Solution:

In optimal page replacement policy, we replace the page which will not be used for the longest period of time in the future. We can determine this by looking at the future references to pages.

Given reference to the following page by a program:
0, 9, 0, 1, 8, 1, 8, 7, 8, 7, 1, 2, 8, 2, 7, 8, 2, 3, 8, 3

If the program contains 3 page frames, we can simulate the reference string and count the number of page faults.

Initially, all the page frames are empty. We start reading the reference string from left to right.

1. The first page referenced is 0. We insert it into the first page frame. (Page Fault)
```
0
```

2. The next page referenced is 9. We insert it into the second page frame. (Page Fault)
```
0 9
```

3. The next page referenced is 0. It is already present in the first page frame. No page fault occurs.
```
0 9
```

4. The next page referenced is 1. We insert it into the third page frame. (Page Fault)
```
0 9 1
```

5. The next page referenced is 8. We insert it into the first page frame. (Page Fault)
```
8 9 1
```

6. The next page referenced is 1. It is already present in the third page frame. No page fault occurs.
```
8 9 1
```

7. The next page referenced is 8. It is already present in the first page frame. No page fault occurs.
```
8 9 1
```

8. The next page referenced is 7. We can replace the page 9 with 7 as it will not be used in the future. (Page Fault)
```
8 7 1
```

9. The next page referenced is 8. It is already present in the first page frame. No page fault occurs.
```
8 7 1
```

10. The next page referenced is 7. It is already present in the second page frame. No page fault occurs.
```
8 7 1
```

11. The next page referenced is 1. It is already present in the third page frame. No page fault occurs.
```
8 7 1
```

12. The next page referenced is 2. We can replace the page 8 with 2 as it will not be used in the future. (Page Fault)
```
2 7 1
```

13. The next page referenced is 8. We can replace the page 7 with 8 as it will not be used in the future. (Page Fault)
```
2 8 1
```

14. The next page referenced is 2. It is already present in the first page frame. No page fault occurs.
```
2 8 1
```

15. The next page referenced is 7. We can replace the page 1 with 7 as it will not be used in the future. (Page Fault)
```
2 8 7
```

16. The