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Cake Theft - Logic Puzzles

During a recent police investigation, Chief Inspector Stone was interviewing five local villains to try and identify who stole the prize cake from the mid-summers fayre. Below is a summary of their statements:
Alex:    it wasn't Emery
         it was Billie

Billie:  it wasn't Charlie
         it wasn't Emery

Charlie: it was Emery
         it wasn't Alex

Dale:    it was Charlie
         it was Billie

Emery:   it was Dale
         it wasn't Alex

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

Puzzle Copyright © Kevin Stone

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