The number of keys on your key ring has been growing steadily over time, and now you already have 15 keys to keep track of! Unfortunately, you are unable to distinguish one key from another (apart from testing on doors), as they all look something like this:
There is no engraving or mark of any kind on any of the keys to tell you which door it opens. So every time you've opened a door, it involved tediously checking each key until you use the right key. Surely there must be a better way!
So, how can you place the keys on the key ring so that every time you want to open a door, the first key you try is guaranteed to work?
- You are not allowed to mark the keys or key ring in any way.
- The keys must always remain on the key ring after the initial arrangement.
- You may not add anything to the key ring except the 15 identical-looking keys you need to keep track of.
- You should always be able to identify the right key only by examining the arrangement of the keys on the key ring.
- Your solution should be easily modifiable if the number of keys increases.
- Between opening doors, the keys sit in your pocket. No holding on to one key as a reference.