As it happens, Art of Problem Solving questions actually fit the bill of being really difficult. Most chapters have about 15 or so "challenge" problems, of which 5 or so are really hard.

The scoring system I used was to (a) give myself double points for answering the really hard challenge problems, and (b) only require a total score of 10 for all the challenge problems combined. So if I got all the regular problems correct + 10 points on the challenge problems (1 point per "standard" challenge problem and 2 points per "hard" challenge problem) then I'd score 100. One side effect of this was that on chapters with a particularly large number of challenge problems it was possible to get something like a 140. But in any case, getting a 100 actually wasn't that easy.