The Locker Problem

The Locker Problem

You get to check out the new digs at HTHMars. The new school has these brand new state of the art expandable lockers. The HTH Village has been asked to test these lockers by opening and closing them. HTHMars has 1000 lockers, all shut.

• Suppose the first student goes along the row and opens every locker.
• The second student then goes along and shuts every other 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 the student shuts it, and if the locker is closed the student opens it.)
• The fourth student changes the state of every fourth locker beginning with number 4.

Imagine that this continues until 1000 students have followed the pattern with the 1000 lockers. At the end, which lockers will be open and which will be closed? Which lockers have been switched the most often? How many lockers, and which ones, were touched exactly five times?

My students were posed with this problem. After two weeks of solving, writing, and revising, they posted their final solutions on their blogs. Read their blogs and learn about perfect squares, factors, and patterns!