Question

. A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie.

You meet five inhabitants: Zoey, Bart, Rex, Dave and Alice. Zoey tells you, `Rex is a knight and Dave is a knave.' Bart claims that Rex is a knave or Zoey is a knave. Rex tells you that only a knave would say that Alice is a knave. Dave tells you, `Alice is a knave.' Alice tells you, `Either I am a knight or Bart is a knight.'

Can you determine who is a knight and who is a knave? If so, who is who? For full credit, you must prove your answer.

Answer 1

Here we start by the assumption that zoey is teling truth and he is a Knight.

so then Rex would be a Knight and Dave would be a Knave.

Now bert claims that Rex is a knave or Zoey is a knave. Which contradicts the statement of zoey that means Bert is Knave.

Now Rex tells that only a knave would say that Alice is a knave. As per our assumption, Rex is a Knight that means alice would be a knight too.

Now Dave tells that Alice is a knave, that means Dave is a knave too.

Now Alice is true that means he is a knight or bart is a knight that means he is true.

Now as we see that Zoey, Rex and Alice is Knight. Similarly, Bert and Dave is knave too.