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#1
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͸ԺÒ¡ÒÃãªé·ÄÉ¯Õ The pigeonhold principle ãËé˹èͤѺ
ÁÕ⨷Âì´éÇÂ
1.There are 51 houses on the street. Each house has an address between 100 and 1099,inclusive.Show that at least two houses have address that are consecutive integers. 2.Construct a sequence of 16 positive integers that has no increasing or decreasing subsequence of 5 terms. |
#2
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àÍÒ¤ÃèÒÇæ¹Ð¤ÃѺ
¢éÍáá µÃ§ 1099 µéͧà»ç¹ 199 ËÃ×Íà»ÅèÒ¤ÃѺ ¶éÒà»ç¹ 199 ¡çãËéÁͧàÅ¢·ÕèºéÒ¹ 100-101 à»ç¹Ãѧ·Õè 1 àÅ¢·ÕèºéÒ¹ 102-103 à»ç¹Ãѧ·ÕèÊͧ ... àÅ¢·ÕèºéÒ¹ 198-199 à»ç¹Ãѧ·Õè 50 â´ÂäÁèàÊչѠ¨ÐãËéàÅ¢ºéÒ¹·Ñé§ 50 ËÅѧááà»ç¹àÅ¢¤Õè â´Â¡¯Ãѧ¹¡ ¨Ðä´éÇèÒ äÁèÇèÒºéÒ¹ËÅѧ·Õè 51 ¨ÐÍÂÙèÃѧä˹ àÅ¢ºéÒ¹¢Í§ËÅѧ·Õè 51 «Öè§à»ç¹àÅ¢¤Ùè¨Ðµéͧà»ç¹àÅ¢àÃÕ§¡ÑºàÅ¢·ÕèÍÂÙèã¹Ãѧà´ÕÂǡѹàÊÁͤÃѺ ¢éÍÊͧ ¢Í¶ÒÁ¹Ô´¹Ö§¤ÃѺ ·ÕèÇèÒ has no increasing or decreasing subsequence of 5 terms ¨Óà»ç¹µéͧ strictly äËÁ¤ÃѺ ¶éÒäÁè ¡çÁÕµÑÇÍÂèÒ§ àªè¹ 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
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¤¹ä·ÂÃèÇÁã¨ÍÂèÒãªéÀÒÉÒÇÔºÑµÔ ½Ö¡¾ÔÁ¾ìÊÑÅѡɳìÊÑ¡¹Ô´ ªÕÇÔµ(¤¹µÍºáÅФ¹¶ÒÁ)¨Ð§èÒ¢Öé¹àÂÍÐ (¨ÃÔ§æ¹Ð) Stay Hungry. Stay Foolish. |
#3
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ÍéÒ§ÍÔ§:
Êèǹ¢éÍÊͧ has no increasing or decreasing subsequence ¡ç¤×ÍäÁèà¾ÔèÁËÃ×ÍÅ´à˵ءÒÃ³ì ¡ç¤×Íà˵ءÒóìÂѧ¤§à»ç¹àËÁ×͹à´ÔÁ ¤ÓµÍº¡ç¤×Í 4,3,2,1,8,7,6,5,12,11,10,9,16,15,14,13 »ÃÐÁÒ³¹ÕéáËÅФѺ |
#4
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#3
âÍतÃѺ ¶éÒ§Ñé¹¢éÍáá¡ç¹èÒ¨Ðãªéá¹Ç¤Ô´¤ÅéÒÂæ·Õè¼Á¡ÁÒãËé´Ùä´é¤ÃѺ à»ÅÕè¹á¤èàÅ¢¹Ô´Ë¹èÍ Êèǹ¢éÍÊͧ ¼Áà¢éÒ㨤ÓÇèÒ subsequence ÇèÒà»ç¹ÅӴѺÂèͤÃѺ «Ö觷Õè¡ÁÒ¹èÒ¨Ðãªéä´éáÅéǤÃѺ áµè¶éÒà¢ÒÍÂÒ¡ãËéáÊ´§ÇèÒ·ÓäÁµéͧÊÃéÒ§ÅӴѺÂèÍÂẺ¹Õé Åͧ´Ù Erdős–Szekeres theorem ¹Ð¤ÃѺ
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¤¹ä·ÂÃèÇÁã¨ÍÂèÒãªéÀÒÉÒÇÔºÑµÔ ½Ö¡¾ÔÁ¾ìÊÑÅѡɳìÊÑ¡¹Ô´ ªÕÇÔµ(¤¹µÍºáÅФ¹¶ÒÁ)¨Ð§èÒ¢Öé¹àÂÍÐ (¨ÃÔ§æ¹Ð) Stay Hungry. Stay Foolish. |
#5
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à¢éÒã¨áÅéÇÍèÐ ¢Íº¤Ø³
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ËÑÇ¢éͤÅéÒ¤ÅÖ§¡Ñ¹ | ||||
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