With a blank grid, I put and number (1-9) any cell, the Sudoku has n solutions. I continue filling any blank cells with numbers that satisfy the constraints, so the Sudoku still has many solutions, but less than n. I keep filling in cell,s so the total solutions will become less and less, until all the cells are either filled or I've hit a dead end (the Sudoku is unsolvable).
While I am doing this, I want to make sure that the current number I am filling into a cell will not produce an unsolvable Sudoku.
Is there any method/algorithm to check the solvability (has at least one solution) of an uncompleted Sudoku without actually solve it? The reason is I am doing it on paper, solve a sudoku with more than one solution need backtracing algorithm that beyond anyone's caluculation limitation to solve it without computer.