A problem from the 1994 Italian Mathematical Olympiad:
Every inhabitant on the island of knights and scoundrels is either a knight (who always tells the truth) or a scoundrel (who always lies). A visiting journalist interviews each inhabitant exactly once and gets the following answers:
A1: On this island there is at least one scoundrel.
A2: On this island there are at least two scoundrels.
An-1: On this island there are at least n – 1 scoundrels.
An: On this island everyone is a scoundrel.
Can the journalist decide whether the knights outnumber the scoundrels?