```python
def starts_one_ends(n):
    """
    Given a positive integer n, return the count of the numbers of n-digit
    positive integers that start or end with 1.
    """
    if n == 1:
        return 1
    
    # Count of n-digit numbers that start with 1
    start_with_1 = 10 ** (n - 1)
    
    # Count of n-digit numbers that end with 1
    end_with_1 = 9 * 10 ** (n - 2)
    
    # Count of n-digit numbers that both start and end with 1
    both = 10 ** (n - 2)
    
    # Inclusion-exclusion: |A ∪ B| = |A| + |B| - |A ∩ B|
    return start_with_1 + end_with_1 - both
```