Problem

Source: 2017 Argentina OMA Finals L3 p5

Tags: algebra, number theory



We will say that a list of positive integers is admissible if all its numbers are less than or equal to 100 and their sum is greater than 1810. Find the smallest positive integer d such that each admissible list can be crossed out some numbers such that the sum of the numbers left uncrossed out is greater than or equal to 1810d and less than or equal to 1810+d .