FRIDAY'S KILLER QUESTION: There are one hundred closed doors in a corridor

Every Friday we'll be posting challenging and cryptic questions for you to answer, provided for us by 7city Learning. Post your answers in the comments box at the bottom of the page. Total deification will be accorded to the person who provides the correct answer first. We'll add the official answer to the bottom of this article on Monday afternoon.

There are one hundred closed doors in a corridor. The first person who walks along the corridor opens all of the doors. The second person changes the current state of every second door starting from the second door by opening closed doors and closing open doors. The third person who comes along changes the current state of every third door starting from the third door.

This continues until the 100th person.

At the end, how many doors are closed and how many open?

ANSWER:

This is a question about how many divisors a number has. For example the 15th door is divisible by one, three, five and fifteen. So it will be opened, closed, opened, closed. Ending up closed. What about door 37?

Thirty seven is only divisible by one and 37. But again it will end up closed. Since only squares have an odd number of divisors we have to count how many squares there are from one to 100. Of course, there are only ten.