BdMO National Junior,Primary 2016/7

[samiul_samin]

The floor of a museum is shaped like a simple polygon where the sides of the polygon have no points of intrsection except the adjacent sides.The walls of the museum are along the sides of the polygon.Guards have to be employed to guard the valuable things in the museum.Every guard can cover up the infinity around him but if there is a wall,he cannot watch beyond the wall.If the number of sides of the polygon is $n$,then prove that it is possible to guard the museum completely with minimum $\lfloor x/3\rfloor$ .[ $\lfloor x\rfloor$ is the biggest integer which is not bigger then $x$]

[samiul_samin]

Hint

Use triangulation

[samiul_samin]

This a wll known problem.It is called The Art Gallery Problem.It is very much important for learning Graph Theory .Here you can see discussion and detailed soution of this problem.
Solution

Just search Art Gallery Problem