perplexus.info :: Logic : Impostor Identification

Impostor Identification (Posted on 2014-01-15)

An impostor's identity is being investigated. The impostor is known to be one of three people: Andy, Barry, or Cal. The three people make the following statements:

Andy
1. Cal is the impostor.
2. Barry's first statement is true.

Barry
1. I am not the impostor.
2. Andy is the impostor.

Cal
1. Andy's second statement is true.
2. Barry's second statement is false.

However, it is known that the impostor makes one true and one false statement but the truthfulness of the other two suspects is unknown.
Who is the impostor?

See The Solution Submitted by K Sengupta

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Analytical Solution (spoiler)

Comment 2 of 2 |

a) Assume Barry is the impostor. Then both of his statements are false. This is a contradiction, so Barry is not the impostor.

b) This makes B1 true, which makes A2 true, which makes C1 true.

c) Assume Cal is the impostor. Because C1 is true, C2 must be false. But that makes B2 true and Andy the impostor, which is a contradiction, so Cal is not the impostor.

d) Therefore, Andy is the impostor. Because A2 is true, A1 is false, and Cal is not the impostor (that checks). This makes B2 true and therefore C2 False, but there are no contradictions.

Posted by Steve Herman on 2014-01-15 23:24:28

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