10 homes in a neighborhood are placed side by side in a straight line with the doors facing the street. There are 10 nigglets who want to prank the homes. All the doors of the homes start closed.

The first nigglet opens all the doors.
The second nigglet closes every other door.
The third nigglet does the opposite of every third door (if it was closed, open it. vis versa).
The fourth nigglet does the opposite of every 4th door.
and so on...

after the 10th nigglet, which doors remain closed?

extra credit: write a function to find any closed door.