The cake

Logic Level 2

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 fayre. 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?

Edward Brian Charles Derek

2 solutions

Saya Suka
Feb 11, 2021

Brian gave 2 denials and Derek 2 accusations, with both telling a lie each. For Brian, his only lie must have involved the criminal (by exclaiming the innocence of the guilty party), while for Derek, his sole truth must also involved the cake thief (by his finger pointing the true criminal), so we just have to scan for a name that popped up in both Brian's and Derek's statements.

Answer : Charles

Gian Sanjaya
Sep 16, 2015

By Brian's statement and the well-known fact stated in the problem, the villain was either Charles or Edward. There are 2 ways afterward to prove that Charles is the villain:

Arnold's statement

Edward can't be the villain because otherwise Arnold's statement are both false.

Derek's statement

By Derek's statement, it was either Charles or Brian, while by Brian's statement, it was Charles or Edward.

Or, you can pair Arnold's and Derek's statement to see that 1. Either Charles or Brian was the villain. 2. By Arnold's statement, it would be impossible for either Brian or Edward to be the villain (no lie or both lie statement is then Arnold's statement). There are many other ways to do it.

The cake

2 solutions

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