The main hall of an abstract art gallery is rectangular, the long walls run east-west and are ten metres long, while the shorter walls run north-south and are five metres long.

The owner of the gallery (who is also a mathematician) decides that, thanks to the position of the doors and the airflow through the room, the following social distancing regulations should apply. Between any two people it must hold that the distance in the north-south direction plus twice the distance in the East-West direction must be greater than or equal to two metres.

Since she is into both maths and abstract art, the gallery owner assumes that the width of a person is zero and that people are capable of standing exactly on the edges of the room.

What is the capacity of the room under these social distancing regulations?

Mathsbombe Competition 2022 is organised by the The Department of Mathematics at The University of Manchester.
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