There are 100 doors, all closed. In a nearby cage are 100 monkeys. The first monkey is let out and runs along with the doors opening every one.

  • The second monkey is then let out, and runs along the doors closing the 2nd, 4th, 6th - all the even-numbered doors.
  • The third monkey is let out. He attends only to the 3rd, 6th, 9th,… doors (every third door, in other words), closing any that is open and opening any that are closed, and so on.

After all 100 monkeys have done their work in this way, How many numbers of doors will be open?

The Answer is an integer. Just put the number without any decimal places.