After a local Post Office burglary, four suspects were being interviewed. Below is a summary of their statements. Police know that each of them told the truth in one of the statements and lied in the other. From this information can you tell who committed the crime? Alan said: It wasn't Derek It wasn't Brian Brian said: It wasn't Charles It was Derek Charles said: It was Alan It wasn't Derek Derek said: It was Charles It wasn't Alan

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Answers

2015-10-05T20:30:11+05:30
It was Derek. Since each suspect told the truth just once, Eric's statements mean that it was either Derek or Alan. If it was Alan, then both of Brian's statements would be true, which isn't allowed (and similarly both of Derek's would be false).
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if it is done by Derek, then Charles said: both true statements.. but he is supposed to have said only one true statement.
2015-10-06T00:13:19+05:30

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Alan       Brian      Charles    Derek
Each person told  one Truth and one False statement.  If Alan or Charles did it, then  what Alan told will both be true statements.  So it is either Brian or Derek.   If it is done by Derek, both statements of Brian will be true.   So only Brian is possible to have done it.

A:                not B                 not D
B:                            not C        D
C:        A                               not D
D:    not A                  C

Suppose, we say that Brian  has done the crime.

A said,  not B  - false.    not D - true
B said:    not C - true       D :    false
C said:    A  - false         not D:  true
D said:    not A  true        C : false

that works.

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