"If you take care of the math, the math takes care of you!"

Lockers, Equators, and Charlie, oh my!

Imagine a hallway with 10,000 lockers numbered with integers 1-10,000, inclusive. We will send 10,000 people down the hallway. The first person walks through and ensures that all the lockers are closed. Person #2 walks through and opens all of the even-numbered lockers. Person #3 reverses the state of every locker that is numbered with a multiple of 3 (i.e., person #3 starts at locker #3, then proceeds to lockers 6, 9, 12, 15, etc. He opens every locker that is closed and closes every locker that is open.) Person #4 reverses the state of every locker of every locker that is numbered with a multiple of 4. This pattern continues until the 10,000th person has traveled through the hallway. At this point: A) Which lockers are closed? B) How many lockers are open? Email me your response and I’ll let you know if you’re right. (Source: Dr. Jimmy Woods, NGCSU)

If you walk around the earth at the equator (for all of you realists, just pretend), would your head travel further than your feet? If you believe the answer is “yes”, if you were to walk from the ACS high school building to the football field, would your head travel further than your feet? What if you took one baby step? (This is also a gift from Dr. Woods.)