Puzzles, and why they work

A good puzzle is a small world with exact rules. You can hold all of it in your head, and yet the answer hides. This site collects the classics: logic puzzles you solve by pure reasoning, math puzzles you can play right here on the page, and the big ideas behind them. Every page has a puzzle to try first, then the thinking that cracks it, and then, in closed boxes you can open if you like, the deeper math.

The picture above holds three answers from the site, worked out by a computer program rather than drawn by hand: eight queens that do not attack each other, a Tower of Hanoi part-way through the fastest solution, and the oldest magic square, where every row, column and diagonal adds to 15. They stand on a Martian evening, with the blue sunset Mars really has.

Where to begin

Start here Six warm-up puzzles, five minutes each, for any age Logic puzzles Knights and knaves, river crossings, Sudoku, nonograms, hats Math puzzles Hanoi, the 15 puzzle, queens, knights, Lights Out, Monty Hall The ideas behind Counting, invariants, game theory, search, how hard a puzzle is

Puzzles you can play here

Tower of Hanoi Move the tower; can you match the fewest moves? The 15 puzzle Slide the tiles, and meet the version that can't be solved Nim Play the computer, then learn its secret Eight queens Place queens on any board from 4 × 4 to 10 × 10 The knight's tour Visit every square once Lights Out Turn off every light; the page can show you how Monty Hall Stay or switch? Play a thousand games Sudoku Three puzzles and a solver that shows its work Nonograms Numbers that draw a picture

How the pages work

Each page is a five to six minute read. A badge under the title says who it is for: Beginner pages need nothing but curiosity, Intermediate pages use school math, and Expert pages reach the research. Answers are always in closed boxes, so nothing is spoiled until you choose. The sources for each page are listed, closed, at its end. Everything here, the text, the puzzles and the pictures, is AI-created; see About.

This is a sister site of Algorithms, Math and Cryptography, and part of Mars – your new home.