Numbers are left open is because, they are the numbers that have multiples of square roots or the amount of factors are odd. The pattern was that before every open locker there were two more closed lockers then the section before it. So for example there are ten lockers and locker one is open then tow and three are closed. Then locker 4 is open and five, six, seven, and eight are closed. This pattern goes on until the number of closed lockers add up to 961 and we are left with only 31 lockers open. Since we started off with 1,000 lockers both amounts of closed and open lockers should add up to 1,000.
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