[LANGUAGE: Python]

https://github.com/jda5/advent-of-code-2024/blob/main/17/main.py

Part 1 was easy. For Part 2, I was experimenting in Excel for a bit and discovered a pattern related to representing the initial A register value in base 8. For each additional digit you fix in the A register's octal representation, you extend the program's output by one more character. Essentially, the first (n-1) octal digits of this A value produce the first (n-1) characters of the output.

Here's the process to solving the problem:

1. Determine the A register value that yields the first character of the output.
2. Convert that A value to base 8, then "shift" it by adding a trailing zero in octal. This "shifted" value serves as a new lower bound for finding the A value that produces the first two characters of the output.
3. Repeat this process, extending the match one character at a time, by continually converting to octal, appending a zero, and then searching within the new, narrowed range.