There are a hundred doors all closed. Starting from the first door, I open every other door. Then from the beginning again, I open/close every 3rd door, depending on it's current state. In this case, I would open the 3rd door, but close the 6th door which was open from the first pass. Repeat this for every 4th, 5th, 6th etc until I only toggle the 100th door.
Given any door number, can you tell me if it will be open or closed at the end?
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