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1) I get upset when professors construct their classes such that overfitters are rewarded to the extent that the opportunity cost associated with actually learning the material might cause one to fall behind. It happens in 70% of introductory courses and 35% of advanced courses. Also, 90% of multiple choice formats are guilty of this.
2) Random samples of the material inherently reward "over-fitters" because they do a shallow memorization of everything so that they can pass, rather than the true learner who does an in-depth treatment of the course topics that interest them in particular. I'm not sure how to solve this problem.
Regarding "2" the professor can have several very difficult questions and only require a subset of them to be answered. This is often done for essay exams.
I've seen it done in math, too.
There was a six question exam, and no one in the class finished more than two problems, and most were only part-way through the second (not the same two problems).
Isn't the median for the Putnam 0?
Well, yes, but that's not a regular exam, is it?