{"id":343,"date":"2011-01-20T20:46:23","date_gmt":"2011-01-20T20:46:23","guid":{"rendered":"http:\/\/matematika.okamzite.eu\/?p=343"},"modified":"2011-01-20T20:46:23","modified_gmt":"2011-01-20T20:46:23","slug":"51-rocniku-medzinarodnej-matematickej-olympiady-imo","status":"publish","type":"post","link":"https:\/\/matematika.besaba.com\/?p=343","title":{"rendered":"51. ro\u010dn\u00edk Medzin\u00e1rodnej matematickej olympi\u00e1dy (IMO)"},"content":{"rendered":"

Martin Vodi\u010dka z Gymn\u00e1zia Alejov\u00e1 v Ko\u0161iciach si na 51. ro\u010dn\u00edku Medzin\u00e1rodnej matematickej olympi\u00e1dy (IMO), ktor\u00e1 bola v j\u00fali v Kazachstane, po\u010d\u00ednal naj\u00faspe\u0161nej\u0161ie. Z\u00edskal zlat\u00fa medailu.<\/strong><\/p>\n

Pre Slovensko je to od roku 1993 v porad\u00ed \u0161tvrt\u00e1 zlat\u00e1 medaila. Predo\u0161l\u00ed traja dr\u017eitelia ju v\u0161ak z\u00edskali a\u017e vo svojom maturitnom ro\u010dn\u00edku, zatia\u013e \u010do Martin m\u00e1 iba 14 rokov a m\u00f4\u017ee si vybojova\u0165 \u00fa\u010das\u0165 na IMO e\u0161te nieko\u013ekokr\u00e1t.
\n
\n\u010eal\u0161\u00ed dvaja \u010dlenovia slovensk\u00e9ho t\u00edmu Ladislav Ba\u010do z Gymn\u00e1zia Po\u0161tov\u00e1 v Ko\u0161iciach a Michal Hagara z Gymn\u00e1zia Jura Hronca v Bratislave z\u00edskali bronzov\u00e9 medaily. Ostatn\u00ed slovensk\u00ed \u00fa\u010dastn\u00edci IMO Martin Bachrat\u00fd z Gymn\u00e1zia Ve\u013ek\u00e1 okru\u017en\u00e1 v \u017diline, Mari\u00e1n Hor\u0148\u00e1k z Gymn\u00e1zia P\u00e1rovsk\u00e1 v Nitre a Jakub Kone\u010dn\u00fd z Gymn\u00e1zia Gr\u00f6sslingov\u00e1 v Bratislave si prevzali \u010destn\u00e9 uznanie. Tie sa ude\u013euj\u00fa t\u00fdm s\u00fa\u0165a\u017eiacim, ktor\u00ed nez\u00edskaj\u00fa medailu, ale vyrie\u0161ia aspo\u0148 jednu zo \u0161iestich \u00faloh na pln\u00fd po\u010det bodov.<\/p>\n

\"\"
\nKonkurencia bola ve\u013ek\u00e1, ve\u010f do Kazachstanu pri\u0161lo 523 \u017eiakov stredn\u00fdch \u0161k\u00f4l z 97 kraj\u00edn. Po\u010das dvoch dn\u00ed rie\u0161ili dve trojice \u00faloh, pri\u010dom za ka\u017ed\u00fa \u00falohu mohli z\u00edska\u0165 najviac 7 bodov. Absol\u00fatnym v\u00ed\u0165azom IMO s pln\u00fdm po\u010dtom 42 bodov sa stal Zipei Nie z \u010c\u00edny. Po vyhodnoten\u00ed s\u00fa\u0165a\u017ee jednotlivcov b\u00fdva zvykom s\u010d\u00edta\u0165 body cel\u00e9ho dru\u017estva a vznikne tak neform\u00e1lne poradie kraj\u00edn. Slovensko v \u0148om skon\u010dilo na 39. mieste. V r\u00e1mci kraj\u00edn E\u00da sme sa zaradili na 11. miesto.<\/p>\n

\u00dalohy na IMO vyber\u00e1 medzin\u00e1rodn\u00e1 jury zlo\u017een\u00e1 z ved\u00facich dru\u017estiev v\u0161etk\u00fdch z\u00fa\u010dastnen\u00fdch kraj\u00edn. Pri v\u00fdbere sa sna\u017e\u00ed pokry\u0165 \u00falohami \u010do najviac matematick\u00fdch oblast\u00ed. Pritom sa db\u00e1 na to, aby ka\u017ed\u00fd s\u00fa\u0165a\u017en\u00fd de\u0148 bola prv\u00e1 \u00faloha naj\u013eah\u0161ia a tretia naj\u0165a\u017e\u0161ia. Tento rok v\u0161ak bola pomerne \u0165a\u017ek\u00e1 aj \u00faloha \u010d. 5 \u2013 vyrie\u0161ilo ju len 50 s\u00fa\u0165a\u017eiacich.<\/p>\n

