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AMC
AMC10_12
  • 2016 AMC10A #20
  • 2008 AMC12B #22
  • 2015 AMC12A #23
AMC8
  • 2015 AMC8 #25
Combinatorics (Counting)
0 - Introduction
  • Introduction
  • Learning Guide
1 - Basic Principles
  • The Addition and Multiplication Principle
  • Application - Count and Sum An Integer's Divisors
  • Mind the Catches
  • Inclusion and Exclusion Principle (Venn Diagram)
  • Application - Euler's $\varphi$ Function
2 - Formulas
  • Permutation and Combination
  • Factorial Defined
3 - Techniques and Patterns
  • Count Like A Pro
  • The Lattice Method
  • Cut the Rope (Stars and Sticks)
  • Bundling and Symmetry
  • Derangement
  • Combining Permutation and Combination
  • Balls in Boxes
  • Recursion
4 - Elementary Probability
  • Probability Basics
  • The Tree Method
  • Geometric Probability
  • Probability Review
  • Example - 2015 AMC12A #23
  • Find the Correct Region
  • Application - Estimate $\pi$
Additional Topics
  • The Binomial Theorem
  • Pascal Triangle
  • Combinatorial Identities
General
  • Introduction to Math All Star Online Course
  • Become a Math Competition Pro
  • Look Beyond Obvious
  • Road Towards a Math Star
  • Generating Function
IMO
  • 1975 IMO
  • 1992 IMO
Indeterminate Equation
0 - Introduction
  • Introducation
1 - Basic Techniques and Patterns
  • The Factorization Method
  • Solving $\frac{1}{x}+\frac{1}{y}=\frac{1}{n}$
  • The Difference of Squares Method
  • Sum of Squares
2 - Intermediate Techniques and Patterns
  • Property of Symmetry
  • Solving $\frac{1}{x}+\frac{1}{y}=\frac{m}{n}$
  • Solving $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{m}{n}$
  • The Squeeze Method
  • The Quadratic Method
  • Pythagorean Triplet
  • Solve Linear Indeterminate Equation
3 - Advanced Techniques and Patterns
  • The Infinite Descent Method
  • Introduction to Pell's Equation
  • Solve Pell's Equation
  • The MOD Method
Number Theory
  • Square Numbers
  • A quick way to find the tens digit of $m^n$
USAMO
  • 2015 USAMO


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