More tests is better?
Leopold takes his final exam for a class (100% of the grade) and only gets 50/100, so he fails the class.
But, later, after thinking about it, he argues that if the questions had been arranged differently and spread out over several tests (and he got the same ones right) he could have passed. For example, if it were three tests, each weighted the same, he could have gotten 25/25 (100%), 25/25 (100%), and 0/50 (0%), and the average would have been ~67%.
By this argument, what is the lowest score he could have gotten initially, but it would allow him to get a 90% average when the problems are redistributed?
Details and Assumptions:
The initial test can be split into any number of "sub-tests" each having a positive integral number of points.
And, each test has the same weight.