- At the Metric Academy there
are 100 students, and 100 lockers numbered 1-100. One
day the lockers are all closed, and student #1 opens all of them. Then
student #2 shuts every other locker, starting with #2, then #4,
etc. Student #3 changes the state of every third one, starting
with #3: opens it if it's shut,
shuts it if it's open.
Student #4 changes the state of every 4th locker, etc. This continues
until the hundredth student changes the state of locker #100.
Exactly which lockers are now
open, and which are closed, after all the students have open
and shut them as described? Show
your steps and reasons.