1. He would have opened the door.
2. He would have solved the math problem.
3. He would have met the person.
4. He might have opened the door.
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From #1 to #3, actually he didn't do that. Right? Does #1 mean #4 sometimes? Is #1 different from #4?
Yes, 1 and 4 mean about the same thing.
And all these sentences are about possibilities, not facts.