The puzzle that is being expressed is a puzzle about
Specifically, one possible problem statement is:
The diagram shows
At the start,
For the bonus question, the problem has been modified slightly in that:
You might think 5⅓ is correct because
I'm going against some of the things you suggested here but one possibility I've found that could work is the following (where each space must be filled by a unique digit between 1 and 9)
Framing it in this way makes it look like a single equation. I checked using a computer and this has exactly two solutions
which look like yours but with the end pairs ...
I have a potential rule set, that almost allows for manual-solving using normal sudoku-like deductions:
Applying those rules gets me to the following position.
Which has two valid solutions:
So either the I have the rules wrong, or I've made a mistake during solving.
[Note: when this answer was written there was a minor error in the puzzle, which had BIRds rather than CIRcus. The puzzle has been fixed but I haven't updated the answer.]
The puzzle is
and David's surname is
So, we start with
and FED the BIRds some DAM GAS
Your program solves
OK, so let's proceed.
The instructions are not perfectly explicit about this, but
And the instructions are even less explicit about this, but
I shall refrain from spoilering literally everything in what follows, to reduce clutter a bit. I'll try to hide the things that give the most away.
I'm going to give the variables shorter names: