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  • 7/23/2019 Solutions to Cross

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    [gfutcgms tg Krgss-Irdcm ^rglf`os

    Odmy ge ygu dr` edocfcdr wctb tb` us` ge lr`dhlgdrh `mhs tg ecmcsb gee prgj`kts. Lr`dhlgdrh `mhs dr` v`ry iggh

    dt icvcmi d prgj`kt tbdt ecmcsb`h fgga. Bgw`v`r, ct cs copgrtdmt tg umh`rstdmh bgw tg kgmstrukt lr`dhlgdrh `mhsprgp`rfy tg dvgch krgss irdcm prglf`os. B`r` cs d fgga dt bgw tg prgp`rfy oda` lr`dhlgdrh `mhs, dmh d kgupf`

    ge `xdopf`s ge krgss-irdcm sgfutcgms. Ps` tb`o cm ygur wgghwgracmi prgj`kts tg icv` ygur eurmctur` tbdt

    ecmcsb`h fgga dmh dvgch krgss-irdcm prglf`os.

    Lr`dhlgdrh @mhs

    Xb` prcodry purpgs` cs tg kdp tb` `mh irdcm ge tb` tdlf` tgp tg icv` ct d ogr` ecmcsb`h fgga. [go` p`gpf` hgm'tfca` tb` fgga ge `mh irdcm, pdrtckufdrfy ce tb`y hgm't amgw bgw tg bdmhf` ct wb`m stdcmcmi. Xb`s` dr` amgwm ds

    "lr`dhlgdrh `mhs", lut tb`y'r` dfsg us`h gm gtb`r dss`olfc`s, sukb ds sgfch wggh tdlf` tgps.

    Krgss Irdcm ^rglf`osH`p`mhcmi gm tb` wchtb ge tb` tdlf` tgp (Eci.4), ct kgufh `dscfy `xpdmh ly 4/8" gr ogr`. Xb` `mh kdps hg mgt

    `xpdmh dmh kgmtrdkt cm f`mitb, l`kdus` fgmictuhcmdf ogv`o`mt cs kgmsch`r`h z`rg egr sbgrt f`mitbs. [g b`r` w`

    bdv` d kfdssck `xdopf` ge "krgss-irdcm kgmstruktcgm" dmh ct's cmb`r`mt prglf`os.

    Ce tb` `mh kdps dr` scopfy ifu`h gm, tb` k`mtr` pdm`f wcff krdka hurcmi p`rcghs ge fgw r`fdtcv` buochcty (\B). Ds

    \B cmkr`ds`s, tb` k`mtr` pdm`f wcff try tg `xpdmh, lut wgm't bdv` `mguib str`mitb tg lr`da tb` `mh kdps pdrdff`f

    tg tb` irdcm hcr`ktcgm. Xb` ifu` ocibt edcf cmst`dh, gr tb` k`mtr` pdm`f wcff tda` gm p`rodm`mt kgopr`sscgm,icvcmi ct dm `v`m bcib`r fca`fcbggh ge krdkacmi wb`m tb` \B kgo`s ldka hgwm.

    Xg dvgch prglf`os wb`m uscmi lr`dhlgdrh `mhs, tb` `mhs ge tb` k`mtr` pdm`f dr` kut cmtg tbr`` gr ogr` t`mgms.Gm` bui` t`mgm igcmi dkrgss tb` wbgf` wchtb wgufh w`da`m tb` `mh kdps tgg oukb (c.`. tgg oukb odt`rcdf

    r`ogv`h egr tb` ogrtcs`). [g tb` t`mgm cs hcvch`h cmtg sodff`r t`mgms, f`dvcmi d sbgrt dr`d cm l`tw``m `dkb tg

    a``p tb` odtcmi suredk`s stcee`r dkrgss tb` wchtb ge tb` tdlf` tgp. Xb`m gm` v`ry sbdffgw ogrtcs` (gr hdhg) cs kutcmtg tb` `mh kdps' `hi`s. [`v`rdf dr`ds dr` kut gut h``p`r tg egro tbr`` gr ogr` h``p`r ogrtcs`s.

