An island is inhabited only by knights and knaves. Knights always tell the truth and knaves always lie. You meet three inhabitants: Alice, Rex and Bob.
Alice tells you that Rex is a knave.
Rex tells you that Bob is a knight.
Bob claims, "Either I am a knight or Alice is a knight."
Who all are knights and who all are knaves?
Difficulty rating:
Solution:
Let's assume that Alice is a truthteller. This would mean that Rex is a knave and is lying when he says that Bob is a truthteller. This would mean that Bob is a liar.
But Bob says that either he is a truthteller or Alice is a truthteller. This is a true statement. So, if Alice were to be a truthteller then Bob would have to be a liar. But, it turns out that if Alice was a truthteller then Bob is speaking the truth which is a contradiction.
So, Alice cannot be a truthteller which means that Alice is a liar. This means that Alice was lying when she said that Rex is a liar. This means that Rex is a truthteller. This means that Rex is telling the truth when he said that Bob is a truthteller.
So, in conclusion, Alex is a knave. Rex and Bob are knights.