Temple chain theft with four statements and one truth
At a village temple, the chain used to secure the donation box is found cut on Tuesday. The theft could only have happened between 8 p.m. and 9 p.m. on Monday. Four persons were near the temple that evening: A, B, C and D. The investigating officer records four statements. A says: 'B took the chain.' B says: 'D took the chain.' C says: 'I did not take the chain.' D says: 'B is lying.' The officer also knows that exactly one of the four statements is true. A later says he saw B near the temple gate at 8:15 p.m., but this is not part of the four statements. C has a previous theft case, while D has no record. The temple priest says the gate was locked at 8 p.m. and opened at 9 p.m., and only someone with a duplicate key could have entered without breaking the gate. The duplicate key was kept in B's shop. The officer must decide whom to arrest and what evidence to collect next.
1. Using the rule that exactly one statement is true, identify the thief and show how each possible suspect fares.
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Test each suspect. If A took the chain: A's statement is false, B's is false, C's is true, D's is true, giving two true statements. If B took the chain: A's is true, B's is false, C's is true, D's is true, giving three true statements. If D took the chain: A's is false, B's is true, C's is true, D's is false, giving two true statements. If C took the chain: A's is false, B's is false, C's own denial is false, and D's statement that B is lying is true. That gives exactly one true statement. Therefore C took the chain, and D's statement is the only true one.
2. If the officer later learns that exactly one statement is false instead, how does the answer change? Explain.
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With exactly one false statement, test again. If A took the chain, A and B are false and C and D are true, giving two false statements. If B took the chain, A is true, B is false, C is true and D is true, giving exactly one false statement. If C took the chain, A, B and C are false and D is true, giving three false statements. If D took the chain, A and D are false and B and C are true, giving two false statements. So the thief would be B. The lesson is that the logical constraint changes the answer completely; the officer must know which rule is actually established by the evidence, not choose the suspect first.
3. What evidence should be collected next, given the duplicate key was kept in B's shop?
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The officer should not rely on C's previous record or D's clean record, because the logical rule already points to C. The duplicate key creates a separate line of inquiry: who had access to B's shop, was the key missing, and are there fingerprints or CCTV images? The officer should verify C's movements between 8 p.m. and 9 p.m., check whether C knew where the key was kept, and look for the cut chain, tools and any recovered gold. B's statement should be re-recorded because B may be protecting someone or may have supplied the key. The arrest decision should rest on the combination of the statement logic, key access and physical evidence, not on character or prior record.