I like that test where some of the questions are wrong and wonder whether we should have that kind of thing in maths textbooks.
I think people need to be trained to be more confident in what they know, and if we gave them that kind of thing we could maybe train them to become so.
"incomplete information" is a standard concept in word problem curriculum. But usually it's explicitly an option in the test, as a fairness to the student.
Making mistakes in lecture is a standard technique used by good teachers, to promote active listening and critical thinking.
Actually - do they do this in LLM benchmarks? As a measure of overconfidence/confabulation? Seems immediately applicable.