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2024 AIME ¹®Á¦ 15.
Find the number of rectangles that can be formed inside a fixed regular dodecagon (-gon) where each side of the rectangle lies on either a side or a diagonal of the dodecagon. The diagram below shows three of those rectangles.
°íÁ¤ µÈ Á¤ 12°¢Çü ³»ºÎ¿¡ Çü¼º µÉ ¼öÀÖ´Â Á÷»ç°¢ÇüÀÇ ¼ö¸¦ ãÀ¸½Ê½Ã¿À.
(´Ü Á÷»ç°¢ÇüÀÇ °¢¸éÀÌ 12°¢ÇüÀÇ ÇѺ¯ ¶Ç´Â ´ë°¢¼±¿¡ÀÖ´Â °æ¿ì.)
¾Æ·¡ ´ÙÀ̾î±×·¥Àº 3°³ÀÇ Á÷»ç°¢ÇüÀ» º¸¿©ÁÝ´Ï´Ù.
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±Ùµ¥ ÄÄÇ»ÅÍ ±Ù°£ÀÌ °è»ê±â Àε¥ °è»ê ¸øÇÏ´Â°Ô ¸»ÀÌ ¾ÈµÇ´Â°Å ¾Æ´Ñ°¡¿ä? Ç×»ó Àΰ£º¸´Ù ºü¸£°Ô °è»ê ÇÏ´Â°Ô ÄÄÇ»ÅÍ Àε¥.. ¹¹¸¸ Çϸé Àΰ£ÀÌ¿´À¸¸é ¾ÆÁ÷µµ ¸øǪ´Â °è»êÀº ÄÄÇ»ÅÍ´Â ¸îÃʸé Ç®°í ±×·¯Áö ¾Ê¾Ò³ª¿ä? |
°³ÀÎÀûÀ¸·Î aime ¹®Á¦ Áß,(¸î³âµµ ÃâÁ¦ÀÎÁö ±î¸Ô¾úÀ½) ¿ø ¾È¿¡¼ÀÇ °æ¿ìÀÇ ¼ö ¹®Á¦¸¦ cotº¸¿©ÁÖ´Â gemini¿Í deepseekÇþ¶ó°í ´øÁ®³ù´õ´Ï µÑ´Ù Ʋ¸².
µÑ´Ù cot¿¡¼ ¿©·¯°¡Áö Á¢±Ù¹ýÀ¸·Î ÇÏ´Ù°¡ ±ÍÂúÀº µí Áö¸¾´ë·Î Áú¹®À» Çؼ®ÇÏ´õ´Ï Ʋ¸².
³ªÁß¿¡ Á¤´ä ¼Ö·ç¼ÇÀ» º¸¿©ÁÖ°í °ËÁõÇ϶óÇß´õ´Ï, Àΰ£Ã³·³ º¯¸íÇϱ⠹ٻÝ. |