Thesis, Undergraduate (BS Appiled Mathematics)-UP Mindanao.

A Sudoku puzzle can be in any n2 x n2 grid. Its standard form is in a 9X9 grid as what is commonly seen in Sudoku puzzle books. The rule for completing a 9X9 Sudoku puzzle is to fill in the grid so that every row, column or 3X3 block contains the digits 1 through 9. A Sudoku problem can also be related to a graph coloring problem since the latter involves labeling each node so that adjacent nodes have different labels. There are many types of Sudoku puzzles and sometimes symmetries which include the mirror-symmetry can be seen. In a mirror-symmetric Sudoku puzzle, the undefined givens are positioned in a mirror-symmetric pattern. Also, every Sudoku puzzle has equivalent puzzles, that is if the puzzle has been modified with permutation of rows or columns within blocks, permutation of a block's rows or columns and permutation of the digits used in the puzzle. In the sudy, the steps in arriving at the solution of a specific mirror-symmetric 9x9 Sudoku puzzle and 3 of its equivalent puzzles were observed. This led to the conclusion that using the algorithm developed and given two equivalent puzzles, a sequence of steps toward the solution of one will work to solve the other.