Number Puzzle Lab Report

MATHEMATICAL EXPLORATION:
SUDOKU PUZZLE-:
INTRODUCTION:
Number puzzle first appeared in the newspaper in the late 19th century. It was published in 1979 by Dell magazine as number place, designed anonymously by Howards Gams. Later introduced in Japan by Nikoli as Suuji wa dokushin ni kagiru (The digits must be single/the digits are limited to one occurrence). Later it was renamed to Sudoku.

I have decided to centre this math exploration around creating sudoku puzzle of three different levels; easy, medium and hard using permutation. The level of the puzzle depends on the number of clues presented, the lesser the clues the harder the level and the key factor to consider while constructing these kind of puzzles is to ensure that there is only one solution to the puzzle and the minimal number of clues is 17.
There are multiple ways

The operations that are going to leave the number of grid completion of the first band unchanged includes, permuting any of the three rows and permuting any of the blocks in the first band.

Permuting the three grids, 3 nPr 3=6 preserves the number of grid completion, since starting with any valid sudoku grid, the only way to maintain its validity is to permute the rest of the blocks in a consistent manner so as each grid remains unchanged.

COMMUTATIVITY OF ROWS AND COLUMNS:
According to Gary McGuire, swapping two different rows (example row 1 and 2) in the same grid still makes a valid Sudoku grid. Same applies with the columns. For instance, There are 6 possibilities that the columns in the grid Q1 can be rearranged based on 3 nPr 3=6 , but for this to satisfy only one rule, the same order has to be applied on the grid Q4 and