Principal Harris has decided to install lockers for each of the 550 students at High Tech High. The lockers are to be numbered 1 – 550. When High Tech High students return from summer vacation next ye

Principal Harris has decided to install lockers for each of the 550 students at High Tech High. The lockers are to be numbered 1 – 550. When High Tech High students return from summer vacation next year, they decide to celebrate the lockers by working off some energy. The first student goes to all the lockers and opens them. The second student goes to every second locker and shuts it. The third student goes to every third locker and changes the state of it (If it was open close it, if it was closed open it). This pattern continues all the way up to the 550th student. 

Answer the following questions:

1. Look at the first 10 lockers. After the first 10 students, which ones are still open? 

2. Now look at ALL of the lockers. After everybody has been marching around the school, which lockers are closed and which ones are open? 

3. If the students were not in order when they went marching, would the same lockers still be closed/open? 

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