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 $1810-d$ and less than or equal to $1810+d$ .