It takes ten men ten hours to build a certain wall. How long does it take five men to build the same wall?

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 its
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?

There are 3 standard on/off switches outside a room. One (and only one) controls a light bulb inside the room . The other two switches do nothing. You can only enter the room once, and cannot touch/change any switches after the door is open (or re-closed, for that matter). Damaging or disassembling the door, walls, or switches is against the rules.You can not see anything inside the room from outside in any way.Within these constraints, can you determine with certainty which switch controls the light bulb?