Let $A$ be a set $A=\{1,2,3,...,2017\}$. Subset $S$ of set $A$ is good if for all $x\in A$ sum of remaining elements of set $S$ has same last digit as $x$. Prove that good subset with $405$ elements is not possible.
Problem
Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2017
Tags: combinatorics, Sets, Subsets