Exercise: 100 doors
- There are 100 doors in a row that are all initially closed.
- You make 100 passes by the doors.
- The first time through, visit every door and toggle the door (if the door is closed, open it; if it is open, close it).
- The second time, only visit every 2nd door (door #2, #4, #6, ...), and toggle it.
- The third time, visit every 3rd door (door #3, #6, #9, ...), etc, until you only visit the 100th door.
- Answer the question: what state are the doors in after the last pass? Which are open, which are closed?