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×÷ÕßÍƼöÓ I am very pleased to publish this problem book in China with my two friends. We thank the AMC and the other contests for giving us permission to use their problems and official solutions. Our hope is that these problems and solutions will provide deeper insights into American mathematical competitions. There are lots of good and interesting problems in this book. Enjoy reading! ¡ª¡ªBy Harold B. Reiter£¬Professor at University of North Carolina Charlotte, former AHSME/AMC committee chair, former SAT II math chair, founder of Charlotte Math Club. Îҷdz£¸ßÐËÄܺÍÁ½¸öÅóÓѺÏ×÷Õâ±¾Ê飬²¢ÔÚÖйú³ö°æ¡£Ò²¸ÐлAMC¼°ÆäËû¾ºÈü»ú¹¹ÊÚȨÎÒÃÇʹÓÃÆäÕæÌâ¼°¹Ù·½½â´ð¡£ÎÒÃÇÏ£ÍûÕâЩÎÊÌâºÍ½â´ð¿ÉÒÔÈôó¼ÒÄܸüÉîÈëµØÁ˽âÃÀ¹úÊýѧ¾ºÈü¡£Õâ±¾ÊéÀïÃæÓÐÐí¶àÓÐȤµÄÎÊÌâ¡£ÏíÊÜÔĶÁ°É! ¡ª¡ª H£®B£®À³ÌØ£¬±±¿¨ÏÄÂåÌØ·ÖУ½ÌÊÚ£¬AHSME£¯AMCίԱ»áÇ°Ö÷ϯ£¬ SAT IIÊýѧίԱ»áÇ°Ö÷ϯ£¬ÏÄÂåÌØÊýѧ¾ãÀÖ²¿´´Ê¼ÈË¡£ This book consists of problems from popular math contests in USA and key instructional points that will make working the problems easier. The problems range from very basic to IMO level. I hope that working problems in this book will make you a better problem solver, will enrich your mathematics education, and will remind you how much fun it can be to do mathematics. ¡ª¡ªBy Jonathan M. Kane, Honorary Fellow at the University of Wisconsin - Madison, AIME committee chair, AMC10/12., USAMO committee member, cofounder of Purple Comet! Math Meet. Author of the book Writing Proofs in Analysis. Õâ±¾Êé°üº¬ÃÀ¹úÁ÷ÐеÄÖÐѧÊýѧ¾ºÈüÊÔÌ⣬¼°Ê¹µÃÄܸüÈÝÒ×½â¾öÎÊÌâµÄ¹Ø¼ü֪ʶµã¡£±¾ÊéÖк¬ÓдӾºÈüÈëÃŵ½IMOˮƽµÄÎÊÌâ¡£ÎÒÏ£Íûͨ¹ýÁ·Ï°Õâ±¾ÊéµÄÎÊÌ⣬ѧϰÕßÄܹ»³ÉΪһ¸ö¸üºÃµÄ½â¾öÎÊÌâÕߣ¬·á¸»Êýѧ֪ʶ£¬²¢ÇÒÖªµÀ×öÊýѧµÄȤζÐÔ¡£ ¡ª¡ª J£®M£®¿­¶÷£¬Íþ˹¿µÐÇÂóµÏÑ·´óѧHonorary Fellow£¬ÏÖAOMEίԱ»áÖ÷ϯ£¬AMC¡¢0£¯1 2£¬ USAMOίԱ»á³ÉÔ±£¬×ÏÉ«åçÐǵÄÁªºÏ´´Ê¼ÈË¡£¡¶Ð´×÷·ÖÎöѧµÄÖ¤Ã÷¡·µÄ×÷Õß¡£ ʹÓÃÕßÍƼöÓ I have used the draft of this book for math enrichment courses in many schools such as SZFL and CDFL, and ENREACH Learning Centers in Nanjing, Beijing, Chengdu, Shenzhen and Shanghai. The materials in this book have been very helpful for me. I am glad it has been published. I trust it will benefit those who are interested in participating math competitions in the USA. ¡ª¡ªBy Binhao Fan£¬AMC coach, member of UK Royal Statistics Society, UKMT and BMO winners. ÎÒÔںܶàѧУµÄÑ¡ÐÞ¿ÎʹÓùýÕâ±¾ÊéµÄ³õ¸å£¬±ÈÈçÔÚSZFL£¬C D FL¼°±±¾©¡¢ÄϾ©¡¢³É¶¼¡¢ÉîÛÚºÍÉϺ£¶àµØµÄÓ¢ÈñѧУ¡£Õâ±¾Êé¶ÔÎÒºÜÓаïÖú£¬ºÜ¸ßÐËÕâ±¾ÊéÄÜÕýʽ³ö°æ£¬ÏàÐŶÔÊýѧ¸ÐÐËȤ²¢ÓÐÖ¾²Î¼ÓÃÀ¹úÊýѧ¾ºÈüµÄͬѧ»áÊÜÒæ·Ëdz¡£ ¡ª¡ª·¶±òºÀ£¬AMCÊýѧ½ÌÁ·£®Ó¢¹ú¸·¼ÒÁ·¼ÆЭ»á»áÔ±£®UKMT£ÜBM0ÓÅʤÕß¡£ ×ÞÔÆÖ¾£¬ËÄ´¨´óѧ½ÌÊÚ¡£