Puzzle 23: Celebrity Problem
Celebrity Britney Hilton is being chased by the notorious paparazzi Gracias Prego. She has shrunk herself to a point x in the unit square [0, 1]2. Not to be out-done, Gracias has shrunk himself to a point y≠x in the same square. He has the latest laser camera and would love to get a picture of Britney in her reduced state. He points his camera and it emits a zero thickness light ray. If it hits a wall it will be reflected. He wants to shoot the ray so that it reaches Britney. She however, can place guards that are points Z1,Z2, . . . , in the square and if the beam tries to go through one of the guards it is blocked. How many guards does Britney need so that no beam from Gracias can reach her? Will a finite number do?