt #"#"#@#

:# 9/;d bcestrut ue fdjkraet bf5ssab *k barbuats *k )cr(d barbufdr d(j tkstcs#

# 9/;d bcestrut ue fdjkraet &rcu 'rde &kr rkbcrrk/f a s/;d rkbcrrk'ut#

7# 9/;d ksta(ufdr fd &krbk&ba0 ,asudf a fd ,asa0 ks&dbadf#

&8

Gai. :=. krksketd#a6 mue fdjkraet #crj #f7ssa# mk 2 #ar#uats dhj


22/51

C## ZK>ZK9KE]DBA$ M/[E DJKZAE] B!ZJ B99AB MK BAZB[A]9 9!JZK9[Z!

C7!"9s>

"# Ird,dr ue fdjkraet bcrj bf5ssab *k trks barbuats scjrk surc#

:# 9a(ufdr kf &rcbs *k bcestrubba0 */ue &ktrc'fa)#

# !jtkear ued sa(ufdba0 */ue &ktrc'fa)#

7# Ksta(ufdr fd (ctrabatdt )aed#

&"&f>

fd&as#

9urc#

Ks&5tufd#

Jdrraed#

>d&kr *k ,a*rk#

Jcf#

>aeturd jfdebd#

>aeturd ek'rd#

Jrctxd#P$!*%'">

Ks bc(ked *ajuaxdet d (5 dfd*d kf fdjkraet scjrk kf surc# >ra(kr fd brku a tct sk'uats/uekaxke kfs &uets kxtkracrs *kf fdjkraet tdf bc( s/kx&fab5 d f/d&drtdt #"#"#

D bcetaeudba0 ks rds+uke d(j fd jdrraed fks f4eaks *ajuaxd*ks detkracr(ket )aesdbcesk'uar 'rd,dr kfs 8bd(aes#

]ct sk'uat ks )d skr,ar f/ks&5tufd &kr sk&drdr kf trcs *k surc trkjdffdt *k fd rkstd# [e bc&dbdjdt s/ks&cfsd a ks ffa(ke kfs bcetcres d(j &d&kr *k ,a*rk#


23/51

C#7# ZK>ZK9KE]DBA$ M/[E DJKZAE] B!ZJ B99AB MK F BAZB[A]9 D H

C7!"9s>

"# Majuaxdr ue fdjkraet bcrj bf5ssab *k F barbuats d (5#

:# D*d&tdr &kr d bc(&5s kf &rcbk*a(ket trcjdt d fd kj?

#xtkb#bdtY^==drkecYdbta,atdtsYfdjkraetsY=d,dYbcestruarQfdjkraetsQbcr*d#;t(

# Dbfdrar f/kx&fabdba0 *k f/d&drtdt #"#"#

7# !jtkear ue ,4*kc *kf &rcbk*a(ket#

# Ksta(ufdr fd (ctrabatdt )aed#

&"&f>

Bc(&5s d(j d*d&td*cr#

fd&as#

Ic(d#

Jcf4'rd)#

MAE-#

Ksbdark#

Bdrtdj0#

fu( *k tdufd#

B5(krd#

: Ic(ks kf5sta+uks#

Hc,ak HdGkr#

]$&>

Ke fd kj batd*d d cj=kbtaus s/kx&fabd +uk d+ukst ta&us *k fdjkraet ks &ct *ajuaxdrbfd,det kstd+uks (drbd*ks df *ajuax d(j ued brku ,kr(kffd a ffa'det ued bcr*d d fdkstdbd : 3)a'# :T@#

9a s/cjskr,d f/dea(dba0 *k fd kj a ks bc(&drd d(j kf ,4*kc rksuftdet */d+ukstdkx&kra.ebad ks &ct ,kurk +uk fks kstd+uks bcaeba*kaxke d(j kfs &uets ce s/;dbfd,dt kf bc(&5s &kr )kr kf fdjkraet#

P$!*%'">

Ks bc(ked *ajuaxdet kf bketrk *kf fdjkraet d ffd&as d(j f/d=u*d *k f/ksbdark a kf bdrtdj0#

]ct sk'uat s/uekaxke kfs &uets (s kxtkres *k fd brku d(j f/d=u*d *kf bc(&5s#

&
http://www.xtec.cat/~jjareno/activitats/laberints/java/construir_laberints_corda.htmhttp://www.xtec.cat/~jjareno/activitats/laberints/java/construir_laberints_corda.htm


24/51

Kf &ra(kr barbuat ks *ajuaxd bcfRfcbdet kf bc(&5s df/kstdbd :# Mks */d+ukstd &csaba0 ks bc(ked kfsk'ce barbuat +uk ks bc(&fktd d(j kf bc(&5s df&uet # Mks *kf &uet ks trdd fd &drt ae)kracr *rktd*kfs barbuats 7 a # >kr dbdjdr d+uksts trks barbuats

bdf bfd,dr kf bc(&5s dftrk bc& df &uet : 3&drtsu&kracr@ a d bcetaeudba0 df &uet " 3ae)kracrks+ukrrd@# 9k'uaet ke kf &uet " ks trdd fd &drtae)kracr ks+ukrrd *kf sas. barbuat +uk s/;d *kbc(&fktdr *ks *k kf &uet : 3su&kracr@ a 3ae)kracr*rktd@# Kf skt. barbuat ks bc(ked bfd,det kf bc(&5sdf &uet 7 a &cstkracr(ket dfs &uets " : a #

