Knights and knaves puzzles with answers
In a knights and knaves puzzle, everyone you meet is either a knight, who always tells the truth, or a knave, who always lies. You can’t tell them apart by looking, only by what they say. Each puzzle gives you a few statements and asks who is which. Below are six original ones, from easy to hard, each with its answer and reasoning hidden until you want it, and then a picture version of the same idea.
The rules
- Knights always tell the truth. Everything a knight says is true.
- Knaves always lie. Everything a knave says is false, so a statement with an “and” in it only needs one false part.
- You can’t tell them apart by looking. Unless a puzzle says otherwise, any number of them can be knaves: none, some or all.
- “X is lying” means X is a knave, and “X is a knight” from a knave means X is really a knave.
How to solve them
- Suppose someone is a knight.Then their statement is true. Follow it: who else does it tell you about?
- Keep going until something breaks.If you reach a statement that has to be both true and false, your first guess was wrong, so that person is a knave.
- Check the answer.Go through every statement once more: each knight’s must be true and each knave’s false.
Two patterns save time. When one person calls another a knave, they’re always opposite kinds: a knight telling the truth about a knave, or a knave lying about a knight. And when someone says “X and I are the same kind”, X must be a knight, whatever the speaker is.
Six puzzles, easy to hard
Each is new, written for this page. For each one, work out who is a knight and who is a knave.
Puzzle 1 (easy)
- Ada: “Ben is a knave.”
- Ben: “Ada and I are both knights.”
Show the answer
Ada is a knight and Ben is a knave.
Ben can’t be a knight. If he were, his words would be true, so Ada would be a knight too, and a knight would never call Ben a knave.
So Ben is a knave. That makes Ada’s statement true, so Ada is a knight. Ben’s claim is false, just as a knave’s should be.
Puzzle 2 (easy)
- Cal: “Dee and I are different kinds.”
- Dee: “Cal is a knight.”
Show the answer
Cal is a knave and Dee is a knave.
Suppose Cal is a knight. Then he and Dee are different kinds, so Dee is a knave. But Dee says Cal is a knight, which would be true, and a knave can’t say anything true.
So Cal is a knave. His statement is false, which means he and Dee are the same kind: Dee is a knave too. Her “Cal is a knight” is false, as it should be.
Puzzle 3 (medium)
- Eve: “Exactly one of us three is a knight.”
- Finn: “Eve is lying.”
- Gus: “Finn and I are the same kind.”
Show the answer
Eve is a knave, Finn is a knight, and Gus is a knight.
Start with Gus. If he’s a knight, Finn is the same kind: a knight. If he’s a knave, his statement is false, so Finn is a different kind from him: a knight again. Either way, Finn is a knight.
So Eve really is lying: she’s a knave, and it isn’t true that exactly one of them is a knight. Finn is one, so there’s another, and it isn’t Eve. Gus is a knight, which fits his own statement too.
Puzzle 4 (medium)
- Hal: “At least one of Ivy and Jo is a knave.”
- Ivy: “Hal is a knave.”
- Jo: “Hal is a knight and Ivy is a knave.”
Show the answer
Hal is a knight, Ivy is a knave, and Jo is a knight.
Ivy calls Hal a knave, so the two of them are opposite kinds. Suppose Hal is the knave. Then Ivy is a knight, and Hal’s statement is false, so Ivy and Jo are both knights. But Jo says Hal is a knight, which would be false, and knights don’t say false things.
So Hal is a knight and Ivy is a knave. Hal’s statement holds, since Ivy is a knave. Jo’s statement is now true in both parts, so Jo is a knight.
Puzzle 5 (hard)
- Oz: “Pip is a knave.”
- Pip: “Quinn is a knave.”
- Quinn: “Rue is a knave.”
- Rue: “Exactly one of us four is a knight.”
Show the answer
Oz is a knight, Pip is a knave, Quinn is a knight, and Rue is a knave.
Each of the first three calls the next one a knave, so each pair are opposite kinds: Oz and Pip, Pip and Quinn, Quinn and Rue. Down the line, the kinds take turns.
That leaves two ways it could go: Oz and Quinn are the knights, or Pip and Rue are. Either way there are exactly two knights, so Rue’s statement is false and Rue is a knave. Then Quinn is a knight, Pip a knave and Oz a knight.
Puzzle 6 (hard)
- Kit: “Exactly three of us four are knights.”
- Lou: “Kit and Max are both knaves.”
- Max: “Lou and Nia are different kinds.”
- Nia: “Kit is a knight.”
Show the answer
Kit is a knight, Lou is a knave, Max is a knight, and Nia is a knight.
Nia says Kit is a knight, so Nia and Kit are the same kind. Suppose they’re both knaves. If Max is a knight, Lou must differ from Nia, so Lou is a knight, but Lou says Max is a knave, which is false. If Max is a knave, then Lou’s statement is true, so Lou is a knight, and Lou and Nia really are different kinds: Max would have said something true. Either way it breaks.
So Kit and Nia are knights. Kit’s statement is true: exactly three knights, so exactly one knave. Lou calls Kit a knave, which is false, so Lou is the knave and Max is a knight. Check: Lou and Nia are different kinds, just as Max says.
A picture version: Lie of Sight
Lie of Sight is a daily puzzle built on the same idea, with three changes. First, there is always exactly one liar: a single knave among knights, like the last puzzle above. Second, nobody talks about anyone’s honesty. Each person only says what they could see, or for Rex the dog, smell: “I saw the clock”, “I didn’t see Grandma”. Third, whether a statement is true depends on where everyone stands in a room, so instead of a table of knights and knaves you move people around a board until every story but one fits.
That room is the first of three mini puzzles, with their answers, on find-the-liar puzzles. For the method on a real board, see how to solve a find-the-liar puzzle, or try today’s case below.
Questions people ask
Who invented knights and knaves puzzles?
The logician Raymond Smullyan made them famous in his 1978 book What Is the Name of This Book? Puzzles about liars and truth-tellers are much older, but his island of knights and knaves gave the genre its name.
Can a knights and knaves puzzle have more than one answer?
A badly made one can. Each puzzle on this page was checked by trying every possible mix of knights and knaves, and exactly one fits every statement.
Can anyone say “I am a knave”?
No. A knight saying it would be lying, and a knave saying it would be telling the truth. So if a puzzle has someone say it, something else is going on.
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