Unit 15 · Truth and Lie Logic

Animal Truth-Teller — Which One Is Honest?

Lesson 2 of 2

Lesson 2 of 2Truth and Lie Logic

Now for the most iconic variant in this unit — the classic "exactly one truth-teller" puzzle, where one character tells the truth and everyone else lies. The method is called assume-and-cascade: pick one character, assume they're telling the truth, follow the chain of consequences, and check whether exactly one consistent world emerges.

Exactly-one truth-teller questions appear across the medium-to-difficult band of OC TS and are among the most frequently tested logic formats in the exam series. The assume-and-cascade technique is identical every time, and students who have practised it can solve even four-character versions in under a minute.

The examiner is testing whether you can apply a consequence cascade: if Character A tells the truth, their statement becomes a fact; since everyone else is lying, every other statement is false; you then check whether this creates exactly one truth-teller and one identifiable culprit. One and only one cascade will be fully consistent.

Several animals or people each make one statement — typically an accusation or a denial. Exactly one is telling the truth; all others are lying. You must identify both who the truth-teller is and who committed the act. Often one character's statement refers to another character's honesty, creating a useful cascade entry point.

Best approach: Start with a meta-statement if one exists (a character saying another character is lying — it's a two-for-one entry point). Assume that character is the truth-teller, cascade to determine everyone else's lying status, and negate all liar statements. Check whether exactly one truth-teller and one culprit emerge with no contradictions. If the cascade fails, try the next character. Typically only one or two candidates need testing.

Question

Only one of these animals tells the truth:

  • Bear: "Fox took the key."
  • Fox: "Duck took the key."
  • Crow: "I didn't take the key."
  • Duck: "Bear is lying."

Who took the key?

Select an answer to see the explanation.

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