On an island, knights always tell the truth and knaves always lie. You meet some islanders and hear what they say. Who is who? These puzzles are a favourite of logicians, and they are easy to crack with one method.
The method: assume and test
- Pick one person and assume they are a knight.
- If they are a knight, their statement is true. Work out what that means for everyone else.
- Check whether anything breaks. If it does, that person must be a knave.
- If you reach no contradiction, check the other assumption too, to be sure the answer is unique.
Example 1
A says: "We are both knaves." What are A and B?
Suppose A is a knight. Then the statement is true, so A is a knave, which is impossible. So A is a knave. Then the statement is false, so it is not true that both are knaves. A is a knave, so B must be a knight.
Example 2
A says: "B is a knave." B says: "A and I are the same type." What are they?
Suppose A is a knave. Then B is not a knave, so B is a knight. But B says they are the same type, and A (knave) and B (knight) differ, so B's statement is false, which a knight cannot say. Contradiction. So A is a knight, B is a knave, and B's false claim fits perfectly.
Handy tricks
- Nobody on the island can say "I am a knave": a knight would be lying, and a knave would be telling the truth.
- "I am a knight" tells you nothing, because both types can say it.
- Translate each statement into a plain claim you can test.
Ready for something harder? The Puzzle Vault has islanders waiting for you.