4) Now we just need to prove that we aren't missing anything. If we were missing an odd length list, the center would have to be a factor of 2025. ❌ Could we be missing some even length list? Lol, I can't remember how I proved this. 😭
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5) So, 2025 has 15 factors. They are all odd. But careful! When k=1, we get a list of just 2025, which we don't want to include. So 14, or 1 less than the number of odd factors, is the final answer!
This is a cool one! It comes from the list centered at 1, with initially 2025 numbers in the list. So this gives you the list -1011, -1010, ..., 1010, 1011, 1012, 1013.
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