Hketrk ks 'rd,d ks rk&ktkax kf &rcbs d(j jcf4'rd) rk&dssdet fks f4eaks *ajuaxd*ks&r.,ad(ket# Dax2 ks )d &kr+u. kf ffd&as ks ,ku (dfd(ket d trd,ks *k fd b5(krd *k)ctc'rd)ad#

>kr 'rd,dr ks )d kf (uetdt'k +uk ks &ct ,kurk d fd )a'urd O# Kf jrd *kf ffu( +uk*d dscjrk kf )uff a fks 'c(ks kf5sta+uks s/utafatke &kr ffa'dr fd b5(krd df jrd *k fd f5(&d*d#

#

>kr rk&dssdr kf fdjkraet bdf (uetdr f/d*d&td*cr df bc(&5s a kebdaxdr-;a ue jcf4'rd)#

[e bc& 'rd,dt ks &dssd kf ,4*kc &kf &rc'rd(d Hc,ak HdGkr a s/dbbkfkrd#

Zs9f"&"s>

"# 9/;d *ajuaxdt ue fdjkraet bcrj bf5ssab *k F barbuats d (5#

:# 9/;d d*d&tdt &kr d bc(&5s kf &rcbk*a(ket trcjdt d fd kj#xtkb#bdtY^==drkecYdbta,atdtsYfdjkraetsY=d,dYbcestruarQfdjkraetsQbcr*d#;t(

# 9/;d dbfdrat fd kx&fabdba0 *k f/d&drtdt #"#"#

7# 9/;d cjtae'ut ue ,4*kc *kf &rcbk*a(ket utafatdt#

# 9/;d ksta(ufdt fd (ctrabatdt )aed#

>kr ,kurk kf ,4*kc cjtae'ut bdf dedr d f/deekx 3MWM@ a bfabdr fd &astd "#

&7

8 &

7 6

I67&8

Gai. 2. Huetdtik kr

Gai. :0.
http://www.xtec.cat/~jjareno/activitats/laberints/java/construir_laberints_corda.htmhttp://www.xtec.cat/~jjareno/activitats/laberints/java/construir_laberints_corda.htm


25/51

C## ZK>ZK9KE]DBA$ M/[E DJKZAE] %[DMZD] B99AB MK F BAZB[A]9 DHJKI! _

C7!"9s>

"# D&fabdr d fd bcestrubba0 kf &rcbk*a(ket tk2rab &kr *ajuaxdr d+ukst ta&us *kfdjkraet 3d&drtdt #"#"#@#

:# Bcestruar ue fdjkraet bf5ssab *k F barbuats *k )cr(d +ud*rd*d a )kr-;a &dssdr uedjcfd &kr f/aetkracr#

# Wkurk kf fdjkraet ke ,cfu(#

7# D&rkbadr fd ffdr'd*d *kf rkbcrrk'ut#

# Ksta(ufdr fd &krbk&ba0 ,asudf#

&"&f>

>kbks *k k'c_#

>cts *k k'c_#

A(det 3ks).rab@#

A(det 3&ctket@#

Wa*rk 3)aekstrd *ks(uetdjfk@#

>d&krs jfdebs#B5(krd#

]r4&c*k )fkxajfk#

Iuad *k bcrtaed#

Hc,ak HdGkr#

P$!*%'">

Bcestruar kf fdjkraet

Ks bc(ked &kf bketrk )ket fd brku sk'uaet kf &rcbk*a(ket kx&fabdt d ]a&us#

Ks )de kfs &dssd*asscs *k fd (dtkaxd d(&fd*d +uk fks &drkts# M/d+ukstd (dekrd ks&c*ke utafatdr fks &kbks *k k'c_ &kr bc(&rc,dr-ek fd (a*d# 9/uekaxke kfs&dssd*asscs &kr scjrk &kr+u. ks (detae'uae rkbtks *urdet kf &rcbs *k bcestrubba0#

&6

Gai. 24. krksketd#a6 mue fdjkraet qudmrdt #f7ssa# mk * #ar#uats dhj


26/51

kr d+ukst (ctau ksjus+uke dftrks (dtkradfs#

Kf &ra(kr (dtkradf +uk ks &rc,d s kf bdrtr0# Ke d+ukst bds s/;d utafatdt kf +uk ks )dskr,ar &kr (uetdr drxa,d*crs# Kf bdrtr0 ks bcrjd sctd kf &ks *kf fdjkraet a fks &kbks *kffdjkraet s/d)fuaxke#

Kf sk'ce (dtkradf +uk ks &rc,d s ued f5(aed *k )ustd &ra(d# d )crd *k f/a(det fd

trd,kssd j a ec ks *cjfk'd sctd kf &ks *k fks &kbks &kr2 s *a)4baf sk'uar fd trd=kbt2rad*kf fdjkraet *ks *k sctd fd )ustd =d +uk ec s trdes&drket#

Kf tkrbkr (dtkradf a *k)aeatau s ued )aekstrd *ks(uetdjfk# Mks *k sctd ks &ct (curk fdjcfd &kr)kbtd(ket d(j f/d=u*d *k f/a(det a ks ,kuke kfs &dssd*asscs *kf fdjkraet#

&

Gai. 2:. Fdjkraet scjrkGai. 22. Fdjkraet scjrk f7haed mk

Gai. 2=. Gaekstrd


27/51

Huetdt'k &kr 'rd,dr

Kf (uetdt'k *k)aeatau ks &ct ,kurk d bcetaeudba0?

d )aekstrd kst5 scjrk ued tdufd kxtkesajfk# 9cjrk fd )aekstrd ;a ;d &d&krs &kr+u. ec ks,k'a fd &krsced +uk (cu f/a(det ks).rab 3jcfd@ a ks ,k'a j kf rkbcrrk'ut *k fd jcfd#

