Knights and knaves puzzles, explained
A knights and knaves puzzle is a logic puzzle about an island where some people always tell the truth (the knights) and the rest always lie (the knaves). You hear what they say and work out who is who. The puzzles were made famous by the logician Raymond Smullyan in his 1978 book What Is the Name of This Book?
How to solve one
Take one person and suppose they're a knight. Follow what that means. If it leads to a contradiction, they must be a knave. Then do the same for the next person. Two cases per person is usually enough.
Puzzle 1: “We are both knaves”
You meet A and B. A says: “We are both knaves.” What are they?
Answer: A is a knave and B is a knight. If A were a knight, the sentence would be true, so A would be a knave: impossible. So A is a knave, the sentence is false, and they are not both knaves. B must be a knight.
Puzzle 2: “At least one of us is a knave”
A says: “At least one of us is a knave.”
Answer: A is a knight and B is a knave. If A were a knave, the sentence would be true (A is one), but knaves can't say true things. So A is a knight, the sentence is true, and since A isn't a knave, B is.
The two guards riddle
Two doors, one to freedom and one to doom. Two guards: one always tells the truth, one always lies, and you don't know which is which. You get one question to one guard.
Answer: ask either guard, “Which door would the other guard tell me leads to freedom?”, then take the other door. The truthful guard faithfully reports the liar's wrong answer; the liar lies about the truthful guard's right answer. Either way you hear the wrong door.
Liars in a whodunnit
Whodunnit takes the same idea into an interrogation booth, with rules that make lies fair to catch:
| Knights and knaves | Whodunnit | |
|---|---|---|
| Who lies | Knaves, about everything | Liars, only about where they were |
| About other people | Knaves lie | Everyone tells the truth |
| Staying quiet | Not allowed | Evasive suspects won't say where they were |
| What you know | Usually nothing | The number of Liars and Evasive suspects |
| The goal | Label everyone | Find the one person at the crime scene, in as few questions as you can |
Because a Whodunnit Liar only lies about their own room, the trick is the same as with the guards: ask the questions whose answers can't be lies. Read how to solve a murder mystery logic puzzle for the full method and a worked case.
Play today's case, #3