This book is about a famous Hungarian mathematics competition that was founded in 1894, and thus, the oldest mathematics competition for secondary school students organized on a national scale. This book is based on Volumes III and IV of the Hungarian work by János Surányi, covering the years from 1964 to 1997.

Hungary, along with Russia, has a well-deserved reputation for proposing important, instructive, and interesting problems. Here, the reader will find a treasure trove of over 100 of them. The solutions are written carefully, giving all the details, and keeping in mind at all times the overall logical structures of the arguments.

An outstanding feature of this book is Part II: Discussion. Here, the problems are divided by topics into six groups. It contains a discussion of the topic in general, followed by the basic results, that precedes the discussions of the individual problems. When a student encounters some difficulty in a problem, this part of the book can be consulted without revealing the complete solution. As an alternative, a student can also start with this part to familiarize with the general topic before attempting any problems. Finally, almost 400 additional problems from the legendary KöMaL (Secondary School Mathematics and Physics Journal) takes the student to mathematical topics beyond competitions.

Contents:

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  Problems:

  
  


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  Answers

  
  


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  Discussion:

  
  
  
  
  • Combinatorics
  
  
  • Number Theory
  
  
  • Algebra
  
  
  • Euclidean Geometry
  
  
  • Solid Geometry and Lattice Geometry
  
  
  • Combinatorial Geometry
  
  
  
  


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  Solutions

  
  


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  Appendix

  
  

Readership: Eager students preparing for the Mathematical Olympiads who are looking for training material. Experienced trainers preparing students for the Mathematical Olympiads who are looking for teaching resources. Professional mathematicians and secondary school teachers interested in problem solving.

Key Features:

• There are two main types of books on mathematics competitions. The first type presents problems from various contests as well as their solutions in chronological order. The second type discusses topics in mathematics competitions, drawing example from various sources. This book combines the benefit of both types


• The focus is on one source only, and what a fantastic source it is! The problems are first presented in chronological order. Then they are organized into six groups, with detailed discussions on the general topics as well as on the individual problems


• The solutions are then presented in chronological order, with two useful cross-reference indices


• The carefully written solutions make clear the overall logical structures of the argument, and details are not glossed over