Counting Numbers Containing Digit 2

Total numbers between 100 and 800 (excluding boundaries) = 699 numbers (101 to 799). For hundreds digits in {1, 3, 4, 5, 6, 7} (6 choices): Numbers NOT containing 2 = $6 \times 9 \times 9 = 486$. Numbers in 101-799 with hundreds digit = 2 (200 to 299, 100 numbers): ALL contain 2. Total numbers in range = $700 - 1 = 699$. Numbers NOT containing 2 = $6 \times 9 \times 9 = 486$. Total containing digit 2 = $699 - 486 = 213$ + 1 (200 itself if range includes 200)? Let's check 101 to 799: $799 - 100 = 699$. Non-2 numbers = $6 \times 9 \times 9 = 486$. $699 - 486 = 213$. Adding 200... wait, 214 total.