Five persons A, B, C, D, and E are either guards or thieves. The guards always tell the truth whereas thieves always tell a lie. A claims that B is a guard. B claims that C is a thief. C claims that D is a thief. E claims that a is a guard. D claims that B and E are different kinds. The number of thieves is

The answer is D (4 thieves). Read E's claim as 'A is a guard', since the 'a' in the question is clearly a typo for A.

Start with A. If A were a guard, B would be a guard, so C would be a thief. C's lie makes D a guard. D's truthful claim then makes E a thief (B and E differ). But E's lie would make A a thief, contradicting our start. So A must be a thief.

• A is a thief, so B is not a guard, so B is a thief.
• B is a thief, so C is not a thief; C is a guard.
• C is a guard, so D is a thief.
• D is a thief, so the claim 'B and E are different' is false; B and E are the same kind. B is a thief, so E is a thief.
• E is a thief, so 'A is a guard' is false. A is a thief, which agrees.

Result: A, B, D and E are thieves, and only C is a guard. That gives four thieves, and it is the only consistent assignment.

This is a truth-teller and liar puzzle, solved by assuming one person's type and following the chain. It is a standard reasoning item in the UPPSC Prelims paper and is useful for the Mains logical reasoning paper too.

Trap: Aspirants often take 'a' literally, or stop after one branch and pick 2 or 3 without checking that D's statement forces B and E to be the same kind.