Worst approximation to 100 by summing subsequences
Source: XIV Rioplatense Mathematical Olympiad (2005), Level 3
July 26, 2011
algebra unsolvedalgebra
Problem Statement
Consider all finite sequences of positive real numbers each of whose terms is at most and the sum of whose terms is more than . For each such sequence, let denote the sum of the subsequence whose sum is the closest to , and define the defect of this sequence to be the value . Find the maximum possible value of the defect.