# Mathematical Potpourri on Airplane Boarding

## Anne Henke, Jesus College, University of Oxford

When passengers board an airplane, they queue in arbitrary order. For simplicity, we assume that passengers are arbitrarily fast to get to their seat row, they are arbitrarily broad and arbitrarily thin. Each passenger will need precisely one minute to store his luagge away and take his seat. During this time, he blocks the way for passengers in rows further back in the plane.

What is a good scenario to minimise the expected boarding times? Should, for example, passengers in back rows board first? Or should passengers on a window seat board first? The solution to these questions is deep and it connects different areas of mathematics: probability, algebra, differential equations.

My talk will be entirely elementary and no particular mathematical background is needed. We will encounter elementary combinatorics, a proof using the pigeonhole principle, and we will learn what the above question has to do with mathematicians going to the cinema.