My 7th grader, who has just started working with first degree equations, was
given the following 'challenge' problem.

The local High School has 1000 lockers.  The students decide to perform the
following experiment:
The first student will open all the locker doors.
The 2nd student will close every door of a locker starting with the 2nd locker
and is a multiple of 2.
The 3rd student will 'change the position' of each locker door, starting with
the 3rd locker and is a
   multiple of 3.
The 4th ....
The 5th ....
 etc.  etc.
After all 1000 students perform their task which locker doors will remain open.

The above can be solved very easily by writing a program but that was not one of
the available options.

Short of manually simulating the above on a quadrille paper and seeing the
developing pattern, which was the method selected, can anyone think of another
method that a 7th grader could have used?

BTW.  The answer is:  Every I**2th locker will remain open where "I" assumes the
values of the natural numbers from 1 to INT(SQRT(numoflockers)).

Regards
Paul Christidis