# Which teacher is telling the truth?

It is generally known that lecturers for some course either always tell the truth or always lie. Arthur and Ignaz are those lecturers. Arthur says: "Exactly one of us is lying". Ignaz says: "Arthur is telling the truth".

Which is the case? Who is telling the truth and who is lying?

If

Arthur is telling the truth, then (from what Arthur says) Ignaz is lying but (from what Ignaz says) Ignaz is telling the truth. That's no good.

So

Arthur is lying. Then (from what Arthur says, which we now know to be false) both must be lying -- and indeed what Ignaz says is false.

Thus:

Arthur and Ignaz are both lying.