On an island every inhabitant either always tells the truth or always lies. Two of them, Anil and Bhavin, come up to you, and Anil announces: "Both of us are liars." What can be said for certain?

Start with Anil. If he told the truth, his own words would make him a liar, which is impossible — so Anil is a liar. His statement is therefore false, meaning it is not true that both are liars. Anil certainly is one, so the part that fails must be Bhavin, who must be a truth-teller. The traps: 'Anil tells the truth' is ruled out by the very first step; 'both lie' is the tempting reading that simply believes what Anil said, but a liar's words are exactly what must not be believed; 'both tell the truth' would mean Anil truthfully called himself a liar.