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Problems like this aren't unsolved, it's just that these problems have different answers depending on the context.
Is it the same trolley that kills the man? Yes because repairing the trolley doesn't change it's name.
Is it the same trolley that kills the man? No because it is physically not the same trolley.
Humans divide their cells until the original cells are gone. Are they a different person?
Yes they are.
No they aren't.
Depends on what you're measuring or what problem you're trying to solve. But both perspectives are simultaneously true. Wait until you get to math and find out there's different lengths of infinity. It's all tools used to solve problems.
depending on the context
This is exactly why these trolley problems don't work. When we strip away all context and ask simplified questions the nuance disappears and the question becomes almost meaningless.
That's why I think these are mostly nonsense. These types of questions aren't philosophical, they're psychological. They don't teach anything, they just test what you value, and they're not the best types of questions for doing that either.
The only way to win is not to play
You can also win sometimes by playing, depending on the context.