Detailed Solutions to the Problems of the 1st to 15th "Hope Cup" National Mathematics Invitational Contest (Grade 11)

Author: Zhou Guozhen, Editor-in-Chief
Publisher:
Publish Date: 2005-07-01
Features: The "Hope Cup" National Mathematics Invitational Competition has been held since 1990 and has now celebrated 15 editions. The 1st edition saw 110,000 middle school students participate, and by the 9th edition, the number of participants each year exceeded one million. Over the past 15 editions, the cumulative number of participating middle school students has surpassed 12 million. Among domestic middle school subject competitions, no other event has achieved such a large scale or attracted such a vast number of participants. This fully demonstrates the popularity of the "Hope Cup" among middle school students. Why do middle school students enjoy participating in the "Hope Cup"? A very important reason is that the problems are well-designed, beautiful, and offer significant intellectual space. The "Hope Cup" problem-setting committee comprises top experts in mathematical competitions in China, who meticulously crafted the questions for each edition. Additionally, over a thousand outstanding mathematics teachers, educational researchers, and university and high school students across the country have contributed many self-developed problems. Through solving these problems, students learn from them, study them, and thereby gain a more solid and broad understanding of knowledge, enhance their wisdom and skills, boost their confidence in learning, and achieve even better results. The "Hope Cup" is like a golden key—it not only opens the door to wisdom for each participating middle school student but also opens the door to confidence. This is the charm of the "Hope Cup." Mathematics teachers who teach in middle schools, just like their students, also love the "Hope Cup"—because the endless stream of problems emerging from this "cup" provides rare materials and valuable insights for improving their teaching and nurturing high-level students.