I have come across the locker problem in the past, kind of in a funny situation - it was when all my colleagues and I from the education institute I worked at were enjoying the Christmas party in 2023! When my colleague first showed me this problem, my initial thoughts were to think about the factors of every locker number. We started writing out the first 20 numbers and their factors to conclude whether they would be same or different from their initial state. We quickly noticed that all the numbers that were perfect squares (1, 4, 9, 16...) ended up being the opposite state. This is because they have odd number of factors because you would need to pair the factors in two to return to the original state.
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It would be great if you added some presentation of the steps you followed, even though you've solved it in the past. This would help show the process you went through, especially for readers who may not be familiar with the problem. Including a more detailed breakdown of your approach would enhance your explanation. Keep up the good work!
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