[PDF] Top 20 Mathematical Excalibur, Volume 17, Number 5

... 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

... 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

... Apart from the first person in the line, every person indicates one of those before him and declares either “this person is a villain” or “this person is a knight”. It is known that the number of villains is ... 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

... 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

... 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

... = CA and CY = BA. The line XY meets the perpendicular bisector of side BC at P. Show that ∠ BPC + ∠ BAC = 180 o . Problem 4. An exam consisting of six questions is sat by 2006 children. Each question is marked right or ... 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

... Below are the problems of the 2011 Canadian Math Olympiad, which was held on March 23, 2011. Problem 1. Consider 70-digit numbers n, with the property that each of the digits 1, 2, 3, …, 7 appears in the decimal ... 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

... same number of cards in a way that the following condition holds: if Andriy has a card with a number n then Nick has a card with a number ...maximal number of cards could be taken by the two ... See full document

... In 1980, Kiev, Moscow and Riga participated in a mathematical problem solving contest for high school students, later called the Tournament of the Towns. At present thousands of high school students from dozens of ... 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

... The rest of the solution follows by induction on the number of sides of the polygon and the two claims. Problem 4. A set of positive integers is called fragrant if it contains at least two elements and each of its ... See full document

... Mathematical Excalibur, Vol. 21, No. 5, ...the number of different starting arrangements for which the books will finally be ordered ... 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