[PDF] Top 20 Mathematical Excalibur, Volume 14, Number 3

... 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 written on ... 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

... Yet another generalization of the van der Waerden Theorem (which says that ( , ) W r k exists for all r, k) is the Hales-Jewett Theorem. The exact statement of the theorem is rather technical, but we can look at an ... See full document

... 38th IMO Kin-Yin Li For the first time in history, the International Mathematical Olympiad (IMO) was held in the southern hemisphere. Teams representing a record 82 countries and regions participated in the event ... 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

... 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

... 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

... | (Here we set A 2n+1 =A 1 . For a set X, let |X| denote the number of elements in X.) Problem 2. In ⊿ABC, AB=AC. Point D is the midpoint of side BC. Point E lies outside ⊿ABC such that CE⊥AB and BE=BD. Let M be ... See full document

... odd number of points on the ...the number of points on the two sides remain the same, except when two points are on the line during the change of ...even number of points on 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

... (continued on page 4) IMO 2016 Logo Design Competition Hong Kong will host the 57th International Mathematical Olympiad (IMO) in July 2016. The Organising Committee now holds the IMO 2016 Logo Design Competition ... See full document

... which satisfies the following condition: for any integers i, j, k, with 1 ≤ i, j, k ≤ n+1, a i +a j ≠ 3a k . Find a 2015 . Problem 3. Let ABC be an equilateral triangle, and let D be a point on AB between A ... 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 1. A local supermarket is responsible for the distribution of 100 supply boxes. Each box is ought to contain 10 kilograms of rice and 30 eggs. It is known that a total of 1000 kilograms of rice and 3000 eggs are ... See full document

... the volume 8, number 1 issue of Math Excalibur, we provided a number of examples of functional equation ...the volume 10, number 5 issue of Math Excalibur, problem 243 in ... 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