Question

If there were 200 lockers and there are 200 students. The first student goes down the row and opens every locker. The second student goes down the row and changes the state of every second locker, starting with locker number 2. The third student then changes the state of every third lockers, starting with locker number 3. If the locker is open the student closes it, if it is closed the student opens it. The fourth student changes the state of every fourth locker, starting with locker number 4. Supposed this process continues for each of the 200 students.

Question: Is the 121st locker opened or closed? Why?

Answer 1

Hi
The 121st locker is opened

Explanation:

div(121)={1,11,121} ( the divisors)

The student 1 opens the 121st locker.

The student 11 closes the 121st locker.

The student 121 opens the 121st locker.