Invitation to a Mathematical Festival
Held annually in Moscow since 1990, the Mathematical Festival is a brilliant and fascinating math competition attended by hundreds of middle school students. Participants of the Festival solve interesting mathematical problems and partake in other engaging activities, while cultivating key skills such as intuitive reasoning and quick thinking. This book contains problems presented at the Festival during the years 1990-2011, along with hints and solutions for many of them. Most of the problems are accessible to students with no additional training in mathematics and may be used as supplementary material at school or at home. Other problems, however, are more advanced and will be enjoyed by students with a deeper interest in mathematics. Most of the problems in this book are specially created for Mathematical Festival competitions by leading Russian experts in school and extracurricular math education and have never been published before. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
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6th Class apartment building apple trees black square blacksmith Botin bulb candies cells center cube chests color column congruent corner cube cups diagonal diggers digit sum divide divisible by 9 dollars eight legs equal number equation exactly example factors figure five-digit numbers floor four gnomes gold coins Grade hobbit irreducible fractions Johnny Johnny’s Khachaturyan knight kronas last digit least letter Master of Sports Mathematical Festival Mersenne primes Minnie Mouse minutes multiple mushrooms natural numbers neighbor number of apartments number of coins octopus odd number Olympiad pairs pear trees Penrose tiling perimeter picture pieces Pinocchio points portobello mushrooms possible prime numbers Prince Charming Princesses prove rectangle remaining rubles segments shaded shown side length smallest number snowballs Spivak Tanya tea bags total number turnips two-digit number vertices walked whole number Yashchenko zero