Knights and Knaves facts for kids

Knights and Knaves are a fun type of logic puzzle. In these puzzles, you meet characters who always tell the truth or always lie. The name for these puzzles was created by Raymond Smullyan in his 1978 book, What Is the Name of This Book?.

Imagine an island where everyone is either a knight or a knave. Knights always tell the truth, no matter what. Knaves always lie, no matter what. When you visit this island, you meet some of its people. Your goal is usually to figure out if they are a knight or a knave based on what they say. Sometimes, you might need to figure out other facts. You might even need to think of a yes-no question to ask them to learn something specific!

Here's an example from Raymond Smullyan himself. You meet three islanders: A, B, and C.

• You ask A what type he is, but you don't hear his answer.
• Then, B says, "A said that he is a knave."
• After that, C says, "Don't believe B; he is lying!"

To solve this, think: Can a knight say they are a knave? No, because knights always tell the truth. Can a knave say they are a knave? No, because knaves always lie, so they would have to say they are a knight. This means no one can ever say, "I am a knave."

Since no one can say they are a knave, B's statement ("A said that he is a knave") must be a lie. This means B is a knave. Because B is a knave, C's statement ("Don't believe B; he is lying!") must be true. This means C is a knight. As for A, since no one can say they are a knave, A must have said, "I'm a knight." But this doesn't tell us if A is a knight or a knave, because both would say "I'm a knight." So, we can't tell what A is!

Another puzzle expert, Maurice Kraitchik, shared a similar puzzle in his 1953 book Mathematical Recreations. In his version, two groups on an island, the Arbus and the Bosnins, either lie or tell the truth.

Some puzzles add more types of islanders. There might be "alternators" who switch between telling the truth and lying. Or "normals" who can say whatever they want. Things get even trickier if the islanders speak their own language. You might know that "bal" and "da" mean "yes" and "no," but you don't know which is which! These complex puzzles helped inspire what's known as "the hardest logic puzzle ever."

Fun Puzzles to Solve

Many simple logic puzzles can be solved using basic logic rules. Thinking about what must be true or false helps a lot.

Let's imagine John and Bill live on the island of knights and knaves.

Both Knaves?

John says, "We are both knaves."

What does this tell us?

• If John were a knight, his statement would be true. But a knight can't be a knave. So John can't be a knight.
• This means John must be a knave.
• Since John is a knave, his statement ("We are both knaves") must be a lie.
• If his statement is a lie, then it's not true that both of them are knaves.
• Since John is a knave, this means Bill cannot be a knave. So, Bill must be a knight!

This puzzle is a bit like the liar paradox, where saying "I am lying" creates a contradiction.

Same or Different?

John says, "We are the same kind." Bill says, "We are of different kinds."

Let's figure this out:

• John and Bill are saying opposite things. If John is right, Bill is wrong. If Bill is right, John is wrong.
• This means one of them must be a knight (telling the truth) and the other must be a knave (lying).
• Bill's statement is "We are of different kinds." Since we just figured out that one is a knight and one is a knave, Bill's statement is true!
• So, Bill must be the knight.
• And John must be the knave.

Just Asking About Identity

If you just want to know if someone is a knight or a knave, you can ask them a question where you already know the answer. For example, in the movie The Enigma of Kaspar Hauser, a character solves this by suggesting asking the person "whether he was a tree frog."

The Fork in the Road

This is one of the most famous Knights and Knaves puzzles.

John and Bill are standing at a fork in the road. John is in front of the left road, and Bill is in front of the right road. One of them is a knight and the other a knave. You don't know which is which. You also know that one road leads to Death, and the other leads to Freedom. By asking one yes–no question, can you determine the road to Freedom?

This puzzle became very popular after it appeared in the 1986 fantasy movie, Labyrinth. In the movie, the main character faces two doors with guardians who follow these rules. One door leads to the castle, and the other to certain death. This puzzle also showed up in the Doctor Who story Pyramids of Mars and in the animated TV series Samurai Jack. It was even used in the Belgian reality TV show De Mol.

Here's how to solve it, as shown in Labyrinth:

• Ask one of the guards: "Would the other guard tell me that your door leads to the castle?"
• Think about it:

* If you ask the knight, he knows the other guard (the knave) would lie about the door. So, the knight will tell you the truth about that lie. * If you ask the knave, he knows the other guard (the knight) would tell the truth about the door. But the knave has to lie, so he will lie about that truth.

• In both cases, the answer you get will always be the opposite of the correct answer about whether that door leads to the castle. So, if they say "yes," the door leads to death. If they say "no," the door leads to the castle!

Another way to solve it is to ask either man if they would say that their own path leads to freedom.

• If you ask the knight, he would truthfully say "yes" if his path leads to freedom, and "no" if it doesn't.
• If you ask the knave, he would lie about what he would say. If his path leads to freedom, he would normally say "yes," but since he must lie, he would say "no." If his path leads to death, he would normally say "no," but since he must lie, he would say "yes."
• This means both the knight and the knave will give you the correct answer about their own path!

Goodman's 1931 Puzzle

The philosopher Nelson Goodman shared another version of this puzzle in a newspaper in 1931. He called the truth-tellers "nobles" and the liars "hunters." Three islanders, A, B, and C, meet.

• A says something like "I am a noble" or "I am a hunter" (we don't know which).
• Then, B says, "A said, 'I am a hunter'."
• After that, B also says, "C is a hunter."
• Finally, C says, "A is noble."

Let's solve it:

• Remember, a hunter (liar) can never say they are a hunter. If they did, they'd be telling the truth about being a liar, which is impossible for a liar. So, A could not have said "I am a hunter."
• This means B's first statement ("A said, 'I am a hunter'") must be a lie.
• Since B lied, B must be a hunter.
• Now we know B is a hunter, so B's second statement ("C is a hunter") must also be a lie.
• If "C is a hunter" is a lie, then C is not a hunter. So, C must be a noble.
• Finally, C says, "A is noble." Since C is a noble (truth-teller), C's statement must be true.
• Therefore, A is a noble.

So, A is a noble, B is a hunter, and C is a noble!