Sorry, not sure how clear this picture will come out. Essentially, I started with the facts given to me and tried to reason with the first few lockers about if they would be open or closed. That led me to thinking about how primes would be open. Then I started thinking about primes being primes because of their factors and realized that even factor having numbers would be open. So I tried to think of what would have an odd number of factors and realized it would actually only be the perfect squares.
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