Na\u0161i \u0161tudenti si v\u00fdborne poradili s \u00falohou \u010d. 1, ke\u010f ju v\u0161etci \u0161iesti vyrie\u0161ili na pln\u00fd po\u010det bodov. I\u0161lo o jednoduch\u00fa funkcion\u00e1lnu rovnicu, na ktorej sa v\u0161ak dali strati\u0165 body za drobn\u00e9 ned\u00f4slednosti.<\/p>\n

Celkom dobre sme skon\u010dili aj pri \u00falohe \u010d. 6 \u2013 v\u00e4\u010d\u0161ina kraj\u00edn mala za t\u00fato \u00falohu \u0161es\u0165kr\u00e1t 0 bodov, a tak zisk 6 bodov Martina Vodi\u010dku mo\u017eno pova\u017eova\u0165 za \u00faspech. Bolo treba dok\u00e1za\u0165 ist\u00fa vlastnos\u0165 \u0161peci\u00e1lnej postupnosti kladn\u00fdch re\u00e1lnych \u010d\u00edsel, a aj ke\u010f bola \u00faloha zaraden\u00e1 do algebry, jej vyrie\u0161enie vy\u017eadovalo kombinatorick\u00e9 uva\u017eovanie. Podobne sme skon\u010dili pri \u00falohe \u010d. 5, ke\u010f\u017ee aj tu zisk v s\u00fa\u010dte 7 bodov znamenal v porovnan\u00ed s in\u00fdmi krajinami dobr\u00fd v\u00fdsledok. T\u00e1to \u00faloha celkom zamie\u0161ala poradie, ke\u010f\u017ee mnoh\u00e9 tradi\u010dne siln\u00e9 krajiny v nej prekvapivo z\u00edskali m\u00e1lo bodov, zatia\u013e \u010do in\u00e9 krajiny, ktor\u00fdm sa na in\u00fdch \u201eklasick\u00fdch\u201c \u00faloh\u00e1ch a\u017e tak nedarilo, v nej bodovali. D\u00f4vod bol zrejme ten, \u017ee v\u00fdsledok \u00falohy bol pomerne neo\u010dak\u00e1van\u00fd.<\/p>\n

Kompletn\u00e9 v\u00fdsledky a \u0161tatistiky z tohtoro\u010dnej a aj z minul\u00fdch IMO mo\u017eno n\u00e1js\u0165 na internetovej str\u00e1nke http:\/\/imo-official.org<\/a>. Bud\u00faci ro\u010dn\u00edk IMO sa uskuto\u010dn\u00ed v Holandsku \u2013 v Amsterdame (http:\/\/www.imo2011.nl<\/a>).<\/p>\n

PETER NOVOTN\u00dd<\/strong>
\nved\u00faci dru\u017estva SR na IMO v Kazachstane<\/em><\/p>\n

Pozn.: Detailnej\u0161iu \u0161tatistiku a zadanie \u00faloh n\u00e1jdete na tejto str\u00e1nke<\/a>.<\/p>\n\n

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Martin Vodi\u010dka z Gymn\u00e1zia Alejov\u00e1 v Ko\u0161iciach si na 51. ro\u010dn\u00edku Medzin\u00e1rodnej matematickej olympi\u00e1dy (IMO), ktor\u00e1 bola v j\u00fali v Kazachstane, po\u010d\u00ednal naj\u00faspe\u0161nej\u0161ie. Z\u00edskal zlat\u00fa medailu. Pre Slovensko je to od roku 1993 v porad\u00ed \u0161tvrt\u00e1 zlat\u00e1 medaila. Predo\u0161l\u00ed traja dr\u017eitelia ju v\u0161ak z\u00edskali a\u017e vo svojom maturitnom ro\u010dn\u00edku, zatia\u013e \u010do Martin m\u00e1 iba 14 … Pokra\u010dova\u0165 na 51. ro\u010dn\u00edk Medzin\u00e1rodnej matematickej olympi\u00e1dy (IMO)<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[9],"tags":[],"class_list":["post-343","post","type-post","status-publish","format-standard","hentry","category-60-rocnik"],"yoast_head":"\n51. ro\u010dn\u00edk Medzin\u00e1rodnej matematickej olympi\u00e1dy (IMO) - Matematick\u00e1 olympi\u00e1da<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/matematika.besaba.com\/?p=343\" \/>\n<meta property=\"og:locale\" content=\"sk_SK\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"51. ro\u010dn\u00edk Medzin\u00e1rodnej matematickej olympi\u00e1dy (IMO) - Matematick\u00e1 olympi\u00e1da\" \/>\n<meta property=\"og:description\" content=\"Martin Vodi\u010dka z Gymn\u00e1zia Alejov\u00e1 v Ko\u0161iciach si na 51. ro\u010dn\u00edku Medzin\u00e1rodnej matematickej olympi\u00e1dy (IMO), ktor\u00e1 bola v j\u00fali v Kazachstane, po\u010d\u00ednal naj\u00faspe\u0161nej\u0161ie. 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