# 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 itâ€™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?