[PDF] Top 20 Mathematical Excalibur, Volume 7, Number 3

... 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

... 2 – xyz 4 hold. Problem 3. We are given a triangle ABC and its circumcircle with mid-point U and radius r. The tangent ' c of the circle with mid-point U and radius 2r is determined such that C lies between c = AB ... See full document

... (What clue can you get from the special cases?) Coloring a board can help to solve the problem. (Can we restate the problem in a related way?) Is it possible to color the cubes of the 10 × 10 × 10 box with four colors in ... See full document

... Canadian Mathematical Olympiad Problem ...2, 3, 5} has this property, but {1, 2, 3, 4, 5} does not, since the pairs {1, 4} and {2, 3} have the same sum, namely ...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

... 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

... 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