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Resolve Two Knights-and-Knaves Statements

SIG (Susquehanna)Data Scientist · Online Assessment
EasyData ScientistOnline AssessmentStatistics & Math

Last updated

This question tests logical deduction and systematic case analysis under binary truth constraints.

The Puzzle

You encounter two individuals, Perlica and Chen, on an island where inhabitants are either Knights (who always tell the truth) or Knaves (who always lie).

Perlica says: "At least one of us is a knave." Chen says: "Perlica is a knave."

Determine the identity of both Perlica and Chen. Explain your reasoning using a truth table or case-by-case analysis.

Constraints

  • Knights always tell the truth.
  • Knaves always lie.
  • Every inhabitant is either a knight or a knave.

Expected Output

Identify if Perlica is a Knight/Knave and if Chen is a Knight/Knave. Provide the logical derivation for your conclusion.

Hints

Hint 1

Assume Perlica is a Knight and see if that leads to a logical consistency or a contradiction.

Hint 2

Assume Perlica is a Knave and see if that forces Chen's statement to be true or false.

Hint 3

Evaluate Chen's statement based on the identity of Perlica determined in your hypothesis.

Follow-up questions

  • What happens to the logic if Perlica instead said 'We are both knaves'?
  • If you met a third person, Dasha, who said 'Both Perlica and Chen are lying,' could Dasha be a knight?
  • How would you represent this problem using Boolean algebra (letting 1 be a Knight and 0 be a Knave)?