Four persons: P, Q, R and S are in police custody and one of them has…
2022
Four persons: P, Q, R and S are in police custody and one of them has committed a crime. They confess as follows:
A. Person P: Q did it.
B. Person Q : S did it.
C. Person R: I did not do it.
D. Person S : Q lied.
If exactly one of the statements is false, which of the following is the guilty person.
- A.
P
- B.
Q
- C.
R
- D.
S
Attempted by 58 students.
Show answer & explanation
Correct answer: B
Concept: This is an 'exactly one statement is false' logic puzzle, solved by the assumption-and-count method: assume one suspect is guilty at a time, evaluate every person's statement as true or false under that single assumption, and count how many statements turn out false. The assumption that produces exactly the number of false statements stated in the problem — here, exactly one — identifies the guilty person.
Applying this to each suspect in turn:
If P is guilty: P says "Q did it" (false); Q says "S did it" (false); R says "I did not do it" (true); S says "Q lied" (true). False statements = 2 → Reject.
If Q is guilty: P says "Q did it" (true); Q says "S did it" (false); R says "I did not do it" (true); S says "Q lied" (true). False statements = 1 → Accept (meets the condition).
If R is guilty: P says "Q did it" (false); Q says "S did it" (false); R says "I did not do it" (false); S says "Q lied" (true). False statements = 3 → Reject.
If S is guilty: P says "Q did it" (false); Q says "S did it" (true); R says "I did not do it" (true); S says "Q lied" (false). False statements = 2 → Reject.
Cross-check: statements B (Q: "S did it") and D (S: "Q lied") are directly linked — D is true exactly when B is false. Only the Q-guilty case makes B false and D true while keeping A and C true, giving exactly one false statement; no other case matches.
Answer: Q is the guilty person — assuming Q's guilt is the only case that produces exactly one false statement.