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?


Alternate:
As noted in this page's   discussion page,   the only doors that remain open are those whose numbers are perfect squares.

Opening only those doors is an   optimization   that may also be expressed;
however, as should be obvious, this defeats the intent of comparing implementations across programming languages.




' version 27-10-2016
' compile with: fbc -s console
 
#Define max_doors 100
 
Dim As ULong c, n, n1, door(1 To max_doors)
 
' toggle, at start all doors are closed (0)
' 0 = door closed, 1 = door open
For n = 1 To max_doors
    For n1 = n To max_doors Step n
        door(n1) = 1 - door(n1)
    Next
Next
 
' count the doors that are open (1)
Print "doors that are open nr: ";
For n = 1 To max_doors
    If door(n) = 1 Then
        Print n; " ";
        c = c + 1
    End If
Next
 
Print : Print
Print "There are " + Str(c) + " doors open"
 
' empty keyboard buffer
While InKey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End