At Singapore Polytechnic, there
were 1,000 students and 1,000 lockers
(numbered 1-1000).
At the beginning of our story,
all the lockers were closed.
The
first student come by and opens every locker.
Following
the first students, the second student goes along and closes every second
locker.
The
third student changes the state, ( if the locker is open, he closes it;
if the locker is closed, he opens it) of every third locker.
The
fourth student changes the state of every fourth locker, and so forth.
Finally, the thousandth student changes the state of the thousandth
locker.
When
the last student changes the state of the last locker,
Which
lockers
are open?
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