[PDF] Top 20 Mathematical Excalibur, Volume 6, Number 2

... On-line: http://www.math.ust.hk/mathematical_excalibur/ The editors welcome contributions from all teachers and students. With your submission, please include your name, address, school, email, telephone ... See full document

... A/P. Solution 1. CHAO Khek Lun (St. Paul’s College, Form 6). Draw four rectangles on the sides of the quadrilateral and each has height A/P pointing inward. The sum of the areas of the rectangles is A. Since at ... See full document

... Fax: (852) 2358 1643 Email: [email protected] Let d be a positive integer that is not a square. The equation x 2 − dy 2 = 1 with variables x , y over integers is called Pell’s equation. It was Euler who ... See full document

... Volume 6, Number 4 Volume 6, Number 4 Volume 6, Number 4 Volume 6, Number 4 October October 2001 October 2001 October 2001 –––– December ... See full document

... Example 2. (Crux Problem 2333) D and E are points on sides AC and AB of triangle ABC, respectively. Also, DE is not parallel to CB. Suppose F and G are points of BC and ED, respectively, such that BF : FC = EG : ... See full document

... Solution.: Independent solution by CHEUNG Cheuk Lun (S.T.F.A. Leung Kau Kui College). The positive integers are separated into two subsets with no common elements. S[r] ... See full document

... If the starting point lies within a distance of 1 from the origin, the subsequent points will get closer and closer to the origin.. If the intial point is more than a distance o[r] ... See full document

... On-line: http://www.math.ust.hk/excalibur/ The editors welcome contributions from all teachers and students. With your submission, please include your name, address, school, email, telephone and fax numbers (if ... See full document

... On-line: http://www.math.ust.hk/mathematical_excalibur/ The editors welcome contributions from all teachers and students. With your submission, please include your name, address, school, email, telephone ... See full document

... On-line: http://www.math.ust.hk/mathematical_excalibur/ The editors welcome contributions from all teachers and students. With your submission, please include your name, address, school, email, telephone ... See full document

... On-line: http://www.math.ust.hk/mathematical_excalibur/ The editors welcome contributions from all teachers and students. With your submission, please include your name, address, school, email, telephone ... See full document

... Solution. LAM Cho Ho (CUHK Math Year 1). Take a circle of radius r so that all intersection points of the n lines are inside the circle and none of the n lines is tangent to the circle. Now each line intersects the ... See full document

... On-line: http://www.math.ust.hk/mathematical_excalibur/ The editors welcome contributions from all teachers and students. With your submission, please include your name, address, school, email, telephone ... See full document

... On-line: http://www.math.ust.hk/mathematical_excalibur/ The editors welcome contributions from all teachers and students. With your submission, please include your name, address, school, email, telephone ... See full document

... This year’s International Mathematical Olympiad (IMO) has been of considerable significance to Hong Kong. At the 1997 IMO held in Mar del Plata, Argentina, shortly after our official transfer of sovereignty, the ... See full document

... Problem 1, which was supposed to be a number theory problem, is more like an algebra problem (no prime numbers, no factorization of integers, merely algebraic manipulation and some induction). And finally of ... See full document

... Mathematical Excalibur, Vol. 19, No. 2, Sep. 14 – Oct. 14 Page 2 Problem ...• 2 be an integer. Consider a n ×n chessboard consisting of n 2 unit ...k 2 unit ... See full document

... polynomials in problem 1 and numbers in problem 2. Like vectors expressed in coordinates, the v i 's are objects that may take on different values at different positions. So functions corresponding to solutions of ... See full document

... Kin-Yin Li, Dept of Mathematics, Hong Kong Wniversiv of Science and Technology, Clear Water Bay, Kowloon. Eight students took part in a contest with eight problems[r] ... See full document

... x 2 , ..., x 1996 and let s i = x 1 + x 2 + ... + x i for i = 1, 2, ...1995 2 ), ..., [ 1994 1995 ,1) and the 1996 numbers {s 1 }, {s 2 }, ... See full document