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.
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.