A problem from the National Bank of New Zealand Competition 2000, via Crux Mathematicorum, November 2006:
Humanity is visited by three alien races, the Kweens, the Ozdaks, and the Merkuns. Kweens always speak the truth, and Ozdaks always lie. In any group of aliens, a Merkun never speaks first; when it does speak, it tells the truth if the previous statement was a lie and lies if the previous statement was truthful. The three alien races can tell one another apart, but to humans they all look the same. A delegation of three aliens visits Earth. At least one of them is a Kween. When they arrive they make the following statements, in order:
First alien: The second alien is a Merkun.
Second alien: The third alien is not a Merkun.
Third alien: The first alien is a Merkun.
Which aliens can we be sure are Kweens?