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#1
15 ¾ÄȨԡÒ¹ 2014, 10:18
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Ê¶ÔµÔ : ¢éÍÊͺÊͧªØ´
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¢³Ð·Õè´Ô©Ñ¹¡ÓÅѧàÊǹҡѺ¼Í§à¾×è͹ʵÃÕá¡Ãè§ã¹§Ò¹ÃÒµÃÕÍÂÙè¹Ñé¹ à´ç¡àÊÃÔ¿ÁÒ¡ÒÃͧä´é¹Ó⨷Â줳ԵÈÒʵÃìÁÒ¶ÒÁ¤èÐ Ê׺ä´éÇèÒ à»ç¹¢éÍÊͺ Math Prize For Girls (USA) »Õ¹Õé ¤èÐ ´Ô©Ñ¹àËç¹ÇèÒ ÁÕ¤ÇÒÁÊǧÒÁ ¹èÒʹ㨠ÅéÓÅÖ¡ ʧèÒ§ÒÁ àËÁ×͹µÑǴԩѹ àŹÓÁÒà¼Âá¾Ãè¤èÐ There are two math exams called A and B. 2014 students took the A exam and/or the B exam. Each student took one or both exams, so the total number of exam papers was between 2014 and 4028, inclusive. The score for each exam is an integer from 0 through 40. The average score of all the exam papers was 20. The grade for a student is the best score from one or both exams that she took. The average grade of all 2014 students was 14. Let G be the greatest possible number of students who took both exams. Let L be the least possible number of students who took both exams. Compute G - L. á»Åà»ç¹ä·Â ÁÕ¡ÒÃÊͺ¤³ÔµÈÒʵÃìÊͧ¤ÃÑé§ ¨ÐàÃÕ¡ÇèҪش A áÅÐ B ¹Ñ¡àÃÕ¹¨Ó¹Ç¹ 2014 ¤¹à¢éÒ·Ó¡ÒÃÊͺ A áÅÐ/ËÃ×Í B ¹Ñ¡àÃÕ¹áµèÅФ¹ ¨ÐÊͺà¾Õ§ªØ´à´ÕÂÇ ËÃ×ÍÊͧªØ´ ¹Ñ蹤×Í ¨Ó¹Ç¹¡ÒÃÊͺ·Ñé§ËÁ´·Õèà»ç¹ä»ä´é ÍÂÙèµÑé§áµè 2014 ¶Ö§ 4028 ¤Ðá¹¹ÊÓËÃѺ¢éÍÊͺáµèÅЪشà»ç¹¨Ó¹Ç¹àµçÁ¨Ò¡ 0 ¶Ö§ 40 ¤èÒà©ÅÕèÂÊÓËÃѺ¡ÒÃÊͺ·Ø¡ªØ´¤×Í 20 à¡Ã´ÊÓËÃѺ¹Ñ¡àÃÕ¹áµèÅФ¹¤×Í ¤Ðá¹¹·ÕèÁÒ¡·ÕèÊش㹺ÃôҤÐá¹¹¨Ò¡¡ÒÃÊͺ ¶éÒ à¡Ã´à©ÅÕèÂÊÓËÃѺ¹Ñ¡àÃÕ¹·Ñé§ 2014 ¤¹ ¤×Í 14 ãËé G ¤×ͤèÒÁÒ¡ÊØ´¢Í§¨Ó¹Ç¹¹Ñ¡àÃÕ¹·ÕèÊͺ·Ñé§ÊͧªØ´ L ¤×ͤèÒ¹éÍÂÊØ´¢Í§¨Ó¹Ç¹¹Ñ¡àÃÕ¹·ÕèÊͺ·Ñé§ÊͧªØ´ ¨§ËÒ¤èҢͧ G-L ´Ô©Ñ¹¤Ô´ÇèÒ â¨·Âì¢é͹ÕéÁÕ¤ÇÒÁÊǧÒÁ áÅЪǹãËéÅÔéÁÅͧ à»ç¹ÍÂèÒ§ÂÔ觤èÐ ÊÇÑÊ´Õ¤èÐ  
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#2
17 ¾ÄȨԡÒ¹ 2014, 00:48
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¡ÃмÁ¡ç¤Ô´ÇèÒÊǧÒÁ ËÒ¡ÁÕàÇÅÒ¨ÐÅͧ¾ÂÒÂÒÁ´Ù
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