An Improved Hybrid Method Combining Backtracking with Pencil and Paper for Solving Sudoku Puzzles

Sudoku is a puzzle which can be solved by putting digits in a two-dimensional grid/matrix so that no row, column or sub-grid contains any digit more than once. Many methods as well as their hybrids are available to solve Sudoku puzzles. However, these methods face some shortcomings such as not being able to solve puzzles of different difficulty levels and being time-consuming. This is because of overlooking some constraints, leading to violations of Sudoku rules, and/or executing fruitless steps as well as missing potential opportunities to find a solution faster. In this paper, we propose an improved hybrid of backtracking algorithm and pencil and paper method to overcome the limitations of the existing methods. Experimental results show that the proposed method is more effective as well as efficient in solving puzzles of different difficulty levels than the other available methods.