[PDF] Top 20 Mathematical Excalibur, Volume 1, Number 2

... 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

... 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 ... 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

... Right: A photo of the six members of the Hong Kong Team and one of the editors (far right) taken at the Shatin Town Hall after the closing ceremony of the 35th International [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 ... 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

... Our team brought home 1 silver and 5 bronze medals. Among 97 teams, we ranked 31. I cannot say that our team did badly. Indeed all our team members managed to get medals, indicating they achieved certain standard. ... See full document

... d This problem is nice and easy. It gave us no problem. All of us got full scores in this problem. Nevertheless the problem is not entirely trivial, and indeed about 100 contestants scored nothing in this problem! First ... 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

... Problem 44. For an acute triangle ABC, let H be the foot of the perpendicular from A to BC. Let M, N be the feet of the perpendiculars from H to AB, AC, respectively. Define L A to be the line through A perpendicular to ... 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

... Problem 2. Let ABC be a scalene triangle with incenter I and circum- circle (ω). The lines AI, BI, CI intersect (ω) for the second time at the point D, E, F, respectively. The line through I parallel to the sides ... See full document

... Problem 2 is a functional equation, showing f(f(x)f(y))+f(x+y)=f(xy) for all real x and y will imply f(x)=0 or f(x) = ...problem 2 of his team, apparently he was dismayed by the ...scored 1 more ... See full document

... 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 ... See full document