\documentclass[11pt]{scrartcl}
\usepackage{evan}
\begin{document}
\title{IMO 2021/5}
\subtitle{Evan Chen}
\author{Twitch Solves ISL}
\date{Episode 79}
\maketitle
\section*{Problem}
Two squirrels, Bushy and Jumpy, have collected 2021 walnuts for the winter.
Jumpy numbers the walnuts from 1 through 2021, and digs 2021 little holes
in a circular pattern in the ground around their favourite tree.
The next morning Jumpy notices that Bushy had placed one walnut into each hole,
but had paid no attention to the numbering.
Unhappy, Jumpy decides to reorder the walnuts by performing a sequence of 2021 moves.
In the $k$th move, Jumpy swaps the positions
of the two walnuts adjacent to walnut $k$.
Prove that there exists a value of $k$ such that, on the $k$th move,
Jumpy swaps some walnuts $a$ and $b$ such that $a