There are 2 rooms, each with a label that is either true or false.
There's a princess inside one of these room, and a monster inside the other room.
The labels read:
Room 1
: One of these labels is true, and the other is false.
Room 2
: This room has a princess inside.
Which room has a princess?
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Relevant wiki: Truth-Tellers and Liars
If Room 1's label is true, that means Room 2's label is false. That means the princess is in Room 1.
If Room 1's label is false, that means Room 2's label is false. That means the princess is in Room 1.
Either way, the princess is in Room 1.