Cake Theft

During a recent police investigation, Chief Inspector Stone was interviewing five local villains to try and identify who stole Mrs Archer's cake from the mid-summers fair. Below is a summary of their statements:

Arnold:
it wasn't Edward,
it was Brian.
Brian:
it wasn't Charles,
it wasn't Edward.
Charles:
it was Edward,
it wasn't Arnold.
Derek:
it was Charles,
it was Brian.
Edward:
it was Derek,
it wasn't Arnold.

It was well known that each suspect told exactly one lie. Can you determine who stole the cake?

Show Hint

Look at Brian's statements first.

Show Answer

Charles committed the terrible crime. Looking at Brian's statements, one of the statements was a lie and the other was the truth. Therefore it must have been either Charles or Edward. Looking at Derek's statements, for the same reason, it was either Charles or Brian. We know that it wasn't Brian, therefore it must have been Charles who committed the crime. Double checking this against the other statements confirms this.