    Ogr` Xbdm O``ts Xb` @y`

    Xbcs dff fggas v`ry fgickdf, `xk`pt tbdt sgo` sp`kcdf kgmsch`rdtcgms dr` m`k`ssdry tg dffgw tb` k`mtr` pdm`f tgefgdt er``fy cmsch` tb` `mh kdps.

    Dffgw Egr @xpdmscgmGmfy tb` k`mtr` t`mgm sbgufh l` ifu`h cmtg tb` k`mtr` ogrtcs`. Ifu` kdm't l` us`h gm tb` gutsch` t`mgms, gr ct

    wgufh r`strckt wggh ogv`o`mt.

    Xb` gut`r ogrtcs`s oust l` wch`r tbdm tb` t`mgms ly tb` odxcouo dogumt ygu `xp`kt tb` tdlf` tgp tg `xpdmh

    ergo s`dsgm tg s`dsgm. F`dvcmi d lct ogr` tbdm ygu m``h cs l`tt`r tbdm mgt `mguib. (Eci.;)

    L` sur` tg f`dv` `xtrd wchtb cm tb` ogrtcs` ge tb` gut`r t`mgms.

    Mgtck` tbdt d tcmy lct ge rggo cs f`et dt tb` lgttgo ge tb` ogrtcs`. Dftbguib tbcs csm't t`kbmckdffy m`k`ssdry egr

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    tb` gut`r t`mgms (wbckb wcff mgt l` ifu`h) ct cs stdmhdrh prdktck` tg dffgw rggo egr `xk`ss ifu`. [cmk` tb` gut`rt`mgms dr` mgt ifu`h cm tb` trdhctcgmdf s`ms`, tb`y oust stcff l` dttdkb`h sgo`bgw tg a``p tb` `mh kdps ecrofy cm

    pfdk`. Ybcf` tb` k`mtr` t`mgm kdm l` pcmm`h wctb d hgw`f (cm dhhctcgm tg ifu` gm tb` `mtcr` t`mgm), tb` gut`r

    t`mgms oust l` er`` tg ogv` sch`wdys cm tb` ogrtcs`s.

    Xb` sgfutcgm cs tg oda` dm `fgmidt`h hgw`f bgf` (gr sfgt) cm tb` t`mgm. D hgw`f wcff tb`m ig tbrguib tb` r`iufdr

    bgf` dt tb` tgp dmh lgttgo wdffs ge tb` ogrtcs` (gm tb` `mh kdps), dmh tbrguib tb` sfgt ge tb` t`mgms. Xb`r` oust

    l` mg ifu` l`tw``m tb` t`mgm dmh tb` ogrtcs`, mgr l`tw``m tb` t`mgm dmh tb` hgw`f.

    Xb` hgw`fs kdm l` ifu`h tg tb` mh kdps, lut mgt tg tb` t`mgms (`xk`pt egr tb` k`mtr` gm`). @dsc`r sdch tbdm hgm`.

    Xb` `dsc`st wdy cs tg put ifu` bcib `mguib gm tb` hgw`f tbdt ct wcff mgt r`dkb cmtg tb` t`mgm sfgt. Ce tb` hgw`fects tb` bgf` smuify, tb`m tb` ifu` wcff trdv`f up tb` hgw`f (mgt hgwm) wb`m hrcv`m cm wctb fcibt bdoo`r tdps.

    Xb` hgw`f bgf`s hrcff`h cmtg tb` `mh kdps kdm stgp just sby ge pusbcmi tbrguib tb` gppgsct` sch`. Ce ygu fca` tb`fgga ge tbr`` gr ogr` pr`kcs`fy pfdk`h hgw`fs (ds d h`kgrdtcv` dkk`mt) tb`m bdv` tb`o sbgwcmi gm tb` tgp ge tb`

    tdlf` tgp. Xb`y kdm dfsg l` hgm` cm d kgmtrdstcmi wggh tg stdmh gut `v`m ogr`. Lut `v`m hgw`fs ge tb` sdo`

    sp`kc`s wcff stdmh gut quct` mck`fy, ds tb`cr `mhs dr` kgopgs`h ge `mh irdcm dmh wcff dpp`dr hdra`r tbdm tb` r`st

    ge tb` tdlf` det`r ecmcsbcmi.

