🤥 Liars and Truth-Tellers
1.If A is a Liar, "at least one is a liar" is false → both would be truth-tellers → contradiction (A can't be both). So A must be a Truth-teller. Their statement is true, meaning A or B (or both) is a liar. Since A is a truth-teller, B is a liar.
2.A Truth-teller cannot say "I am a liar" — that would be a false statement. A Liar cannot say "I am a liar" — that would be a true statement. Therefore no one on Puzzlia can say "I am a liar" — the statement is self-contradictory (a paradox).
3.(a) If A = Truth-teller → B is a truth-teller (A's claim). But B says "A is a liar" — contradiction (A is actually a truth-teller). (b) If A = Liar → B is a liar (opposite of A's claim). B says "A is a liar" — this is true, but B is a liar and can't say true things — contradiction. Wait — re-examine: if A=Liar, B=Liar (from A's false claim). B's statement "A is a liar" is TRUE — but B is a liar so must say false things. Contradiction again. Re-examine case (a): A=TT → B=TT. B says "A is a liar" = false. But B is TT so can't say false. Contradiction. Case (b): A=Liar → B=Liar. B says "A is a liar" = true. But liars can't say true things. Contradiction. Answer: A is a liar, B is a truth-teller — re-examine: if A=Liar, then "B is a truth-teller" is false → B is a liar. B says "A is a liar" (true) — contradiction. If A=TT, "B is a truth-teller" is true → B is TT. B says "A is a liar" — false, but B is TT → contradiction. The puzzle has no solution under strict rules — this demonstrates an important point about self-referential statements. Award marks for systematic reasoning.
4.A says "We are all liars." If true, A would be a liar who told the truth — contradiction. So A is a liar. Since A is a liar, "we are all liars" is false → at least one is a truth-teller. B says "exactly one is a truth-teller." C says "B is lying." If B is the truth-teller: B's statement is true (exactly one TT = B). C says B is lying — false, so C is a liar. A=liar, B=TT, C=liar → exactly one TT ✓. Consistent! B is the Truth-teller; A and C are Liars.
5.Ask: "If I asked you which path is safe, what would you say?" A truth-teller points to the safe path (telling the truth about their honest answer). A liar would lie about what they would say — they would have pointed to the dangerous path, but lying about that means they point to the safe path. Both point to the safe path.