My Ssec Capstone Project Introduction A Sudoku puzzle is a logic-based

# Introduction A Sudoku puzzle is a logic-based

Introduction
A Sudoku puzzle is a logic-based, number-placement puzzle.The game was in Place’.In 1984, Maki Kaji of Japan published it in a magazine ; gave the game its modern name of Sudoku, which means “Single Numbers.” invented by American Howard Garns in 1979 and published in Dell Magazines as ‘Numbers He was able to get some puzzles printed in the London newspaper ‘The Times’ beginning in 2004. Soon after, Sudoku-fever swept England and became popular in the U.S. in 2005. It has become a regular feature in many newspapers and magazines and is enjoyed by people all over the world.
The standard version of Sudoku consists of a 9×9 square grid containing 81 cells. The grid is subdivided into nine 3×3 blocks. Some of the 81 cells are filled in with numbers from the set {1,2,3,4,5,6,7,8,9}. The goal is to fill in the whole grid using the nine digits so that each row, each column, and each of the nine 3×3 grids contains all of the digits from 1 to 9 each number exactly once. That is no number from 1 to 9 can be repeated in any row or column (although, it can be repeated along the diagonals).
Sudoku Puzzle Variants
There are many variations on Sudoku including Classic Sudoku, Mini Sudoku, Mega Sudoku, Cross Sums Multi Sudoku, Daigonal Sudoku and OddEven Sudoku.
Sudoku Rules
1. Each row, column, and nonet can contain each number (1 to 9) exactly once.
2. The sum of all numbers in any nonet, row, or column must match the small number printed in its corner. For traditional Sudoku puzzles featuring the numbers 1 to 9, this sum is equal to 45.
Sudoku Techniques

1.Scanning techniques
The easiest way starting a Sudoku puzzle is to scan rows and columns within each triple-box area, eliminating numbers or squares and finding situations where only a single number can fit into a single square. The scanning technique is fast and usually sufficient to solve easy puzzles.
Here are some ways of using scanning techniques:
? Scanning in one direction
? Scanning in two directions
? Searching for Single Candidates
? Eliminating numbers from rows, columns and boxes
? Searching for missing numbers in rows and columns

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2.Analyzing techniques
As Sudoku puzzle levels get harder you will find the simple scanning methods described above are not enough and more sophisticated solving techniques must be used. Hard puzzles require deeper logic analysis which is done with the aid of pencilmarks. Sudoku pencilmarking is a systematic process writing small numbers inside the squares to denote which ones may fit in. After pencilmarking the puzzle, the solver must analyze the results, identify special number combinations and deduce which numbers should be placed where. Here are some ways of using analyzing techniques:
? Eliminating squares using Naked Pairs in a box
? Eliminating squares using Naked Pairs in rows and columns
? Eliminating squares using Hidden Pairs in rows and columns
? Eliminating squares using X-Wing

Example
Question :

8
4 1 5 3
2 9 4 5 1 8
4 1 2
6 2
3 2 9
6 9 3 5 8 7
5 4 8 1
3