1,000 Lockers Explanation

There are there are are 31 lockers open. These are the numbers of lockers open. 1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400,441,484,529,576,625,676,729,741,900,and 961. This is the answer because, first I drew 1-30, as numbers. Then I went through 30 to see which ones would be closed and which ones would be opened. They changed a lot, especially 30. After I did the closing and opening, I found which one was opened. This is because the question is which locker doors are opened. I saw that all the numbers that were opened were square numbers. Square number a the product of a number multiplied by itself.  Like, 6 times 6 = 36. So, I found all the square numbers to 1000 because all the ones that were opened for 30 was square. So, the answers is the square numbers.

I observed that on the the first opened their is 2 in between until the next opened number, second is 4in between, the 6, then 8, so in those up to thirty it’s 2 in between. Another way to do this is finding the pattern of each number. So, like the 2 person, the pattern is open,close,open, and close etc. then do the pattern with 3, 4,5,6, and so on. That would though take longer. So, the first way is better.

They will remain open because you're moving on, and every person will go to their locker first, and not got to the number below them. So, what ever number is in front of that number, it will stay like that, because they are moving on, not staying on the number.