Đề thi giải toán mở rộng Hà Nội-Nguyễn Văn Mậu mang tính chất tham khảo, giúp ích cho các bạn tự học, ôn thi, với phương pháp giải hay, thú vị, rèn luyện kỹ năng giải đề, nâng cao vốn kiến thức cho các bạn trong các kỳ thi sắp tới. Tác giả hy vọng tài liệu này sẽ giúp ích cho các bạn. | HANOI MATHEMATICAL SOCIETY NGUYEN VAN MAU HANOI OPEN MATHEMATICAL OLYMPIAD PROBLEMS AND SOLUTIONS Hanoi 2009 Contents Questions of Hanoi Open Mathematical Olympiad 3 Hanoi Open Mathematical Olympiad 2006 . 3 Junior Section Sunday 9 April 2006 . 3 Senior Section Sunday 9 April 2006 . 4 Hanoi Open Mathematical Olympiad 2007 . 5 Junior Section Sunday 15 April 2007 . 5 Senior Section Sunday 15 April 2007 . 7 Hanoi Open Mathematical Olympiad 2008 . 10 Junior Section Sunday 30 March 2008 . 10 Senior Section Sunday 30 March 2008 . 11 Hanoi Open Mathematical Olympiad 2009 . 12 Junior Section Sunday 29 March 2009 . 12 Senior Section Sunday 29 March 2009 . 14 2 Questions of Hanoi Open Mathematical Olympiad Hanoi Open Mathematical Olympiad 2006 Junior Section Sunday 9 April 2006 Q1. What is the last two digits of the number 11 12 13 2006 2 Q2. Find the last two digits of the sum 200511 200512 20 0 52006. Q3. Find the number of different positive integer triples x y z satisfying the equations x2 y z 100 and x y2 z 124. Q4. Suppose x and y are two real numbers such that x y xy 155 and x2 y2 325. Find the value of x3 y3 . Q5. Suppose n is a positive integer and 3 arbitrary numbers are choosen from the set 1 2 3 . 3n 1 with their sum equal to 3n 1. What is the largest possible product of those 3 numbers
