Unity Puzzle Solver Visualization -- 2

I have an early-stage puzzle game and need a more rigorous, mathematics-driven solution engine built directly in Unity. The goal is for the program to ingest a set of parameters, run the necessary calculations, and then render the resulting solution as an interactive 3-D scene I can drop straight into the game. Visual fidelity is welcome, but the true priority is mathematical accuracy; the puzzle must always produce a provably correct answer on every run.

I already possess the source files and partial codebase from a previous developer, so you won’t be starting from scratch. What’s missing is the applied-math backbone: I’m unsure whether the final model will rely on geometry, algebra, optimisation, or a hybrid approach, and I’ll lean on you to make that call, explain the rationale, and document the formulae you implement.

Deliverables
• A Unity project (C#) that accepts input parameters and outputs a fully navigable 3-D solution scene.
• Well-commented code plus a short technical note explaining the mathematical methodology.
• Brief hand-off session (video or written) so I can iterate confidently without you later.

If you’re comfortable designing algorithms and enjoy seeing them come alive as real-time graphics, let’s talk—I’m ready to share the existing assets and dive into the details right away.