Five guards stand in a row on a staircase. Each guard either always speaks the truth or always lies. They each say: Guard 1: 'Exactly one of us lies.' Guard 2: 'The liar is to my right.' Guard 3: 'I am not lying.' Guard 4: 'Guard 5 lies.' Guard 5: 'Guard 2 speaks the truth.' Who lies?
Hints
Test who must be lying to satisfy each claim.
Answer
Guard 4 lies and everyone else tells the truth. Guard 1's claim that exactly one person lies is satisfied only if every other guard speaks the truth. Guard 2's statement then points to Guard 4 as the liar, Guard 3 confirms he tells the truth, Guard 5 vouches for Guard 2, and Guard 4's false claim about Guard 5 being a liar completes the consistent scenario.