This problem involves with needing precise math. Because once you got something wrong, then you got the entire thing wrong. And I learned you shouldn’t over think it, or else you would get confused, then think of the wrong answer, making it not have the correct answer afterwards. So in conclusion, precision is the answer to this problem.
At first, my partner and I thought of just doing 100 circles and crossing them off, or “opening” them. But then we realized that it would take forever. So like Mr. Munden had said, it was all the square numbers and was either up to 1,000 or a little less than a 1,000. So when I got back home, I started doing all the square numbers until I got 1,000. In total: I got 31 lockers were open. And I got this by the square numbers that are up/a little below 1,000. Here’s the square numbers:
1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,2256,289,361,400,441,484,529,576,625,
675,729,784,841,900, and 961. If you had counted them, you would have gotten 31 numbers. and that is the answer to the question! And at the bottom, as I had explained, you only needed to find all the square numbers up to 30. so here’s the 100 chart and showing you how many square numbers or opened lockers should be there. 
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