AI-created

The ideas behind

Five big ideas that explain almost every puzzle on this site

Puzzles look like a jumble of separate tricks: a parity argument here, a doubling there, a clever strategy for a game of stones. But the same few ideas come back again and again. Learn them, and a new puzzle stops being a mystery and becomes a question you know how to ask. Each page below explains one idea, shows where it appears in the puzzles, and points to where it leads in real mathematics and computing.

Counting How many ways? Products, factorials, and the pigeonhole principle Invariants and parity The quantity that never changes, and the puzzles it rules out Game theory and Nim Winning positions, a binary secret, and play against the computer Search and backtracking How a computer solves a puzzle by trying, and how it avoids trying everything How hard is a puzzle? P, NP, and why Sudoku, Minesweeper and Tetris are hard in a precise sense

Where each idea appears

Puzzle	Counting	Invariants	Games	Search	Hardness
Tower of Hanoi	✓			✓
The 15 puzzle	✓	✓		✓	✓
Eight queens	✓			✓	✓
Lights Out	✓	✓
Bridges of Königsberg		✓
Sudoku	✓			✓	✓
Hat puzzles	✓	✓
River crossings	✓			✓
Monty Hall	✓		✓

The pages here are a little more mathematical than the puzzle pages, but each one starts with something to try, and the formulas are always explained in words first.