Exercise: 100 doors

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• 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.

Task

• Answer the question: what state are the doors in after the last pass? Which are open, which are closed?

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