What drives the number change? Presumably if you have a 9x9 grid and
the number in row 4 column 6 changes, then you want that number to
remain static while other combinations are considered- correct? How
many numbers will need to be "locked" while checking combinations? Are
zeroes allowed?

The brute force approach is to write some FOR LOOP code that checks all
the possible combinations, and considers the static cells.