Did anyone else have to take these tests as a kid? There was no real reward for doing well, but if you fail, you get labeled as "not-up-to-standard". I can't remember any of their problems, but thought of something else today: An election has five candidates finish with double-digit percentages, though, all less than 30%. After about 20 hours, the committee assigned to count votes decides at first to announce only 62% of all results. Define an "exclusion scenario" as a set C_1, C_2, ..., C_n of candidates who are announced to have zero percent support on a fair tally of the 62% subset. How many different exclusion scenarios are possible when allowing for any 62% subset? Is it possible to completely exclude the overall winner? I think this can be solved using standard combinatorics, but I am wondering if anyone would understand the implications. --Brad