9cjrk kfs &d&krs ks bcfRfcbd kf fdjkraet#

>kr+u. ec trcetcffa fd b5(krd ks ffa'd d(j ue tr4&c*k )fkxajfk d ued 'uad *k bcrtaed ke*kss +uk s/d'udetd rkbcfd*d &kfs *cs kxtrk(s d fks bdaxks *k k'c_#

]ct +uk*d afRfu(aedt &kf ffu( *k scjrk fd tdufd#

Zs9f"&"s>

"# 9/;d d&fabdt kf &rcbk*a(ket &kr *ajuaxdr d+ukst ta&us *k fdjkraet 3d&drtdt #"#"#@

:# 9/;d bcestrut ue fdjkraet bf5ssab *k F barbuats *k )cr(d +ud*rd*d s/;d )kt&dssdr ued jcfd &kr f/aetkracr a s/;d 'rd,dt#

# 9/;d &c'ut ,kurk a tcbdr kf fdjkraet ke ,cfu(#

7# 9/;d bc(&rc,dt +uk fd ffdr'd*d *kf rkbcrrk'ut s (s 'rde *kf +uk ks &c*ada(d'aedr ke ue &raeba&a#

# D (s *k bc(&far kfs cj=kbtaus s/;d cjtae'ut ued ,astd aeks&krd*d *kf fdjkraet*ks *k sctd fd tdufd#

C# 9/;d ksta(ufdt fd &krbk&ba0 ,asudf#

>kr ,kurk kf ,4*kc cjtae'ut bdf dedr d f/deekx 3MWM@ a bfabdr fd &astd :#

&I

Gai. 2$. Huetdtik kr ird>dr. Gai. 2(. Fdjkraet mks mk


28/51

C#C# ZK>ZK9KE]DBA$ M/[E DJKZAE] J]AB MK B!ZMD

C7!"9s>

"# Bcestruar ue fdjkraet J5ftab d(j bcr*d#

:# Bcestruar ue fdjkraet &kr rkssk'uar-fc d(j kf tdbtk#

# D&rke*rk d *ajuaxdr d+ukst ta&us *k fdjkraet#

7# Wkurk fd ffdr'd*d *kf rkbcrrk'ut#

# Mk(cstrdr +uk d+ukst fdjkraet kst5 )cr(dt &kr *uks &drkts 3bcr*ks@#

C# cts *k k'cZ#

Hc,ak HdGkr#

P$!*%'">

Bcestruar kf fdjkraet

>ra(kr ks *ajuaxd kf fdjkraet d (5 dfd*d ke ue &d&kr#

]ct sk'uat ks bcfRfc+uke fks bcr*ks d tkrrd sk'uaet kf *ajuax *k (cstrd &kr sdjkr sa s0e&rcu ffdr'uks 3)a'# F@#

Mks&r.s s/d'd)d ue bcax4 *k sc)5 a s/k(jcfabd d(j ue ffkecf &kr tdf +uk fd bcr*d ;arkssdfta#

Ks bcfRfcbd &ra(kr ued bcr*d 3)a'# P@ a *ks&r.s f/dftrd 3)a'# T@ a s/ke'dexke df bcax4 d(jd'uffks *k bd Ks &rcburd *kaxdr sk(&rk kf (dtkax ks&da ues *cs *ats#

&


29/51

kr fta( ks &dsske fks )ctcs d f/cr*aed*cr a s/utafatd kf &rc'rd(d Hc,ak HdGkr &kr )krued dea(dba0#

Zs9f"&"s>

"# 9/;d bcestrut ue fdjkraet J5ftab d(j : bcr*ks *k(cstrdet dax4 +uk kfs fdjkraetsj5ftabs kstde )cr(dts &kr *uks &drkts#

:# 9/;d d&r.s bc( ks *ajuaxke d+ukst ta&us *k fdjkraets#

# 9/;d ,ast +uk a'udf +uk ke kf fdjkraet brktkeb kf rkbcrrk'ut s (cft (s ffdr' *kf+uk kes a(d'aek( d &ra(krd ,astd#

7# 9/;d &c'ut sk'uar kf fdjkraet 'uadet-sk ec(s &kf tdbtk#

# 9/;d )kt fd dea(dba0 a dax4 s/;d (cstrdt +uk t ued ketrd*d a ued scrta*d*a)krkebad*ks#

C# 9/;d ksta(ufdt fd &krbk&ba0 ,asudf a fd (ctrabatdt )aed#

>kr ,kurk kf ,4*kc cjtae'ut bdf dedr f/deekx 3MWM@ a bfabdr fd &astd #

C#F#ZK>ZK9KE]DBA$ MK ]ZK9 DJKZAE]9 Z!HDE9 DHJ 9\K]BL[>

&

Gai. 2*. Fdjkraet df Gai. 2/. Prahkrd Gai. 20. &cf3fc#det fd skiced

Gai. =. krksketd#a6 mue fdjkraet 17fta# mkGai. =4. Huetdtik kr gkr


30/51

C7!"9s>

"# Zk&rksketdr ue fdjkraet rc(5 *k bd*d ta&us d(j ,cfu(#

:# Mk(cstrdr +uk kfs fdjkraets rc(des kstde )cr(dts &kr ued eab &drkt kebdrd

+uk d+ukstd tae'ua rd(a)abdbaces#

# [tafatdr f/9Gktb;[&

7# Ksta(ufdr fd ,asa0 ks&dbadf#

&"&f>

Majuax *kfs trks ta&us *k fdjkraet rc(5#

!r*aed*cr#

9Gktb;[

P$!*%'">

Ks bc(ked dedet d 8us;Y>uff # #]ct sk'uat ks trku f/ks+uk(d *k sctd kf *ajuax d(j f/kaed 8Hc,ka &kr dbdjdr ks &aetd kf fdjkraet d(j f/kaed >daet JubGkt #

