1. Visuals
A. Back Calculation
B. Shortest and Longest Paths
C. Math Grids
D. Nets
2. Logic and Reasoning
A. Magic Squares
B. Tiling Problems
C. Folding Paper
D. Balls and Boxes
E. Probability Problems
F. Possible Ways to Walk
G. Problems on Clocks
H. Harder Clock Problems with Proportions
I. Permutations of Digits and Sums of N-Digit Numbers
3. Number Theory
A. Integer Solutions (Part 1)
B. Integer Solutions (Part 2)
C. Special Numbers
D. Advanced Number Sense
E. Divisibility and Divisors
F. Cyclicity of Remainders
G. Diophantine Equations
H. Greatest Common Factor and Least Common Multiple
I. Modular Arithmetic
4. Counting Techniques
A. PIE (Principle of Inclusion and Exclusion)
B. How Many Faces Are Painted
C. Counting Rectangles
D. How Many Triangles with Integer Lengths
E. How Many Ways to Walk
5. Inequality
A. Maximal Inequality
6. Arithmetic Sequence
A. Newton’s Little Formula
B. Page Numbers
C. Arithmetic Sequences and Common Terms
7. Sequences
A. Solving Recurrence Relations
8. Algebra
A. Pythagorean Triples
B. Absolute-Value Inequalities
C. Consecutive Integers
D. Work Word Problems
9. Geometry
A. Heronian Triangles
B. Dividing Regions
C. Geometry Potpourri
D. Analytic Geometry