How to guard an hotel in St tropez

Last week end it was the Voiles of Saint Tropez.
We stayed in an amazing hotel at Sainte Maxime, in front of St Tropez, where we could see the golf of St tropez and all the ships.



This hotel is like "plugged" on a small hill, and you consequently have to cross a lot of lifts and corridors to join your bedroom.
It reminded me a chapter of Proofs from the BOOK, by Martin Aigner and Gunter M. Ziegler.

This chapter is called "how to guard a museum". Adapted to the Sainte Maxime's hotel, it gives:

The manager of the hotel wants to make sure that at all times every point of the hotel is watched by a guard. The guards are stationed at fixed posts, but they are able to turn around. How many guards are needed?

It is for instance easy to guess that if the walls of the hotel form a convex polygon, then one guard is enough.

There is a useful theorem for managers of such hotels:

For any hotel with n walls, n/3 guards suffice.

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