Detective Trepka gathered up Alan, Brian, and Stu yesterday, because one of them was suspected of having stolen Old Lady Amber's bicycle. The trio of suspects made the following statements during questioning: Alan: I'm innocent. Brian: I'm innocent. Stu: Brian stole the bike. If only one of these statements is true, who stole the bike? How do you know?

The correct answer is - Alan stole the bike.

Explanation:

According to the question, only one statement is true among three statements by suspects Alan, Brian and Stu. Then there will be three combination or cases:

Case 1. if the statement made by Alan - I'm innocent, is true.

It is not possible if Brian saying he is innocent is false and the statement of Stu is false because both statements contradict if Brain is not innocent and Brian did not steal the bike can not be possible.

Case 2. if the statement made by Brain -I am innocent - is true.

In this case, the other two would be false, so if Alan is not innocent then it means Alan is guilty and stole the bike and the statement of Stu is also false which means Brian is innocent then either alan stole the bike or Stu himself stole the bike.

This is most likely the case and Alan stole the bike

Case 3. if the statement made by Stu - Brian stole the bike, is true

This can not be true due to the fact if its true it will automatically make the statement of Alan true who says he is innocent.

Thus, Alan stole the bike.

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