The Mathsbombe Competition

2022 edition. From the people behind the Alan Turing Cryptography Competition.
Home Archive

Problem 5

Twenty seats are arranged in a row. A couple enters the room, picks a pair of adjacent seats randomly and sits in them. Then a second couple enters the room and picks a pair of adjacent unoccupied seats randomly and sits in them. This process keeps going until there are no more pairs of unoccupied seats which are next to each other.

What is the expected number of empty seats remaining? Write down your answer to two decimal places.

Mathsbombe Competition 2022 is organised by the The Department of Mathematics at The University of Manchester.
© The University of Manchester 2012–2022, All Rights Reserved
Contact us | Privacy notice