In a certain village each person belongs to one of two kinds: a truth-teller, who never says anything false, or a liar, who never says anything true. Chetna says, "Dinesh is a truth-teller." Dinesh says, "Chetna and I are not of the same kind." What are the two of them?

Suppose Chetna were a truth-teller. Then Dinesh really is a truth-teller, so his own words are true and the two are of different kinds — but we have just made them both truth-tellers, a contradiction. So Chetna is a liar. Her claim about Dinesh is therefore false, so Dinesh is a liar too. Check that this holds together: Dinesh's words, 'we are not of the same kind', are false, and indeed they are of the same kind. The traps: 'both truth-tellers' is the case just shown to break down; 'Chetna truthful, Dinesh a liar' makes Chetna's own statement false while she is supposed to be truthful; 'Chetna a liar, Dinesh truthful' makes Chetna's statement true while she is supposed to be lying.