Ks rk&ktkax kf (dtkax &rcbs d(j kfs dftrks *cs fdjkraets#

L

Gai. =:. squkhd mkfs trks taus mk fdjkraets


31/51

8

Gai. =2. Fdjkraet rch7 mk taus

Gai. ==. Fdjkraet rch7 mk taus


32/51

Zs9f"&"s>

"# 9/;d rk&rksketdt ue fdjkraet rc(5 *k bd*d ta&us d(j ,cfu(#

:# 9/;d *k(cstrdt +uk kfs fdjkraets rc(des kstde )cr(dts &kr ued eabd &drktkebdrd +uk d+ukstd tae'ua rd(a)abdbaces#

# 9/;d utafatdt f/9Gktb;[

7# 9/;d ksta(ufdt fd ,asa0 ks&dbadf#

C#F# ZK>ZK9KE]DBA$ MK DJKZAE] HKMAKWD MK BLDZ]ZK9 DHJ W![HDHJ 9\K]BL[>

C7!"9s>

"# Zk&rksketdr kf fdjkraet (k*ak,df *k B;drtrks 3)a'# 7F@ d(j 9Gktb;[

:# Zk&rksketdr d(j 9Gktb;[& ue fdjkraet d(j bcrjks#

# D&rke*rk d )kr skr,ar fks kaeks *k f/9Gktb;[& rkfdbaced*ks d(j fks bcrjks#

7# Wkurk bc( +uk*d ue fdjkraet cra'aedf(ket &fd d(j ,cfu(#

# Ksta(ufdr fd ,asa0 ks&dbadf#

&"&f>

Ks+uk(d *kf fdjkraet *k B;drtrks 3)a'# 7C@#!r*aed*cr#

9Gktb;[

P$!*%'">

Ks bc(ked a(&crtdet f/ks+uk(d dedet d 8us;Y>uff

#

]ct sk'uat ks trkuke fks &drts scjrdets *kfs bkrbfks a s/d)k'kaxke fks bdetced*ks *kfs&dssd*asscs d(j f/kaed 8drb# Df )aedf s/ksjcrrke fks f4eaks scjrdets d(j fNkaed 8krdskra ks trku f/ks+uk(d *k sctd kf *ajuax d(j f/kaed 8Hc,k #

&

Gai. =$. Fdjkraet rch7 mk taus


33/51

>kr dbdjdr ks &aetd kf fdjkraet d(j f/kaed 8>daet JubGkt # >kr d fd &drtsu&kracr *k fd &drkt ks jusbd ue bcfcr sudu d 8HdrGkrs8 a &kr d fks &drkts ks jusbd uedtkxturd *k tctxdeks &csdet 8JrabG de* Bfd**ae' d fd &kstde6d +uk s/cjrk df bfabdr f/kaed8>daet JubGkt #

Zs9f"&"s>

"# 9/;d rk&rksketdt kf fdjkraet (k*ak,df *k B;drtrks d(j 9Gktb;[&

:# 9/;d rk&rksketdt d(j 9Gktb;[& ue fdjkraet d(j bcrjks#

# 9/;d d&r.s d )kr skr,ar fks kaeks *k f/9Gktb;[& rkfdbaced*ks d(j fks bcrjks#

7# 9/;d ,ast bc( +uk*drad ue fdjkraet cra'aedf(ket &fd d(j ,cfu(#

# 9/;d ksta(ufdt fd ,asa0 ks&dbadf#

Gai. =/. krksketd#a6 mkf fdjkraet hkmak>df mk &+drtrks dhj

Gai. =*. Fdjkraet mkGai. =(. squkhd mkf fdjkraet mk


34/51

1. FDJKZAE]R A ODZMAER.

D &drtar *kf Zkedaxk(ket ks ,de bcestruar kfs &ra(krs fdjkraets (uftabursdfs ke =dr*aes#D+ukstks bc(&fabd*ks bcestrubbaces tkeake ue cj=kbtau f*ab#

9a ks &rkstd dtkeba0 df (dtkradf d(j +u. kstde )kts ks &c*ke trcjdr fdjkraetsbcestruts d(j xa&rkrs bc( kf *k Lcrtd c */dftrks bcestruts d(j tkax bc( kf fdjkraet*k fd &du 32rfdemd;.4dhj% ks trcjke fdjkraets bcestru7ts dhj "ard-scfs, bch kfZka'edb-sur-Ae*rk 3)a'# 7T@ bcesa*krdt kf (s 'rde *kf (0e# Kf &ra(kr fdjkraet *k jfdt*k (crc ,d skr bcestrut d(j f/cj=kbtau *k 'rd,dr fd &kfRf4bufd 9urdssab Pdr>kf "TT a*ks *k ffd,crs sk/e ;de bcestrut (cfts (s#

9a ks jus+uke fdjkraets td(j sk/e trcjke *k bcestruts d(j tctxdeks bc( f/DrG,affHdk *k Ec,d VcrG 3)a'# O@ c d(j &fdexks (kt5fRfa+uks bc( drd kf cc*ke


35/51

?. FDJKZAE]R D JDZBKFCED (PZB]ABD)

Ke d+ukst d&drtdt s/kstu*ake kfs *cs fdjkraets (s a(&crtdets *k fd ecstrd bautdt kfdjkraet */Lcrtd a kf *k fd 9d'rd*d


