To calculate the total number of possible Sudoku solutions for a board of size n, one can utilize combinatorial mathematics and backtracking algorithms. The discussion highlights the importance of understanding the constraints of Sudoku, such as the unique placement of numbers in rows, columns, and grids. While the focus is on counting possibilities rather than solving the puzzle, resources like the Wikipedia page on the mathematics of Sudoku provide valuable insights into the underlying principles. The conversation emphasizes the need for an efficient algorithm that can handle varying board sizes, not just the standard 9x9 configuration.