King Tut has a castle with one hundred rooms that all have doors labeled 1 to 100 that are shut. His
crazy son Calvin runs around the castle and opens all the doors. Then he runs around the castle and
closes every other door (2, 4, 6, 8, ... 100). Then he runs around the castle and when he comes to
every third door (3,6,9,12,...99) if it is open he closes it and if it is closed he opens it. He then does
the same for every 4th door, then every 5th door and then every 6th door, and so on until then does
it for every 100th door. At the end of this exhausting run clearly door 1 is open, but what other door
are also open? (hint: Grappling would suggest you try using a smaller number like 20 doors and see
if there is a pattern)