- 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.