Math · Exploration
Knights and Knaves
Who tells the truth, and who must be lying?
An island of two kinds
On this island, every inhabitant is either a knight, who always tells the truth, or a knave, who always lies. Your task is to work out which is which from what they say.
The first puzzle
You meet A and B. A says: We are both knaves.
B says nothing. Who are A and B?
Choose the only possibility that makes A’s statement fit the speaker.
Work it backwards
Suppose A were a knight. Then A’s statement would be true, making A a knave—a contradiction. A must be a knave. Therefore A’s statement is false: they are not both knaves. Since A is one knave already, B must be a knight.
A more complicated version
You now meet A, B, and C. A says, B is a knave.
B says, C is a knave.
C says, A and B are of different kinds.
Can you determine all three?
A is a knight, B is a knave, and C is a knight. If B were a knight, C would be a knave; then C’s statement would be false, so A and B would be the same kind—making A a knight. But A would be saying B is a knave, a contradiction. So B is a knave; C is a knight; and C truthfully says A and B differ, so A is a knight.
The useful habit
These puzzles reward a small but powerful move: assume one possibility, then follow each statement until it either fits or contradicts itself. The words may be playful, but the method is the same one used in proofs, programs, and careful debugging.