Task: In SST, there is a row of 100 closed lockers numbered 1 to 100. A student goes through the row and opens every locker. A second student goes through the row and for every second locker if it is closed, she opens it and if it is opened, she closes it. A third student does the same thing for every third, a fourth for every fourth locker and so on, all the way to the 100th locker. The goal of the problem is to determine which lockers will be open at the end of the process.
In words, explain your thinking to the following problems clearly. Be sure to use appropriate mathematical language and methods:
• Which lockers remain open after the 100th student has passed?
• If there were 500 students and lockers, which lockers remain opened after the 500tth student has passed?
Identify another problem that uses the same method or technique to solve and post it to this blog