The Locker Problem!!

Mr. Dunaway's Problem for this Week

The Problem:

There are 100 lockers in the long front hall of our school. Each August, the custodians add a fresh coat of paint to the lockers and replace any of the broken number plates. The lockers are numbered from 1 to 100.

When the students arrive on the first day, they decide to celebrate the start of the school year with our school tradition. The first student inside runs down the hall opening all of the lockers. The second student runs down the hall closing every second locker, beginning with locker number 2. The third student changes the state of every third locker, beginning with locker number 3. (If the locker is open, she closes it. If it’s closed, she opens it.) The fourth student changes the position of every fourth locker, beginning with number 4. This continues until the 100th student has a turn, changing the position of the 100th locker.

Your task is to work with your partner - come up with a strategy to find out:

At the end of the day, which lockers are open?

How did you come up with that conclusion?