How to Play Knights & Knaves

Background

Knights & Knaves puzzles are classic logic puzzles popularized by mathematician Raymond Smullyan. They take place on a fictional island where two types of people live: Knights, who always tell the truth, and Knaves, who always lie.

The Rules

  • 1.Two types: Each character is either a Knight or a Knave. There are no other types.
  • 2.Knights always tell the truth: Every statement made by a Knight is true.
  • 3.Knaves always lie: Every statement made by a Knave is false.
  • 4.Use logic: Analyze the statements and use deduction to determine each character's type.

Character Types

⚔

Knight

Always tells the truth. If a Knight says something, it must be true.

🗡

Knave

Always lies. If a Knave says something, it must be false.

Example Puzzle

A says: "B is a Knave."
B says: "We are both Knights."
Show Solution & Reasoning

Answer: A is a Knight, B is a Knave

Step 1: Assume B is a Knight. Then B's statement "We are both Knights" is true, so A is also a Knight.

Step 2: But if A is a Knight, A tells the truth. A says "B is a Knave" - contradiction!

Step 3: So B must be a Knave. B's statement "We are both Knights" is false, which is consistent.

Step 4: Now check A. A says "B is a Knave" which is true, so A is a Knight.

Tips & Strategies

  • Self-reference: A Knight cannot say "I am a Knave" (that would be lying). A Knave cannot say "I am a Knave" (that would be telling the truth). So "I am a Knave" is impossible!
  • Assume and test: Pick a character, assume they're a Knight, and see if all statements remain consistent.
  • Contradictions: If your assumption leads to a contradiction, the opposite must be true.
  • "Same type" statements: When someone says "We are the same type," they're a Knight if true, Knave if false.
  • "Different type" statements: When someone says "We are different types," they're a Knave if they're the same type as the other person.

Common Statement Types

  • "X is a Knight" - Claim about another person's type
  • "X is a Knave" - Claim about another person's type
  • "We are the same type" - Both Knights or both Knaves
  • "We are different types" - One Knight, one Knave
  • "At least one of us is a Knave" - Logical OR statement
  • "Exactly N of us are Knights" - Counting statement