36/51

P#" ZK>ZK9KE]DBA$ MK DJKZAE] MK D 9DIZDMD


37/51


38/51

PDZ] :>Zk&rksketdba0 *kf fdjkraet ae,krs *k fd 9d'rd*d kr rk&rksketdr kf fdjkraet d(j Dutcbd* s/;d utafatdt kf rkffku *k fd )a'urd C +uk kstrcjd d fd &crtd *k Iktsk(de4 d fd )dded *k fd >dssa0 a bcrrks&ce d f/ae,krs *kffdjkraet bcestrut d fdpdrt kr dbcesk'uar ,kurk *a)krkets ,astks *kf fdjkraet df (dtkax tk(&s ks ,d d Wketdeds-,ketdeds'udr*d*ds### a s/cjrk ued )aekstrd ce ks &ct tradr kf ec(jrk *k ,astks +uk ksekbkssatke ,kurk d f/ ;crd 3)a'# C F P@#

PDZ] #> Zk&rksketdba0 *kf fdjkraet *k fd 9d'rd*d


39/51


40/51

7L


41/51

PDZ] => Zk&rksketdba0 *kf fdjkraet *k fd 9d'rd*d


42/51

?.:. ZKPZKRKE]DBA2 MKF FDJKZAE] M


43/51

&"&f>

Zktdffdjfk *kf fdjkraet */Lcrtd# D=uetd(ket *k Jdrbkfced# 9kr,ka *k >drbs a dr*aes#Ksbcfd ]dffkr *k Zk;djafatdba0 *kf >dtra(cea# d Bautdt *k >d&kr# Jdrbkfced "TPT#

]ascrks#

>k'd *k jdrrd#

>k'd *k bcetdbtk#

Bdrtr0 &fc(d#

D'uffks *k bd

B5(krd#

9Gktb;[

P$!*%'">

PDZ] 4 > Zk&rksketdba0 *kf fdjkraet */Lcrtd d &drtar */ue rktdffdjfk#

Ks bc(ked ke'dexdet fd jdsk scjrk ued su&kr)4bak *urd bc( kf bdrtr0 &fc(d#

D bcetaeudba0 ks rktdffke a s/ke'dexke fks *a)krkets &kbks tdf bc( *auke fksaestrubbaces *kf rktdffdjfk# >kr ke'dexdr fks &kbks 'rdes ks &ct )kr skr,ar fd &k'd *kjdrrd &kr2 &kr fks (s &ktatks s (affcr fd *k bcetdbtk#

[e bc& dbdjd*d fd bcestrubba0 ks rktdffke kfs drjrks d &fdkr a ks bfd,ke d(j d'uffks dfks ceks jcsbcsks *kf &drb *kf fdjkraet# 1s jc &csdr ued (abd *k &k'd *k bcetdbtk dfd &uetd su&kracr *k f/d'uffd &kr k,atdr +uk kf &d&kr ,d'a ffasbdet bd& d jdax 3)a'# CO@#

PDZ] :>Zk&rksketdba0 *kf fdjkraet */Lcrtd d(j 9Gktb;u

Gai. (. krksketd#a6 mkf fdjkraet m-crtd d drtar mue


44/51

>kr bc(kedr ks )d ued )ctc'rd)ad *k fd /&" 4ke +u. ec(s surta kf fdjkraet a ks'udr*d d f/cr*aed*cr#

D bcetaeudba0 s/cjrk f/9Gktb;u& a ks ,d d 8kr dbdjdr s/d)k'kaxke )a'urks ;u(deks dedet d 8ae*c bc(&ceket a ksbra,aet dfjusbd*cr 8&kc&fk 3)a'# C"@#

Zs9f"&"s>

"# 9/;d ,ast kf fdjkraet *aetrk *kf bce=uet *kf &drb#

:# 9/;d )kt ue ,cfu( *kf fdjkraet */Lcrtd d(j f/ 9Gktb;[

# 9/;de (affcrdt kfs bcekaxk(kets scjrk fd utafatdba0 *k f/ 9Gktb;[

7# 9/;d ksta(ufdt fd &krbk&ba0 ,asudf fd (ctrabatdt a fd ,asa0 ks&dbadf#

6. []AFA]D] DB][DF MKFR FDJKZAE]R

77

Gai. (4. krksketd#a6 mkf fdjkraet m-crtd dhj


45/51

Dbtudf(ket kfs fdjkraets ks &c*ke trcjdr ke ffcbs (cft *a)krkets a d(j utafatdts *a)krkets#Ks &c*ke *a,a*ar kfs uscs ke *cs 'ru&s? f*absYbufturdfs a &k*d'2'abs#

Ke kf &ra(kr 'ru& 3f*absYbufturdfs@ ks trcjke ketrk */dftrks kfs fdjkraets *kfs ffajrks a&kfRf4bufks# A'udf +uk kfs ecstrks d,det&dssdts utafatk( kfs fdjkraets ke fks ;ast2raks#

Ecr(df(ket kfs fdjkraets *kfs ffajrks a fks &kfRf4bufks s0e d&drket(ket a(&cssajfks a*ae5(abs ks (cuke d (krb. *k fd ;ast2rad# La ;d fdjkraets */d+uksts ta&us d fd&kfRf4bufd 8!aes kf fdjkraet 1ga". 56;c 8Mdrry Pcttkr 1ga".5G;. >kr2 td(j ;a ;d ffajrksce surtke fdjkraets skeaffs a d'rd*djfks sk(jfdets dfs *kfs =dr*aes bc( drd d *dMast'rad aetkrhaedjfk 1ga". 5;.

