IMO 2024 Shortlist C1
Let n be a positive integer. A class of n students run n races, in each of which they are ranked with no draws. A studen...
Category: Combinatorics
Problem
Let n be a positive integer. A class of n students run n races, in each of which they are ranked with no draws. A student is eligible for a rating pa,bq for positive integers a and b if they come in the top b places in at least a of the races. Their final score is the maximum possible value of a ´ b across all ratings for which they are eligible. Find the maximum possible sum of all the scores of the n students. (Australia)