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You wake up in the center of a large, homogeneous, nearly-circular room. Along the edge of the room, are many doors, each looks identical to the last. When you stand at one door and look across the room at the doors on the far side, they appear so closely spaced that you cannot resolve them; the room is just that large.

Behind each door is a lever. Some of the levers are down, and some of the levers are up.

The room appears simple, you know everything that it contains, many identical doors and levers; however there is one thing that you do not know: how many doors there are. Deep inside, you know that the only way to get out is to find this missing piece of information, because when you fully know the room, it no longer has any purpose.

You set about trying to count the doors in the room. You leave one door open as a starting place and begin counting. But as soon as you reach the second door, the first one closes, and you lose your starting position. Next you try taking your shoe off and jamming it in a door to mark your place, but as you move to the next door a robot comes out from the floor boards and removes the shoe and the door closes; the robot disappears again into a hatch before you can catch it and get your shoe back. You ditch the other shoe for symmetry. Finally you try scratching your name into a door, and start counting from there. But as you reach the second door, you hear a loud whirring sound behind you. One robot is unscrewing the door you scratched and another robot replaces the door with a new one. I guess if they can make a room with such a large number of doors, they probably have plenty of spares as well.

Finally you open a door and set the lever down. Then you move over two doors and return, and the lever is still down. You change it a few more times and repeat just to confirm that the state has been saved; and it has. Your only way of marking your spot is with the levers, but remember some of them were down and some were up before you started.

How can you count all of the doors in the room?

Sorry if this is a duplicate.

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  • $\begingroup$ Can you move down or up all the levers? $\endgroup$
    – Chill Fruit
    Commented Mar 21, 2016 at 1:47
  • $\begingroup$ @ChillFruit you sure can!! But how will you know when you have set all of them? $\endgroup$
    – Tony Ruth
    Commented Mar 21, 2016 at 1:50
  • $\begingroup$ I'm not sure I quite get this, only if a lever is set will it not go back to their normal postition? Or does the lever trigger the robots thingies for each door? $\endgroup$
    – Chill Fruit
    Commented Mar 21, 2016 at 1:51
  • $\begingroup$ The robots are only there to prevent you from cheating. You can set a lever and they will not mess with it. But if you try to do something else to alter the room they will revert it. $\endgroup$
    – Tony Ruth
    Commented Mar 21, 2016 at 1:54
  • $\begingroup$ (The objective is different, but it's essentially the same puzzle.) $\endgroup$
    – Deusovi ♦
    Commented Mar 21, 2016 at 2:12

1 Answer 1

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Okay, so according to a first instinct of mine, here's what you do:

First, go around the room, making sure to set every lever that's up down and not touching those that are already down. After you're sure you have every lever down, it's just a question of time until you go around setting them up, counting them as you go.

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    $\begingroup$ How can you ever be sure you have set every lever down? If you find an up lever and set it down and then the next 10 levers are down, have you reached the beginning again? What if the next 100 levers are down? 1000 levers? If the room were large enough, then it would be almost guaranteed to have a stretch of 1000 levers down in a row. $\endgroup$
    – Tony Ruth
    Commented Mar 21, 2016 at 2:11
  • $\begingroup$ You haven't said anything about a time limit; theoretically, one can just continue walking around and around and around until they're perfectly satisfied that they set every lever. $\endgroup$
    – Chill Fruit
    Commented Mar 21, 2016 at 2:20
  • $\begingroup$ But when will you stop and decide that you have visited all the rooms? $\endgroup$
    – Trenin
    Commented Mar 21, 2016 at 16:30
  • $\begingroup$ Since we're not working with a time frame, any given time you want. If at any time you find a lever up closer than what should logically be possible, given at least some sense of time and space, start walking backwards and set every lever down, until you're satisfied again. If you do count wrongly, the knowledge of the number of doors shouldn't help you, which tells you counted wrong and just need to restart your work. $\endgroup$
    – Chill Fruit
    Commented Mar 21, 2016 at 17:05

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