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11. príklad 2. letnej série 2007/2008

Zadanie:
Uvažujme mnohouholník s celočíselnými stranami taký, že každé dve jeho susedné strany sú na seba kolmé (nemusí byť konvexný). Dokážte, že ak ho vieme pokryť neprekrývajúcimi sa dominovými kockami veľkosti $2\times 1$ umiestnenými rovnobežne s jeho stranami, tak aspoň jedna z jeho strán má párnu dĺžku.


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RKg4rpef <h1vtmcr5k4~mail~com> - 03. 03. 2014 - 18:15:44 z 58.22.28.133
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bZ9VCmBX47 <qe4n83ij9fg~gmail~com> - 03. 03. 2014 - 15:35:32 z 78-83-34-101.spectrumnet.bg
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eZOEldSfTXc <sansfa~daehyunfa~co~kr> - 08. 11. 2013 - 00:02:28 z ks4001511.ip-198-245-51.net
c1no, odpovedajfa neze1visle, napr. na hlvoasaced papierik. c1no, nemajfa žiadnu informe1ciu o svojom klobfaku. A predsa, kežže z tfdchto favah vyplfdva, že stredne1 hodnota počtu tfdch čo sa pomfdlia je nekonečno, existuje spf4sob ako sa dohodnfa tak, že vždy sa pomfdli len konečne veľa z nich (tie dve veci sa nevylučujfa).Ten proble9m so 100 ve4zňami určite pride1m do sfaťaže.

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HqvJvTVy <sbfo~yahoo~com> - 07. 11. 2013 - 10:24:15 z 188.143.232.12
Katka: klobfak dolu! Toto ma teda vf4bec nenapadlo! Oproti toutmo riešeniu je moje ako Šofola v porovnaned s Kofolou (disclaimer: nič proti Šofole neme1m, iba to nie je "ono").Rado: peknejšed predklad než som pf4vodne myslel!

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JNLCeHH6AV <492898300~qq~com> - 07. 11. 2013 - 03:57:28 z lamb01.sit.uc.cl
Ked sa tak pozeram na tie obazrky 6-uholnikov a nepredstavim si to v 2D, ale v 3D, tak to vyzera ako kocka s hranou dlzky n rozdelena na n^3 jednotkovych kociek, pricom ide o taky pohlad, ze na jednu telesovu uhlopriecku sa pozerame kolmo, takze 2 protilahle vrcholy splyvaju (takyto bod je presne v strede toho 6-uholnika na obrazku). Kazdy z tych 6-uholnikov, ktorych pocet treba zistit, je potom vlastne tiez kocka (zlozena z niekolkych jednotkovych kociek) splnajuca tu vlastnost, ze niektora jej stena je castou prednej, pravej alebo vrchnej steny velkej kocky (kocky s hranou n). Kazda takato kocka je jednoznacne urcena svojim zadnym lavym dolnym rohom, resp. rohovou jednotkovou kockou, a kedze jednotkovych kociek je vo velkej kocke n^3, je to aj riesenie ulohy :).

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K8fFtnMk <mueller~firmenname~de> - 06. 11. 2013 - 06:29:38 z 188.143.232.12
rozlozenie a struktura webu zzelai na kazdom jednom pripade. Neda sa povedat pre vsetky univerzalne ze to ma byt tak a tak. Velkost nadpisov nehra ziadnu ulohu kludne mozes dat aj font 50, nepomoze to. Tieto otazky sa tykaju skor pouzitelnosti webu ako nejakeho seo vplyvu.

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jtiMr0la8d <kamir~home~pl> - 06. 11. 2013 - 05:57:59 z 188.143.232.12
No tak aby som upresnil zopar deotjlav.1) čedm kvalitnejšed text me1te, tfdm viac prirodzenfdch odkazov na ve1s pf4jde. To nie je pravda a plati to plati len v niektorych pripadoch (hlavne spravodajstvo). Malo by byt napisane skor cim kvalitnejsi obsah . (text, obrazky, informacna hodnota, pridana hodnota, ). Text je len jeden z faktorov.2) 5. cool url Dolezite su aj pre to, ze je mozne do nich pridat kw, co prida k relevancii a tym padom vyssiemu umiestneniu v SERP-e. 3) 2. hľadanosť vfdrazu Podla hladanosti sa tazko da odhanut aka bude velka navstevnost na webe Treba este zvazit konkurenciu. Aj keby malo slovo hladanost 300 000 vyhladavani / mesiac, moze sa stat ze na toto slovo nikto nepride, pretoze je obrovska konkurencia Takze je to skor Hladanost/Konkurencia

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VgrPSvlvu366 <support~thinkpositive~co~uk> - 05. 11. 2013 - 11:21:00 z zonal-p.eusa.ed.ac.uk
Rado, na mojom blogu je teraz tiez mrtvo ;-) Ludia su asi v soku z padu investicnych bank, vyrkoov istych politikov, alebo jednoducho skoncili prazdniny.Ja osobne sa na tvoje prispevky vzdy tesim, odkedy som teda objavil QED, a mnohe ulohy ma pekne pobavia! Tato konkretna je naozaj pekna, velmi sa mi paci ze ta take elegantne napadaju!Zatial prezradim, ze riesenie je n^3, pre stranu sestuholnika rozdelenu na n casti. To som moc ale nepovedal, kedze to je lahke uhadnut z tvojich dvoch prikladov. Mne sa to podarilo dokazat pomocou indukcie [mam to tu nacarbane pred sebou na papieri]. Ked budes netrpezlivy s dalsim prikladom, na ktory sa tesim, napis do poznamky a ja sem s radostou napisem moje riesenie. Zaujimalo by ma potom, ci sa na to da ist aj inak! Zatial ma napada len toto jedno riesenie; take follow-your-nose...

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bus - 10. 04. 2008 - 21:45:44 z dsl-static-251.213-160-168.telecom.sk
Okej tak predsa len ešte jeden človek sa našiel čo dal do rohov bielu farbu, Vladko Ujházy, takže nie si na svete sám Jaro :D.

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Jaro - 10. 04. 2008 - 18:56:05 z kms.sk
Wow, tak to je blbé, ja som ale použil biele rohy:)) Asi to svedčí o mojej duševnej nevyrovnanosti...

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bus - 10. 04. 2008 - 17:05:32 z dsl-static-251.213-160-168.telecom.sk
Viacerí ste si všimli, že keď sa ten mnohouholník vyfarbí ako šachovnica, budú všetky políčka v rohoch rovnakej farby.... dosť by ma ale zaujímalo, prečo si zatiaľ //úplne// všetci riešitelia (a dokonca nezávisle na seba aj ja a Feráč) zvolili za túto farbu práve čiernu??? Že by nejaká drsná psychológia? :)

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