Understanding Numbers and Operations
Text Box 4.1 A Math Happening 4: The Locker Problem
There are 100 lockers in one hallway of the Excel School. In preparation for the beginning of school, the janitor closed all of the lockers and put a new coat of paint on the doors, which are numbered from 1 to 100.
When the 100 students returned from summer vacation, they decided to celebrate by working off some energy. The came up with a plan: The first student ran down the row of lockers and opened every door. The second student started with locker #2 and closed every second door. The third student started with locker #3, and changed the state of every third locker door. The fourth student started with locker #4 and change the state of every fourth locker door, the fifth student started with locker #5 and changed the state of every fifth locker door, and so one, until 20 students had passed by the lockers.
Which lockers are still open after the 100th student is finished? Which locker or lockers changed the most?