Enumeration was the first method that came to my mind. At first, it was difficult to see a clear relationship, but as I listed out the changes in the lockers’ states, I gradually started to notice a pattern. I noticed that after a certain student changes a locker’s status, its state remains fixed because no more students change that locker. As the number got larger, we can see there is a pattern that only square-numbered lockers change status. After finding this pattern, I started to think about why it happens. It took me a while to connect the pattern to the factors of each locker number.
2026年9月14日星期一
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