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Exam questions have two wonderful property: they have an answer, and the person who wrote it knows that you have the knowledge to find the answer.

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Nope, good teachers understand when the question they wrote thinking to test certain concepts falls flat, because of some unforeseen oversight or quirk. Something being clear and intuitive to a math professor is not the same as something being clear and intuitive to the students.

The best professors strike and ignore questions that "failed", ie didn't accurately test what they thought they would.

I don't quite see how that's relevant to what I said.

>the person who wrote it knows that you have the knowledge to find the answer.

This isn't always true. The person who wrote it only knows what they taught, not what you have learned. The point of the test is to find what you have learned.

This is just a nitpick I think.

Not a very interesting nitpick then. I guess I should have written "knows that you should have the knowledge to find the answer". If we could teach and be sure that students had learned, we wouldn't need to test them.

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