While wandering, you encounter a pond, in which two demons are bathing. One is labelled 'honest', meaning they always tell the truth, and the other is labelled 'liar', which means they always lie. As you turn around and leave, you hear a demon's voice say "We aren't labelled correctly". Which of the demons said this?
It must be
the demon labelled "liar".
There are two options:
If they are labelled correctly, then the one who spoke is a liar and labelled as a liar.
If they aren't labelled correctly, then the one who spoke is honest but labelled as a liar.
Note that the puzzle is not entirely well-posed, since it assumes that the only options are that either both or neither are labelled correctly, i.e. it precludes the possibility of both being honest or both being liars. There is a slight ambiguity in the English phrase "We aren't labelled correctly" - does it mean that they're both labelled incorrectly, or just that they're not both labelled correctly? - and the puzzle exists in this ambiguity.
The demon labelled "Liar" because he's actually honest who's labelled as liar. So he must be the one who said it and he's right, in one case.
In another case, it becomes a vicious circle. If the honest one said and we believed , so he's trying to say in real he's actually a liar . It means he can't be believed and they're labelled correctly.