Lockers Solution

If you do it out for 10, you will find that 1, 4, and 9 are locked. These numbers are perfect squares. Only perfect squares have an odd number of factors so they will end up locked. You can think of it this way, normally all the numbers would at least have 1 and themselves as factors. For the other factors, they all come in pairs. For example, 12 has the factors: 1,2,3,4,6,12. 2 and 6 are a pair, 3 and 4 are a pair. But for 9, the factors are 1,3,9. 3 is a pair with itself and so the total number of factors is odd.
So the locked lockers are all the perfect squares from 1-100. 1,4,9,16,25,36,49,64,81,100.

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