Four friends P, Q, R, and S make the following statements about a stolen trophy:
- P: 'Q took the trophy.'
- Q: 'S took the trophy.'
- R: 'I did not take the trophy.'
- S: 'Q is lying.'
If exactly one person is telling the truth and only one person stole the trophy, who stole the trophy?

Answer and explanation

Correct answer: B. R

  1. Step 1: Note that Q and S make contradictory statements: Q says 'S took it' and S says 'Q is lying'.
  2. Step 2: Between Q and S, exactly one must be telling the truth and one must be lying.
  3. Step 3: Since only ONE person among the four is telling the truth, that truth-teller must be either Q or S.
  4. Step 4: Therefore, P and R are both lying.
  5. Step 5: Since R is lying ('I did not take it' is false), R must have taken the trophy.
Answer
R.
Why not the others: If P, Q, or S stole the trophy, R would be telling the truth, creating two truth-tellers and violating the problem condition.

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