H9A: Count How Many Times a Digit Appears in Any Range

A classic trick question: how many times does the digit 9 appear between 1 and 100? Most people answer 19. The correct answer is 20 — 9, 19, 29, ..., 99 give 10 in the ones place, and 90–99 give 10 in the tens place. The number 99 is counted twice.

I turned this into a small Python package, H9A.

Install and use

pip install h9a

h9a                       # 9 in 1..100 -> 20
h9a --digit 0 --start 0 --end 9
h9a --json                # machine-readable output
h9a --screenshot          # terminal-style PNG

Why it's fast

The first version iterated the range. A range of a billion numbers meant a billion iterations. I replaced it with a closed-form, per-place formula: for each decimal position, the count comes from division and modulo on the endpoints. Ranges up to 1,000,000,000,000 now resolve in microseconds.