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Contents:

• 
  

  Combinatorics:

  
  
  
  
  • A Quick Reminder
  
  
  • Partial Fraction
  
  
  • Geometric Progressions
  
  
  • Extending the Binomial Theorem
  
  
  • Recurrence Relations
  
  
  • Generating Functions
  
  
  • Of Rabbits and Postmen
  
  
  • Solutions
  
  
  
  


• 
  

  Geometry 3:

  
  
  
  
  • The Circumcircle
  
  
  • Incircles
  
  
  • Exercises
  
  
  • The 6-Point Circle?
  
  
  • The Euler Line and the Nine Point Circle
  
  
  • Some More Examples
  
  
  • Hints
  
  
  • Solutions
  
  
  • Glossary
  
  
  
  


• 
  

  Solving Problems:

  
  
  
  
  • Introduction
  
  
  • A Problem to Solve
  
  
  • Mathematics: What is it?
  
  
  • Back to Six Circles
  
  
  • More on Research Methods
  
  
  • Georg Pólya
  
  
  • Asking Questions
  
  
  • Solutions
  
  
  
  


• 
  

  Number Theory 2:

  
  
  
  
  • A Problem
  
  
  • Euler's ϕ-function
  
  
  • Back to Section 4.2
  
  
  • Wilson
  
  
  • Some More Problems
  
  
  • Solutions
  
  
  
  


• 
  

  Means and Inequalities:

  
  
  
  
  • Introduction
  
  
  • Rules to Order the Reals By
  
  
  • Means Arithmetic and Geometric
  
  
  • More Means
  
  
  • More Inequalities
  
  
  • A Collection of Problems
  
  
  • Solutions
  
  
  
  


• 
  

  Combinatorics 3:

  
  
  
  
  • Introduction
  
  
  • Inclusion–Exclusion
  
  
  • Derangements (Revisited)
  
  
  • Linear Diophantine Equations Again
  
  
  • Non-taking Rooks
  
  
  • The Board of Forbidden Positions
  
  
  • Stirling Numbers
  
  
  • Some Other Numbers
  
  
  • Solutions
  
  
  
  


• 
  

  Creating Problems:

  
  
  
  
  • Introduction
  
  
  • Counting
  
  
  • Packing
  
  
  • Intersecting
  
  
  • Chessboards
  
  
  • Squigonometry
  
  
  • The Equations of Squares
  
  
  • Solutions
  
  
  
  


• 
  

  IMO Problems 2:

  
  
  
  
  • Introduction
  
  
  • AUS 3
  
  
  • HEL 2
  
  
  • TUR 4
  
  
  • ROM 4
  
  
  • USS 1
  
  
  • Revue
  
  
  • Hints — AUS 3
  
  
  • Hints — HEL 2
  
  
  • Hints — ROM 4
  
  
  • Hints — USS 1
  
  
  • Some More Olympiad Problems
  
  
  • Solutions
  
  
  
  

Readership: School students keen to learn more of mathematics and specifically mathematics related to the IMO; coaches and instructors of mathematical competitions.

Key Features:

• An introduction to the main mathematical topics covered in the IMO


• Easily comprehensible to students


• Full solutions provided to all mathematical problems