Kfs =cbs *k tdufd s0e ued dftrd )cet aeks'ctdjfk *k fdjkraets &krtde6kets df 'ru&f*absYbufturdfs# La ;d =cbs */kstrdt.'ad bc( drd 8%ucramcr= 1ga". 5?;ce bd*d =u'd*cr ;d*k brkdr ue fdjkraet &kr df sku c&ceket +uk fa *a)abufta f/drrajd*d d fd (ktd (ketrk kff ;a

drrajd# 8hdk=

bcesastkax ke )kr fdjkraets *ae5(abs ce ks &c*ke (curk df'ueks&drkts# ]d(j ;a ;d =cbs */;djafatdt bc( kf 8*djyraet&= 1ga". 55;ke kf +udf =u'det d(jfd aebfaedba0 *kf tdufkff s/;d */dbcesk'uar +uk ued jcfd )dba kf rkbcrrk'ut bc(&fkt#]d(j ks trcjke =cbs */cr*aed*cr jdsdts ke fdjkraets a s +uk edturdf(ket ks &ctbcesa*krdr fd &detdffd *kf 8bchkbcbcsue fdjkraet 3)a'# CF@#

>kr2 kf =cb (s )d(0s ke )cr(d *k fdjkraet s *cbd# 1s d&drket(ket ue fdjkraetueabursdf &kr2 kst5 &fk *k trd(&ks? bufs *k sdb bc( kf &cu a bd(aes d(d'dts bc(kfs &cets c fks c+uks# ]ct dax2 kf bce,krtkax ke (uftabursdf# ] ued bdskffd (cft buracsdke )cr(d *k fdjkraet ce kf =u'd*cr ks +uk*d kebdffdt ue fdjkraet *aetrk */ue fdjkraet#

Kfs fdjkraets bc( d rk&rksketdbaces drt4sta+uks td(j )cr(ke &drt *kf 'ru&f*abYbufturdf# Maes fks rk&rksketdbaces drt4sta+uks ke &c*k( *astae'ar trks ta&us# Kf

&ra(kr s0e kfs =dr*aes +uk =d s/;de bc(ketdt ke f/d&drtdt F# [e kxk(&fk (cft dbtudf s8Kf c(c quk ffcrd *kf :OOC a(d 3>kr@# Kf sk'ce ta&us s0e fks ksbufturks bc( 8kf

76

Gai. (:. Pkf3f@#ufd INaes kf Gai. (=. AFd +astcradGai. (2. Fdjkraet mk A-drrO Pcttkr =A.

Ga . ($. ucramcr=. Gai. ((. Gai.(*.


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fdjkraetc mk fd hkhcrad *k Zd(0e *k 9ctc :OOT 3)a'# CP@ c fd *k Hab;dkf D6rtce d(jkf t4tcf *k Iue $dk"TFO# Kf tkrbkr s0e kfs +ud*rks bc( 8Kf *djkraet*k kcecrd *kBdrrae'tce "TT" 3)a'# CT@ c 84&k sprae" fdjyraet& *k dbkG VkrGd :OO7 3)a'# FO@#

Ketrdet df 'ru& *k fdjkraets &k*d'2'abs kf &ra(kr +uk ks &ct &kesdr s +uk ks *cekefdjkraets dfs ekes &ktats &kr+u. kfs )dbae tdet d bdsd bc( d f/ksbcfd# Dax2 sk'urd(ketks rkbcfd ke f/kxast.ebad *kf 8A9B-Z 3)a'# F"@ ued *k fks &rc,ks +uk ks )de &kr*ktkr(aedr kf Bck)abaket AetkfRfkbtudf# [ed &drt */d+ukstd &rc,d bcesastkax ke rkscf*rk"O fdjkraets (uftabursdfs cr*kedts *k (s skeaff d (s bc(&fkx# 9/;de *k rkdfatdrskesk daxkbdr kf ffd&as a k,atdet fks &drkts a kfs bufs *k sdb# Ke d+ukstd &rc,d ks ,dfcrdfd bd&dbatdt *kf eke *k *ur d tkr(k aestrubbaces f/dtkeba0 f/dutcrk'ufdba0 *k fd,kfcbatdt f/detaba&dba0 fd &rkbasa0 *kf trd a fd bd&dbatdt *k sk'uar ue &dtr0 ,asudf#

]d(j kxastkax ue tkst dec(kedt 8djkraets *k >crtku +uk ks )d skr,ar &kr d,dfudr kf

trdstcre &kr *.)abat */dtkeba0 skesk c d(j ;a&krdbta,atdt 3]MDY]MDL@# D+ukst tkstd,dfud f/dtkeba0 a fd bd&dbatdt *k &fdea)abdba0# Mk )kt ue *kfs kxkrbabas &rc&csdts &kr fdrkk*ubdba0 *k &krsceks d(j ]MD s fd rkscfuba0 *k fdjkraets#

Ks &ct *ar +uk fd rkscfuba0 *k fdjkraets (uftabursdfs d=u*d d (affcrdr tctks fks bd&dbatdtsdetkracrs kxbk&tk fd bd&dbatdt *k *ur d tkr(k aestrubbaces =d +uk ec ks rkjkeaestrubbaces */ued dftrd &krsced sk(&rk +uk ks )de fdjkraets#

]d(j ks &ct *ar +uk kfs fdjkraets ueabursdfs d=u*ke d (affcrdr fks sk'kets bd&dbatdts?f/dtkeba0 f/dutcrk'ufdba0 *k fd ,kfcbatdt fd &rkbasa0 *kf trd a fd bd&dbatdt *k sk'uar ue&dtr0 ,asudf#

6.4. KE]ZK8AR]D D [ED PKMD5C5D>

K,d >dfdbacs s ued &k*d'c'd +uk trkjdffd d ue K+ua& */Dssksscrd(ket

>sabc&k*d'2'ab 3KD>@

7

Gai. (0. Af FdjkraetI mk

Fkcecrd mk &drraeitce.Gai. *.B+k sraei

fdjOraet+A mk d#k, kr,d.

