Raymond Smullyan has made a career of writing logic problems. His most famous have to do with a mythical island of Knights and Knaves. Knights always tell the truth, and Knaves always lie.
As you approach the island, you spot three inhabitants on the shore. You call out to them, “Are you Knights or Knaves?” The first says something but you do not hear what he says, so you ask, “What did you say?” The second inhabitant says, “He says he is a Knight, he is and so am I.” The third responds, “He is a Knave, but I am a Knight.” Figure out the true identities of the three individuals.
They are Knight, Knight and Knave. The most basic rule of Knight and Knave island is that no one ever says they are a Knave. Knights always say they are Knights because they tell the truth, Knaves say they are Knights because they always lie. The second must be a Knight, otherwise he would have lied about the firsts response and if so, he must be telling the truth about the first. The third must therefore be a Knave.