Martin Hock, a computer science grad student in UW Madison who was working for me as a grader in Spring 2004 did some work on a problem we called the generous grader problem, and we're wondering if it has been described in the literature before. The problem arose from an unforeseen collision between my announced grading policy ("I will drop your two lowest homework scores") and the fact that not all of the problem sets had the same weight (each problem was worth 10 points, so that problem sets with more problems were weighted more heavily). It turns out that dropping the two lowest scores is not always the best thing a grader can do for the purpose of boosting a student's score; e.g., it might be better to drop the third and fourth lowest scores if those two problem sets carried a lot of weight. This made us wonder about the general problem lurking here: How do you find the subset N of {1,2,...,n} of fixed cardinality m that maximizes sum_{i in N} s_i ---------------- sum_{i in N} h_i (where s_i is a student's actual score on the ith assignment and h_i is the maximum possible score for that assignment)? Hock devised an algorithm that always finds the optimal choice of N, and the algorithm appears to be quite fast in practice (although Martin hasn't proved a polynomial bound on the running time yet). Jim Propp