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There are one thousand students at the George Washington
High School. Each student is assigned a locker, numbered 1 through
1000. On the first day of school each year, the students participate
in an unusual ritual: The students enter the school through one door,
parade past the all the lockers, and then exit through another door.
While in the school, the first student reverses the door position of each
locker -- if the door is open, he closes it, and if it is closed, he opens
it. The second student reverses the door position of every other
locker, starting with locker number 2. The third student
reverses every third locker, starting with locker number 3, etc.
After all 1000 students have completed this ritual, which lockers will be
left open? |