    Ce ygu hgm't fca` tb` fgga, gr ce tbcs cs l`ygmh ygur sacff f`v`f, tb`m bdv` tb`o igcmi cm ergo tb` lgttgo wb`r`tb`y wgm't l` s``m.

    [cocfdr [ctudtcgmsSgu ody l` wgmh`rcmi bgw get`m ygu'ff dktudffy m``h tbcs t`kbmcqu` ce ygu hgm't pfdm gm uscmi lr`dhlgdrh `mhs

    gm ygur m`xt tdlf` tgps, gr ce ygu'r` mgt pfdmmcmi gm lucfhcmi dmy lr`dhlgdrhs cm tb` m`dr eutur`. Xda` mgt`: tbcs

    tb`gry dmh t`kbmcqu` dppfc`s tg dff acmhs ge krgss-irdcm sctudtcgms wb`r` d pdm`f wgufh gtb`rwcs` bdv` ctsogv`o`mt r`strckt`h ly dmgtb`r eurmctur` pdrt.

    Ce ygu wdmt d fdri` sgfch wggh pdm`f ecx`h l`tw``m twg l`h pgsts (Eci.8) (wctb tb` pdm`f's wggh irdcm rummcmi

    bgrczgmtdffy) tb`m ygu bdv` d "krgss irdcm" prglf`o. Xb` sgfutcgm cs d vdrcdtcgm ge tb` dlgv`. Sgu us` ogrtcs`-dmh-t`mgm jgcm`ry dmh sfchcmi hgw`fs. Xb` upp`r t`mgm ects cts ogrtcs` smuify dmh cs ifu`h `v`rywb`r`. D hgw`f

    kdm dfsg l` us`h (kdff`h d "pcmm`h" ogrtcs`-dmh-t`mgm jgcmt).

    Xb` fgw`r ogrtcs` bds tg l` wch`r tbdm tb` t`mgm. Xb` hgw`f sfch`s tbrguib d bgf` cm tb` l`h pgst dmh dm

    `fgmidt`h sfgt cm tb` t`mgm. Ifu` cs r`strckt`h tg tb` l`hpgst dmh hgw`f gmfy. Xb`r` kdm't l` dmy ifu` gm tb`

    t`mgm gr gm tb` ogrtcs` wdffs.

    Dmgtb`r sgfutcgm tg tb` krgss irdcm prglf`o cs erdo`-dmh-pdm`f h`scim (Eci.0). Xb` l`h pgsts l`kgo` stcf`s cm d

    erdo`-dmh-pdm`f s`t-up, dffgwcmi tb` pdm`f tg efgdt cm tb` ochhf`. Xb` erdo` dmh pdm`f h`scim cs `dsc`r tgdkbc`v`, lut ce ygu pr`e`r tb` styf` ge tb` b`dhlgdrh cm eciur` 8, ygu kdm dkbc`v` tbcs fgga gmfy ly uscmi tb`

    sfchcmi hgw`f t`kbmcqu` ds sbgwm.

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    Kgmkfuscgm

    Gm` ge tb` ogst copgrtdmt tbcmis ygu kdm hg tg coprgv` ygur wgghwgracmi prgj`kts cs tg f`drm ogr` dlgut tb`odt`rcdf ygu'r` wgracmi wctb. Yggh cs d umcqu` lucfhcmi odt`rcdf. F`drm bgw ct ogv`s dmh wby. F`drm tg

    h`scim dmh lucfh sg ds tg tda` cmtg dkkgumt wggh's cm`vctdlf` ogv`o`mt.

    Xb`r` cs mg scmif` h`scim `rrgr ds s`rcgus ds edcfcmi tg dkkgumt egr sukb ogv`o`mt. Mg odtt`r bgw l`dutceuf, gr

    w`ff lucft d ecmdf pc`k` ody l`, ce ct hg`sm't dffgw egr wggh ogv`o`mt, ct wcff mgt stdmh tb` t`st ge tco`.

    B@MH\CA UD\JP cs d ecm` eurmctur` h`scim`r/lucfh`r wbg prgvch`s wgghwgracmi cmstruktcgm dmh s`ocmdrs

    m`dr Dktgm, GM.

    EP@MX@

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