A cop arrested four suspects for the bank robbery. When he interviewed them, each made two statements. From his infrared lie-detector he knew that each man made one "true" and one "false" statement. As a result, he soon found out the culprit.

Given the following statements, can you determine who the culprit was?

‘A’ said: “I did not do it. B did.”

‘B’ said: “A did not do it. C did.”

‘C’ said: “B did not do it. I did.”

‘D’ said: “C did not do it. A did.”

Lets start with A's statement.
‘A’ said: “I did not do it. B did.”
If first part is false it means that B did it and amazingly A also did it since first part is false.. hence we get that First part must be true and second must be false.
Now analysing B's statement,
‘B’ said: “A did not do it. C did.”

First part cant be false as already A have made it true and if this becomes false then A must have done it and which cant be true so again
1st part is true and second false.
Now analysing C's statment,
‘C’ said: “B did not do it. I did.”
First part must be true in support of A's false statement "B did it".
Hence first must be true and second false.
Now lets analyse D's statement
‘D’ said: “C did not do it. A did.”
If "A did" will be true then and C didnt false then it means that both A and C have done it and it means that "A did" must be a false statment and "C didnt" true.
Hence
Person/Statement Part 1 Part2
A T F
B T F
C T F
D T F

Conclusion that each of them have told that non did it except D.
D is the culprit.

Posted by Dalveer on 2003-01-31 23:32:14