To solve this problem, we need to carefully track the student's movements and the lockers he opens. Let's break down the process step-by-step.

1. First Pass (Forward):
- The student starts at locker 1 and opens it.
- He then skips one locker and opens the next one, continuing this pattern until he reaches the end of the hall.
- This means he opens all odd-numbered lockers: 1, 3, 5, ..., 1023.
- Total lockers opened in this pass: $\frac{1024}{2} = 512$.

2. Second Pass (Backward):
- The student turns around and starts back from locker 1024.
- He opens the first closed locker he encounters, which is locker 1022 (since all odd-numbered lockers are open).
- He then skips one closed locker and opens the next one, continuing this pattern.
- This means he opens every fourth locker: 1022, 1018, 1014, ..., 4.
- Total lockers opened in this pass: $\frac{512}{2} = 256$.

3. Third Pass (Forward):
- The student turns around again and starts from locker 1.
- He opens the first closed locker he encounters, which is locker 2.
- He then skips one closed locker and opens the next one, continuing this pattern.
- This means he opens every eighth locker: 2, 10, 18, ..., 1018.
- Total lockers opened in this pass: $\frac{256}{2} = 128$.

4. Fourth Pass (Backward):
- The student turns around again and starts from locker 1024.
- He opens the first closed locker he encounters, which is locker 1022.
- He then skips one closed locker and opens the next one, continuing this pattern.
- This means he opens every sixteenth locker: 1022, 1006, 990, ..., 14.
- Total lockers opened in this pass: $\frac{128}{2} = 64$.

5. Fifth Pass (Forward):
- The student turns around again and starts from locker 1.
- He opens the first closed locker he encounters, which is locker 6.
- He then skips one closed locker and opens the next one, continuing this pattern.
- This means he opens every thirty-second locker: 6, 38, 70, ..., 998.
- Total lockers opened in this pass: $\frac{64}{2} = 32$.

6. Sixth Pass (Backward):
- The student turns around again and starts from locker 1024.
- He opens the first closed locker he encounters, which is locker 1014.
- He then skips one closed locker and opens the next one, continuing this pattern.
- This means he opens every sixty-fourth locker: 1014, 950, 886, ..., 54.
- Total lockers opened in this pass: $\frac{32}{2} = 16$.

7. Seventh Pass (Forward):
- The student turns around again and starts from locker 1.
- He opens the first closed locker he encounters, which is locker 22.
- He then skips one closed locker and opens the next one, continuing this pattern.
- This means he opens every 128th locker: 22, 150, 278, ..., 918.
- Total lockers opened in this pass: $\frac{16}{2} = 8$.

8. Eighth Pass (Backward):
- The student turns around again and starts from locker 1024.
- He opens the first closed locker he encounters, which is locker 982.
- He then skips one closed locker and opens the next one, continuing this pattern.
- This means he opens every 256th locker: 982, 726, 470, ..., 214.
- Total lockers opened in this pass: $\frac{8}{2} = 4$.

9. Ninth Pass (Forward):
- The student turns around again and starts from locker 1.
- He opens the first closed locker he encounters, which is locker 86.
- He then skips one closed locker and opens the next one, continuing this pattern.
- This means he opens every 512th locker: 86, 598.
- Total lockers opened in this pass: $\frac{4}{2} = 2$.

10. Tenth Pass (Backward):
- The student turns around again and starts from locker 1024.
- He opens the first closed locker he encounters, which is locker 854.
- This is the only locker he opens in this pass.
- Total lockers opened in this pass: $\frac{2}{2} = 1$.

Thus, the last locker he opens is locker number $\boxed{854}$.