[PDF] Top 20 Mathematical Excalibur, Volume 7, Number 1

... Mathematical Excalibur Mathematical Excalibur Mathematical Excalibur Mathematical Excalibur, ...Vol. 7, No. 1, Mar 02- Apr 02 Page 2 而當質數 p > 2 時，(p + ... See full document

... Looking back at the above very clever computatioii method, everyone should respect the inathematiciaiis in the past for their creativity and instiiict in the relations of numbe[r] ... See full document

... color 1 in a corner square, then extend the coloring to the whole box by putting colors 1, 2, 3, 4 periodically in each of the three perpendicular directions parallel to the edges of the ...color 1 ... See full document

... Solution. Let S be the sum of all the mn numbers in the table. Note that after an operation, each number stay the same or turns to its negative. Hence there are at most 2 mn tables. So S can only have finitely ... See full document

... Canadian Mathematical Olympiad Problem 1. Let S be a subset of {1, 2, …, 9}, such that the sums formed by adding each unordered pair of distinct numbers from S are all ...maximum number of ... See full document

... many mathematical game problems involving strategies to win or to ...involve number theoretical properties or combinatorial reasoning or geometrical ... 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

... 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

... FOK (Homantin Government Secondary School), Michael LAM Wing Young (St. Paul's College), LIN Kwong Shing (University of Illinois). and LIU Wai Kwong (Pui Tak Canossian[r] ... See full document

... For any polynomial Q(x) with real coefficients, leading coefficient 1 and a non-zero constant term, we group consecutive terms of the same signs together to express [r] ... See full document

... hours. Letf be an odd prime. The display initially shows 0. Given any positive rational number q, show that pressing some finite sequence of buttons will yield q. Assume that [r] ... See full document

... 例 11 2n名選手參加象棋循環賽，每 一輪中每個選手與其他 2 n − 1 人各賽 一場，勝得 1 分，平各得 1 2 分，負得 0 分．證明：如果每個選手第一輪總 分與第二輪總分至少相差n分，那麼 每個選手兩輪總分恰好相差n分． ... See full document

... (continued from page 2) For the proof of the second step, we follow the approach in J. Michael Steele’s book The Cauchy-Schwarz Master Class, MAA-Cambridge, 2004. For a n×n matrix M, we will denote its entry in the j-th ... See full document

... C 1 , C 2 , ⋯, C n in a plane such that for each 1 ≤ i < n, the center C i is on the circumference of C i+1 , and the center of C n is on the circumference of C 1 ...the number of pairs ... 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

... Olympiad Corner The following were the problems of the 2009 Asia-Pacific Math Olympiad. Problem 1. Consider the following operation on positive real numbers written on a blackboard: Choose a number r ... 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 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 expression ... 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