AI-created

Logic puzzles

Puzzles solved by reasoning alone: no guessing, no arithmetic beyond counting

A logic puzzle gives you a few facts and asks what must follow. The skill it trains is the one a detective, a scientist and a programmer share: hold several possibilities in mind, follow each one until it breaks, and keep only what survives. Each page here starts with a puzzle, then shows the reasoning, then opens into the history and the mathematics.

Knights and knaves Truth-tellers, liars and the art of the contradiction River crossings Wolf, goat and cabbage, and puzzles as maps of states The zebra puzzle Five houses, fifteen clues, one answer Sudoku Play three puzzles; see how people and computers solve them Nonograms Number clues that draw a picture Hat puzzles Prisoners, hats and a surprising use of parity

Three habits that solve most logic puzzles

Suppose, then test. Pick one possibility ("suppose A is a knight") and follow it. If it leads to something impossible, the supposition was wrong. This is proof by contradiction, the oldest tool in mathematics.

Write the states down. A puzzle that seems to need cleverness often needs only bookkeeping: a grid of who could be where, or a list of every position the puzzle can be in. Once the possibilities are on paper, the answer often appears by itself.

Look for what is forced. In Sudoku, a square where only one digit fits; in the zebra puzzle, a clue that leaves a single house. Fill in what is forced, and new forced moves appear. Most published puzzles can be solved this way from start to finish, with no guessing at all.