Gai. (/. Af fdjkraetc mk fd

hkhcradI mk dh6e mk

Gai. *4. ')&J
http://www.fotobazar17.com/2009/11/wiosna-jacek-yerka-arte-pintura.htmlhttp://www.fotobazar17.com/2009/11/wiosna-jacek-yerka-arte-pintura.htmlhttp://www.fotobazar17.com/2009/11/wiosna-jacek-yerka-arte-pintura.htmlhttp://www.fotobazar17.com/2009/11/wiosna-jacek-yerka-arte-pintura.html


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4. B$% & /s!$/*&3$3& 9"f"@s f&'"s / *&3'$s"!& 9's K' 9's!&s$s

D f/;crd *k )kr ued d,dfudba0 &k*d'2'abd bdf )kr ue *ad'e2stab 'kekrdf#Aetkrkssd rkbcffar ae)cr(dba0 scjrk *a)krkets ds&kbtks ?

"# Bd&dbatdts bc'eata,ks#

:# Mkske,cfu&d(ket &krbk&tau#

# >kr)af &sabc(ctrau#

7# Mas)uebaces bkrkjrdfs#

# Ldjafatdts &sabcfae'4sta+uks#

Ke kf bds *kfs fdjkraets s/d,dfuke kfs *cs &ra(krs?

ks bd&dbatdts bc'eata,ks +uk ae*a+uke ke +uaes 5(jats kf eke s a((d*ur a kf*kske,cfu&d(ket &krbk&tau +uk ks rk)krkax d fd aetkr&rktdba0 fd &krbk&ba0###

Ke kfs ekes (s 'rdes sk/fs ;a &ct bcetrcfdr kf tk(&s a s/d,dfud fd rd&a*ksd *kf)uebaced(ket (ketdf#

%ude ks *u d tkr(k ued &rc,d d(j fdjkraets td(j ks &ct ,kurk f/dbtatu* *kfeke sa &kesd djdes *k bc(kedr c s/;a ffked *arkbtd(ket sa )d fks f4eaks j c&kr tdf *k dedr r5&a* surt *kf fdjkraet###

ks &rc,ks d(j fdjkraets s/utafatke &kr bc(&fk(ketdr fks &rc,ks

kstde*dr*atd*ks# >rc,ks kstde*dr*atd*ks s0e &rc,ks kfdjcrd*ks &kr ue&sab2fk' *ktkr(aeke d(j )adjafatdt +uae rksuftdt ;d *k trkurk ue eke sk'ces fdsk,d k*dt &kr ec &rksketdr ue rktdr* (ketdf#

ks &rc,ks +uk utafatc a bcetkeke fdjkraets s0e kf A9B-Z a kf A9B-7 +uk s0e&rc,ks &kr d,dfudr kf 'rdu */aetkfRfa'.ebad# Kf Hbdrt;6 +uk d,dfud fdaetkfRfa'.ebad *ks *k tds+uks (dea&ufdta,ks a f*a+uks s d*k+udt &kr d ekes*k -C de6s a kf tkst */d&tatu*s */k*ubdba0 ae)detafs 3DKA@#

7I


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:. K' f& "+& '& s


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4. BCEBF[RACER>

Kf &ra(kr cj=kbtau +uk k( &rc&csd,d krd bce.axkr (affcr kfs fdjkraets# Mks&r.s*/ksbraurk fd sk,d ;ast2rad kx&fabdr-ek tcts kfs ta&us a rk&rksketdr-fcs ke fd &drt &r5btabd

s k,a*ket +uk ke s (cftks (s bcsks# 9a drd ,ka' ue fdjkraet ec &dssdr5 &kr fd(k,d (ket skesk +uk (/dtura ue (c(ket d &kesdr-;a#

Kf sk'ce cj=kbtau +uk k( &rc&csd,d krd ksjraedr fd sk,d utafatdt# E/;k trcjdt *k (cft,drad*ks? f*a+uks bufturdfs &k*d'2'a+uks sa(j2fa+uks### ks ;k kx&fabdt d f/d&drtdt*/;ast2rad a )ced(ketdf(ket ke f/d&drtdt 8[tafatdt dbtudf *kfs fdjkraets#

Kf tkrbkr cj=kbtau krd d&rke*rk d *ajuaxdr bd*d ta&us *k fdjkraet a d *a)krkebadr-fcs)5baf(ket# D+ukst cj=kbtau f/;k bc(kedt d bc(&far (ketrk kx&fabd,d kfs skus ta&us&kr2 ce rkdf(ket kfs ;k d&r.s d *ajuaxdr a d a*keta)abdr ;d sa'ut )ket fks &r5bta+uks#

Kf +udrt cj=kbtau krd trcjdr df'ued kstrdt.'ad &kr ec &kr*rk/s *aes */ue fdjkraet a trcjdrsk(&rk fd scrta*d# D+ukst cj=kbtau sk(jfd,d *a)4baf *k bc(&far &kr2 ;d rksuftdt +uk]r(dux df "P: =d ;c ;d,ad )kt# >ub *ar +uk ;k bc(&r.s fd sk,d kstrdt.'ad a ;k*asske6dt ue drjrk *k *kbasaces#

