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Problem Solving Classroom

Tips from a Master Teacher (This is a work in progress.)

Hallway Door

Hallway Door

You are in a slightly curving white hallway, and as far as you can see, the outside wall is lined with doors. You know that the hallway forms a very large circular ring, but you are not sure just how large it is. All you know is that some doors are open, and some doors are closed. You have no devices with which to measure the radius of curvature of the hallway. If you’ve got lots of time on your hands, how do you go about finding the number of doorways in the ring?

Oh, I should mention that you are not allowed to mark, scratch, or in anyway mar the appearance of the doors or hallway. Nor do you have anything in your possession you can leave behind… and keep your clothes on!

Difficulty: 5/5

Keywords: door

Solution
The Solution

Let’s say the door you are standing in front of is #1. Note whether this door is open or closed. Count the number of doors in your visual range. Let’s say it is 20. Walk to the 21st door and change its status. If it’s open, close it. If it’s closed, open it. Then count back to door #1. Is it as you left it? If not, there are 21 doors. Keep following this procedure. Count out to the nth door and change its status. Then count back to door #1. If the status of the door has been changed, you must have done it, so you know there are n doors.

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