100 doors

Problem: You have 100 doors in a row that are all initially closed. You make 100 passes by the doors, starting with the first door every time. The first time through, you visit every door and toggle the door (if the door is closed, you open it; if it is open, you close it). The second time you only visit every 2nd door (door #2, #4, #6, …). The third time, every 3rd door (door #3, #6, #9, …), etc, until you only visit the 100th door.

Question: What state are the doors in after the last pass? Which are open, which are closed? [1]

Ada

with Ada.Text_Io; use Ada.Text_Io;

procedure Doors is
   type Door_State is (Closed, Open);
   type Door_List is array(Positive range 1..100) of Door_State;
   The_Doors : Door_List := (others => Closed);
begin
   for I in 1..100 loop
      for J in The_Doors'range loop
         if J mod I = 0 then
            if The_Doors(J) = Closed then
               The_Doors(J) := Open;
            else
               The_Doors(J) := Closed;
            end if;
         end if;
      end loop;
   end loop;
   for I in The_Doors'range loop
      Put_Line(Integer'Image(I) & " is " & Door_State'Image(The_Doors(I)));
   end loop;
end Doors;

Perl

my @doors;
for my $pass (1..100) {
    for (1..100) {
        if (0 == $_ % $pass) {
            if (1 == $doors[$_]) {
                $doors[$_] = 0;
            } else {
                $doors[$_] = 1;
            };
        };
    };
};

print "$_\t$doors[$_]\n" for 1..100;