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