Problem

Source: Belarusian olympiad 2022

Tags: combinatorics



$n$ distinct integers are given, all of which are bigger than $-a$, where $a$ is a positive integer. It turned out that the amount of odd numbers among them is equal to the biggest even number, and the amount of even numbers is equal to the biggest odd numbers a) Find the least possible value of $n$ for all $a$ b) For each $a \geq 2$ find the maximum possible value of $n$