[PDF] Top 20 Mathematical Excalibur, Volume 17, Number 2

... 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 2. As it turned out, this problem caused quite a bit of trouble and many students didn’t know how to tackle the problem at all. More sophisticated inequalities such as Muirhead do not work, since 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

... Apart from the first person in the line, every person indicates one of those before him and declares either “this person is a villain” or “this person is a knight”. It is known that the number of villains is ... See full document

... ℝ →ℝ such that for all real numbers x and y holds f(x 2 + f(y)) = (f(x) + y 2 ) 2 . (Tonći Kokan) Problem 2. Along the coast of an island there are 20 villages. Each village has 20 fighters. ... 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

... 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

... With an even parity code, the receiver can detect one transmission error, but unable to correct it... Mathematical Excalibur, Vol.[r] ... See full document