Lightbulb Messaging

You and 99 friends of yours (in total, you're 100 people) are in a house. In the house there is a room with a lightbulb, which can be switched on or off. There is also some sort of director, who each time, chooses one of you randomly and takes you to the room. Your goal, as a group, is to know when every person has been in the room.

It is provided that every person will visit the room infinite times (the director does not "starve" anybody), and you have infinite time. You can discuss a strategy before the game starts, but you cannot talk once the game starts. It is enough for one of you to notice that everybody has been in for the group to "win" the game.

Set a strategy if:

• (a) The light is known to be off in the beginning of the game
• (b) There is no knowledge of the light's status in the beginning of the game.

Solution