Question

Three friends, P, Q, and R, are solving a puzzle with statements: 
(i) If P is a knight, Q is a knave. 
(ii) If Q is a knight, R is a spy. 
(iii) If R is a knight, P is a knave. Knights always tell the truth, knaves always lie, and spies sometimes tell the truth. If each friend is either a knight, knave, or spy, who is the knight?

• A. P
• B. Q
• C. R
• D. None

Hint:

For logic puzzles with knights, knaves, and spies, systematically test each person as a knight, use implications to assign roles, and ensure consistency with truth values.

Answer 1

The Correct Option is B

Assume each friend (P, Q, R) is a knight, knave, or spy. Knights always tell the truth (statement is true), knaves always lie (statement is false), and spies make statements that can be true or false. Analyze the statements:

• Statement (i): "If P is a knight, then Q is a knave." (P → ¬Q)
• Statement (ii): "If Q is a knight, then R is a knave." (Q → ¬R)
• Statement (iii): "If R is a knight, then P is a knave." (R → ¬P)

Test Q as a knight (Q = Knight, statement must be true):

• Statement (i): "If P is a knight, then Q is a knave."
  Since Q is a knight (not a knave), the conclusion is false. For the implication to be true, the antecedent must be false. So, P is not a knight → P is either a knave or a spy.
• Statement (ii): "If Q is a knight, then R is a knave."
  Q is a knight, so this must be true. That means R is a knave.
• Statement (iii): "If R is a knight, then P is a knave."
  R is a knave (not a knight), so the antecedent is false. A false antecedent makes the implication true, so the statement holds regardless of P.

Now we have:

• Q = Knight
• R = Knave
• P ≠ Knight, ≠ Knave → P must be the Spy

Verification:

• P (Spy): Statement (i) is false (P is not a knight), which a spy may say.
• Q (Knight): Statement (ii) is true (Q is a knight, R is a knave), which a knight must say.
• R (Knave): Statement (iii) is false (R is not a knight), which fits a knave's nature.

Thus, the only consistent scenario is:

• P = Spy
• Q = Knight
• R = Knave

Correct answer: Q