This problem boils down to implementing a sudoku solver.
So thats what I did (initially as a stand-alone project).
And then I wrote a program around that inputs the 5  puzzles 
into the solver and calculates the result.

This means in this post I'm trying to describe how to build a sudoku solver in befunge.

Because all the logic is practically a stand-alone sudoku solver, I simply wrote one. You can read about the development and a few of my design decisions in [this blogpost here](https://www.mikescher.com/blog/9/A_complete_sudoku_solver_in_Befunge93).
The rest was looping 50 times through the solver code and adding the results together.

Really all the interesting stuff is written in the blogpost about the sudoku solver, go read it!