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My other favorite one is to require an answer with more significant digits
than their calculator can provide. e.g. find the square root of 1/(0.98) to
13 (or 14 or 15) places. It's simple to do by expanding it, but students
hate expansions more than they hate to think.
But, I can't think of any real use of such a calculation other than to show
students that their calculators cannot do everything for them.