(You might wonder, if you're from Earth, why Erler pronounced the question so carefully. It's impossible for a mental patient to actually get the answer right, after all. And - an Earthling might imagine - if Erler did claim a patient had gotten it right, wouldn't everyone promptly believe that he was lying or crazy?
This is why Erler does not know the correct answer himself, and is entering Thellim's answer into a numpad.
Erler is also tested with fake patients on a regular basis, to make sure he asks the question correctly. And those fake patients sometimes give correct answers to the math question, to make sure the system is functioning correctly and would detect any correct answers given.
It's not that dath ilan thinks that any of their prospective mental patients are actually likely to be talking to powerful entities, when they hear voices inside their heads.
It's that Civilization has made representations to prospective mental patients that this test is fair. So of course it's going to be fair. It has not actually occurred to Helorm that this test might be faked. If that thought did occur to her, she would correctly estimate that if the test was found to be faked, it would be a civilization-shaking scandal, and anyone who had anything to do with it any way would be fired, and the entire dath ilani Legislature and Keeper leadership would resign for bearing ultimate responsibility.
The government is not supposed to defect in the Prisoner's Dilemma. Not even the Epistemic Prisoner's Dilemma. It doesn't matter how sure you are that you're right and the other person is wrong. When Civilization promises cooperation to somebody in exchange for their own cooperation, Civilization cooperates with them, full stop.)