1. No one is to solve the problem.

2. No one can solve the problem.
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Does #1 mean #2?

3. I was never to see him again.
4. I was doomed never to see him again.
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Does #3 mean #4?

5. If you are to succeed, you must study hard.

6. If you intend to succeed, you must study hard.
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Are both the same? (Thank you for your help.)

1and2 are not the same. 1 is a command; 2 is a statement of fact.

3 and 4 mean about the same thing.

5 and 6 mean about the same thing, too.