Recreational Maths
by Terry Tam
1. Speed Arithmetics
1.1. Algebraic Identities
1.2. 24 Game
1.2.1. 5.5.5.1
1.2.2. 3.3.8.8
1.3. Visual Aids
1.3.1. Napier's Bones
1.3.2. Visual Multiplication
2. Number Patterns
2.1. Polygonal Numbers
2.1.1. Triangular Number
2.1.2. Square Number
2.2. Pascal's Triangle
2.3. Fibonacci Number
3. Magic Squares
3.1. 2n-1
3.2. 4n
3.3. 4n+2
4. 7 Elevators Stop at 6 Floors
5. Weighing a Counterfeit Coin
5.1. 1 Fake Coin in 9 Coins, Lighter/Heavier Known
5.2. 1 Fake Coin in 9 Coins, Lighter/Heavier Unknown
5.3. 1 Whole Pile of 10 Piles of Coins Lighter/Heavier
5.4. Unknown Bottle(s) of 10 Bottles of Pills Lighter/Heavier
6. River Crossing Puzzles
6.1. Bridge and Torch Problem
6.2. Missionaries and Cannibals Problem
6.3. 4 Jealous Husband Problem with Island
6.4. Fox, Goose and Bag of Beans Problem
6.5. Father, Mother, 2 Sons, 2 Daughters, Policeman and Thief Problem
7. Paradoxes
7.1. Missing Dollar Riddle
7.2. Missing Square Puzzle
7.3. Inheriting 17 Horses Paradox
8. Origami
8.1. Flexagon
8.2. Cootie Catcher
8.3. Polyhedra
9. 9 Dots Puzzle
10. Alternative Proofs
10.1. Dissection Proof
10.2. Combinatorial Proof
11. Kirkman's Schoolgirl Problem
12. Social Golfer Problem
13. Magic Tricks
13.1. Handcuff Puzzles
13.2. Linking Paperclips
13.3. Human Knots
13.4. Large Hole in a Small Piece of Paper
13.5. Mobius Strips
14. 3-Switches Puzzle
15. Coconut and Monkey Puzzle
16. Optimization
16.1. Stable Marriage Problem
16.2. Secretary Problem
16.3. Geometrical Optimization
16.3.1. Heron's Shortest Path Problem
16.3.2. Building Bridge Problem
16.3.3. Fagnano's Problem
16.3.4. Shortest Fence for Halving Triangular Field
17. Mathematical Background
17.1. Graph Theory
17.1.1. Bipartite Graph
17.1.2. Hamiltonian Path/Cycle
17.1.3. Planarity
17.2. Modular Arithmetic
17.2.1. Chinese Reminder Theorem
17.2.2. Euclidean Algorithm
17.3. Divisibility Rule
17.4. Number Systems
17.4.1. Binary
17.4.2. Decimal
17.5. Geometry
17.5.1. 4 Centers in a Triangle
17.5.2. Monge's Circle Theorem
17.5.3. Pythagoras' Theorem
17.6. Geometrical Transformation
17.6.1. Reflection
17.6.2. Translation