The $``$N Doors Puzzle$$ is a great challenge to explore various aspects of algorithmic thinking

and Python programming.

$$ Imagine you have N doors in a row that are all initially closed.

$$ You make N pass by each of these 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 $2$ nd door $($i$.$e$.,$ door #$2,$ #$4,$ #$6,...)$ and toggle it$.$

$$ The third time, visit every $3$ rd door $($i$.$e$.,$ door #$3,$ #$6,$ #$9,...),$ etc., until you only visit the

N th door on the N th pass.

Implement your algorithmic thinking using Python programming to determine the state of the

doors after the last pass. That is which doors are open and which are closed after the last pass?

Looking at the $$N doors puzzle$$ we can make the following observations:

$$ There are doors numbered $1$ through N that start closed. You can assume a list of