100 doors in a row are all initially closed. You make
100 passes by the doors. 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?

[Source http://rosettacode.org]