Problem Statement

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.

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.

Let's start with the solution:

$constant DOOR_OPEN = 1
$constant DOOR_CLOSED = 0
$constant MAX_DOORS = 100

var i, j = integer
dim integer doors(MAX_DOORS)

rem - all doors are initially closed
for i = 1 to MAX_DOORS
  doors(i) = DOOR_CLOSED
next i

rem - cycle through at increasing intervals and flip doors
for i = 1 to MAX_DOORS
  for j = i to MAX_DOORS step i
    doors(j) = 1 - doors(j)
  next j
next i

rem - report results
print "The open doors are:"
for i = 1 to MAX_DOORS
  if doors(i) = DOOR_OPEN then
     print i;
next i

end