You have probably seen puzzles involving lights in a room before, but here’s one I heard recently that was new to me.
There’s a room with 64 labeled light bulbs, each of the which can be either on or off, and each of which has its own switch. You walk into the room and find the light bulbs in some arbitrary pattern of on and off. You get to flip one light bulb of your choosing (and you are forced to flip exactly one switch).
Next, you leave the room and I enter. By looking at the pattern now on the lights, I might be able to get some information – you might be able to send me a message.
How much information can we communicate this way? If we convene before hand to create a strategy and write a list of messages we want to be able to send, how long should the list be?