You find yourself in a rectangular room with Osama Bin Laden. Osama has a laser pistol to fire you. The 4 walls of the room are perfectly reflecting mirrors. Osama is about to shoot you either directly or through the mirror. The only way you can save yourself is by placing 16 bodyguards with shields in the room so that any shot from Osama to you (either directly or through a path reflected from the mirrors) is blocked by the bodyguard. You, Osama, and the bodyguards with shields are all points in a 2-D rectangular room with mirrors.
Show how you should place the 16 bodyguards.
via Peter Winkler's lecture video on youtube