Kf bae+u. krd )kr (ku f/ks+uk(d &kr kx&fabdr fks &r5bta+uks# Brkb +uk d+ukst cj=kbtauf/;k bc(&fkrt (ketrk )kad fks &r5bta+uks skesk skr-ek (dssd bcesbaket# Zk*dbtdr fks&ra(krks ,d skr ue &rcbs )kaxub a fket (ketrk +uk ,d skr (cft r5&a* ksbraurk fksfta(ks#

Kf sas. cj=kbtau +uk tkead krd d&rke*rk d utafatdr &rc'rd(ks &kr *ajuaxdr d(jf/cr*aed*cr# Wcfad d&rke*rk d )kr skr,ar f/Dutcbd* a f/9Gktb;[ Brkb +uk &ub *ar +uk kes (s +uk df &raeba&a *kf trkjdff =d +uk ;k )kt jdstdets &r5bta+uks d(j d+uksts&rc'rd(ks# D (s d (s td(j ;k d&r.s d utafatdr kf &rc'rd(d Hc,ak HdGkr#

Kf skt. cj=kbtau krd rkfdbacedr kfs fdjkraets d(j fd &k*d'c'ad# D+ukt cj=kbtau f/;kbc(&fkrt d f/d&drtdt 8[tafatdt dbtudf *kfs fdjkraets ce ks bc(ketd fd utafatdt *kf A9B-Zkfs fdjkraets *k >crtku a s/ketrk,astd ued &k*d'c'd#

Kf ,uat. a fta( cj=kbtau krd k,a*ket(ket )kr ue jce trkjdff *k rkbkrbd a d&rke*rk *kfs(kus krrcrs &kr+u. kf &rc&kr trkjdff surta (affcr# Brkb +uk ;k )kt ue jce trkjdff =d +uk;k d&r.s (cftks bcsks ;k bc(&fkrt kfs cj=kbtaus &rc&csdts a e/;k *kaxdt ue rdstrkksbrat# #

7


50/51

44. JAJFAC5ZDAD

KJ 5ZDAD

K*Gaes Mastcry cg $dks dem *djyraet&s SBcesuftd? "P */djraf :O"`

;tt&?YY'6*ar#*k(ce#bc#uGY=cY(dkY

Bfd*kffds >rcs Zd(ce $cmkfadbae mk prcbkscs bc"eata#cs ahpfabdmcs ke fd scfubae

mk fdjkraetcsSBcesuftd? *k (da' :O"` ;tt&?YY#t*x#bdtY;de*fkY"OPOY7FCF

tkb Masskeykh fdjkraets brktkebsSBcesuftd? */djraf :O"`

;tt&?YY#xtkb#bdtY^==drkecYdbta,atdtsYfdjkraetsYdbta,atdtQ:#;t(

De2ea( 3(daf *k bcetdbtk fdjcfdjfdjcfdj#ekt@*djcfdjSBcesuftd? : */djraf :O"`

;tt&?YY#fdjcfdj#ektY;astcradY&rk;astcradYkf-fdjkraetc-*k-(c'crY

De2ea( 3(daf *k bcetdbtk fdjkraetcsfdjkraetc#cr'@*djkraetcsSBcesuftd? : */djraf

:O"`;tt&?YYfdjkraetcs#kkjf6#bc(Yae*kx#;t(f

9atacs ]ur4stabcs Pdrquk mkf *djkraetc mk Mcrtd SBcesuftd? 7 */djraf :O"`

;tt&?YYsatacsturastabcs#bc(Y&dr+uk-*kf-fdjkraetc-*k-;crtdY

Aestatut */Kstu*as Bdtdfdes !abbacedra mk fd ffke"ud bdtdfdedSBcesuftd? "O */djraf :O"`

;tt&?YY*fb#akb#bdtYrksufts#ds&

Hdjkf Vd(af 9deta Kstkjde Kbu 3kmSBcesuftd? " */djraf :O"`

;tt&?YY#kburk*#buYae*kx#&;&Ydjkraetc

d,akr ]crrks Icjkred *djkraetcs mk $c"cr 1$dre;SBcesuftd? */djraf :O"`

;tt&?YYckstr6(eac#jfc's&ct#bc(#ksY:O":Y":Yfdjkraetcs-*k-(c'cr-(drae#;t(f

Dfkxde*rd ZudecNbac Pdrk(d, *cs


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Deatd !tkrc Jrd,c*djkraetcs Aasb rSBcesuftd? : *k (da' :O"`

;tt&?YYks#sbraj*#bc(Y*cbY"FOPYdjkraetcs-asb-r

9kr'a Jdes fcrt Psabcfc"d aegdetaf y (u#keafSBcesuftd? :F */D'cst :O"`

;tt&?YY#&sabc*ad'ecsas#ksYdrkdks&kbadfad*dYaestru(ketcs*kk,dfudbaceYasbrasba,Yae*kx#&;&

cde Murde->crtd kus BBBO Kf fdjkraetc mkf $JBSBcesuftd? :P */D'cst :O"`

;tt&?YYjfc's#bbbj#cr'Y,kusYkx&csabacesYkf-fdjkraet-*kf-(edbYfde'ks

De2ea( Ha ju;dr*affd SBcesuftd? :P */D'cst :O"`

;tt&?YY=d;drtabG#jfc's&ct#bc(#ksY:O""YOTYkf-=uk'c-*k-fd-cbd#;t(f

Wkra*atds ];k dj6raet; 9cbakt6 SBcesuftd? P !btujrk :O"`;tt&?YYtrdesfdtk#'cc'fk#ksYtrdesfdtk;fkssfketfksu;tt&mDm:

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