Math Playground
Puzzles

Logic riddles

Knights, knaves and lateral-thinking classics — work them out step by step.

Logic puzzles train the same muscles as proof-based mathematics — laying out what you know, what you can deduce, and what's still unknown.

Quick check

On an island, knights always tell the truth and knaves always lie. You meet A, who says 'I am a knave.' What is A?

How to crack a logic puzzle

  • Write down everything you're told as plain statements.
  • Assume one possibility, then chase the consequences — a contradiction kills that branch.
  • Track what's certain, what's possible, and what's ruled out.
  • It's the same discipline as a mathematical proof, just disguised as a riddle.
Your turn

Two islanders. A says 'we are both knaves.' What are A and B?

Try it

Knights always tell the truth, knaves always lie. You meet two: A says 'we are both knaves'. What's A?

If A is a knight, then 'both knaves' is true — but a knight isn't a knave. Contradiction. So A is a knave; the statement is false; so they're NOT both knaves. So B is a knight.