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bloody briliant, a much better exam hack than pointless puns.
Funny but sound like a urban legend.
If it is true I'm sure that the student would have gotten at least a passing grade if was willing to risk using Feynman.
Or would have no chance of passing without him.

Since it's an open-book exam, it's likely going to take a lot of thoughtful work.

Not necessarily. Tests were on the honor system at Caltech (and I suppose still are). You typically took them in your dorm room.
This is the sort of hack that Feynman himself would have pulled, back when he was an undergraduate.
Even if they had explicitly written Feynman's Lectures on Physics on the exam, the students could have asked Feynman to give a special lecture which happens to cover all of the exam material.
Half an hour, why it took him so long?
Obviously, he made sure to use good penmanship.
He can't have been the only person in the class who had the thought. I would have; I just wouldn't have dared.

True or not, funny story.