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MathNet 2003 — Part 02 Question 11

Math Olympiad Vault · MathNet 2003 — Part 02

Question 11

In the country of $\mathrm{Oz}$, in addition to normal people (who can lie or tell the truth), there live knights (who always tell the truth) and knaves (who always lie). A strange law dictates that in every marriage the spouses are either both normal, or one is a knight and the other a knave. Once you arrive at the semi-detached house of the Allegri and Bianchi spouses, ask if Mr. Bianchi, who is absent, is a knight, obtaining an affirmative response from both Mrs. Bianchi and both Mr. and Mrs. Allegri. How many spouses can you determine the type of?
  1. 0
  2. 1
  3. 2
  4. 3
  5. 4 .