[PDF] Top 20 Mathematical Excalibur, Volume 22, Number 2

... April 30 th , 2017) Anna and Berta play a game in which they take turns in removing marbles from a table. Anna takes the first turn. When at the beginning of a turn there are n ≥1 marbles on the table, then the player ... See full document

... Time allowed was 270 minutes. Each problem was worth 10 points Problem 1. A quadrilateral ABCD is inscribed in a circle k, where AB > CD and AB is not parallel to CD. Point M is the intersection of the diagonals AC and ... See full document

... A 2 , …,A n are located on the inside of a circle, and points B 1 , B 2 , …,B n are on the circle, so that the lines A 1 B 1 , A 2 B 2 , …, A n B n are mutually ...A 2 B 2 , …, A ... See full document

... problem 6 is more complicated, but there is a nice and not too complicated complex number solution. In short, leaders generally agreed that those problems are do-able. If one understands what is going on, one ... 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

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