OWN THIS GAME!: HOW TO BECOME A SUDOKU MASTER

By Noah Bhody

If you like an intellectual challenge, then you might enjoy Sudoku. The puzzles are 9x9 grids containing 81 spaces. Of these, 20% to 40% are preloaded; then it is up to you to supply the remaining numbers to complete the puzzle.

We'll start with the easiest puzzles and gradually increase the pain level until we conclude with th

• Language: English
• Publisher: GoldTouch Press, LLC
• Release date: Jan 7, 2022
• ISBN: 9781956803808

Noah Bhody

Crème Puff, the co-author, is a pure bred, copper-eyed Persian with a cream coat, and is an authority on Sudoku. Through Felineancestory.com, she traced her heritage to Abyssinians from three millennia ago. In that time period, the Egyptians were bored and wanted a new game. Not surprisingly, they turned to their revered companions (cats) and requested that they provide them with some new type of amusement. To ensure that the Egyptians would always remember felines, her ancestors developed a grid with a nine-space layout (commemorating their favorite number), and called it tic-tac-toe. However, due to the incredible intellect and cunning of cats, the Ancients were unable to ever beat their furry pets...hence the phrase "cat game". Not wishing to take advantage of a lesser species, the Abyssinians decided to invent a new game which would not compel the Egyptians to compete with cats. As in tic-tac-toe, her ancestors kept the 9-space grid, but this time they arranged nine of these in a square matrix. And so, Sudoku was born.

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OWN THIS GAME!

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How To Become A Sudoku Master

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Noah Bhody

Copyright © 2022 by Noah Bhody.

Library of Congress Control Number:      2021922075

Paperback:    978-1-956803-79-2

eBook:           978-1-956803-80-8

All rights reserved. No part of this publication may be reproduced, distributed, or transmitted in any form or by any electronic or mechanical means, without the prior written permission of the publisher, except in the case of brief quotations embodied in critical reviews and certain other noncommercial uses permitted by copyright law.

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Contents

DEDICATION

HISTORY

OVERVIEW OF THE GAME

TERMINOLOGY

EXAMPLE 1 (Exhibit 3) Solving the Puzzle

EXAMPLE 2 (Exhibit 6) Solving the Puzzle

EXAMPLE 3 (Exhibit 7) Scanning and Initializing

EXAMPLE 3 (Exhibit 8) Guessing

EXAMPLE 4 (Exhibit 9)

EXAMPLE 5 (Exhibit 10)

EXAMPLE 6 (Exhibit 11)

DEDICATION

I dedicate this book to the most important people in my life! That would be my loving wife Sandy, our daughters Sabrina and Melissa, and our grandkids Harry and Darla and Lola.

HISTORY

Contrary to common belief, Sudoku has been around for a long time. Since she is an authority on the subject, I’ll let Crème Puff elaborate.

C.P.: Many thousands of years ago the Egyptians were bored and wanted a new game. Not surprisingly, they turned to their revered companions (cats) and requested that we provide them with some new type of amusement. My ancestors, Abyssinians, acquiesced to their request. To ensure that the Egyptians would always remember us, we developed a grid with a nine-space layout (commemorating our favorite number), and called it tic-tac-toe. However, due to our incredible intellect and cunning, the ancients were unable to ever beat us…hence the phrase cat game.

Not wishing to take advantage of a lesser species, we decided to invent a new game which would not compel them to compete with felines. This resulted in the invention of Sudoku. As in tic-tac-toe, we kept the 9-space grid, but this time we arranged nine of these in a square matrix. And so Sudoku was born.

OVERVIEW OF THE GAME

As Crème Puff stated, Sudoku consists of 81 cells arranged in a nine-by-nine grid. Moreover, the grid is further defined by nine squares of nine cells each. In the solved puzzle, each square, row and column must contain the numbers one through nine.

Initially, the puzzle is preloaded with some numbers (givens). The object is to complete the matrix through a process of elimination. Crème Puff has generated over 250 of these for our dining and dancing pleasure. I’ll show you how to attack Sudoku, with occasional assistance from her.

As you might be aware, there are various levels of difficulty in Sudoku. They range from gentle/easy to diabolical/devilish/difficult. Please understand that you are wasting your time working on the former! They demand very little brain power. We will focus only on the toughest puzzles---those requiring multiple guessing. But trust me, after you master the techniques that we will share with you, never again will you entertain the thought of beating up on easy puzzles.

What differentiates an easy Sudoku from a difficult one? The knee-jerk response might be that the more givens, the easier the puzzle. That certainly is a factor, but the most important aspect is the location and relationship of the givens. Crème Puff will demonstrate this with some upcoming examples.

If you are unfamiliar with Sudoku, you might be interested to know that the range of the number of givens is rather narrow. Supposedly, there are some solvable puzzles with as few as 17 givens. Crème Puff has never been able to go that low---her personal best is 20. Most Sudoku’s have givens ranging from the low 20’s to the low 30’s. In other words, in a properly constructed puzzle, about 20 to 40% of the numbers are provided and we are obliged to complete the puzzle from there.

TERMINOLOGY

For sake of clarity, here are the terms that we will be using. As just mentioned, the puzzle (or matrix) is the nine-by-nine grid. Within the matrix there are nine squares, each containing nine cells. The squares will be referenced as one through nine, as will the cells within each square and the rows and columns (see Exhibit 1). Whenever we refer to a cell it will be in the form of square number followed by location of the cell within the square. For example, in Exhibit 2, a 6 resides in cell 1/3, and a 3 in cell 8/5.

EXAMPLE 1 (Exhibit 3)

Solving the Puzzle

STEP 1: Scanning

Since each square, row, and column (S/R/C) must contain each of the numbers one through nine exactly once, we first scan the entire matrix for….

C.P.: …road kill…easy pickings…those numerals that have only one cell in which to inhabit.

Okay. We start in Square 1 and consider each of its givens one at a time going across Squares 2 and 3. There are two 1’s, one in Row 3 (cell 1/8) and one in Row 2 (cell 3/4). We now know that a 1 must be contained in Row 1 of Square 2. But looking down Columns 4, 5, and 6, a 1 is already present in column 5 (cell 8/5) and in Column 6 (cell 5/3). Therefore, the only position for a 1 in Square 2 is in cell 2/1; pencil in a 1 on Exhibit 3.

Next let’s consider the 3 in Square 1. There’s another 3 in Square 3 (cell 3/8), therefore the 3 in Square 2 must be in Row 1. It can’t be in cell 2/1 because there is now a 1 in that cell, and it can’t be in cell 2/3 since there already is a 3 in Column 6 (cell 8/6). Accordingly, we are able to insert a 3 into cell 2/2.

The last given in Square 1 is a 9. However, there are no other 9’s in Squares 2 or 3, so nothing else can be achieved in Square 1 for now and we move on to Square 2. There is no 2 or 5 in Square 3, so we are done with Squares 1, 2, and 3 (see Exhibit 3a).

We next employ the same methodology in scanning across Squares 4, 5, and 6. In Square 4, the 3 in cell 4/1 in conjunction with the 3 in cell 6/6, means that a 3 is required in Row 6 of Square 5. Fortunately, there is only one spot where it can go: cell 5/7. Enter it on Exhibit 3a. The 5 in Square 4 does not help us because there are no other 5’s in Squares 5 or 6. In Square 5 only the 8 is of interest to us. Coupled with the 8 in Square 6 (cell 6/8), we discover that an 8 must reside in either cell 4/2 or cell 4/3. So, in the middle section of those cells, place an 8 (see Exhibit 3b).

C.P.: By the way, when you insert a number in the center section of a cell, put it approximately where it would go if you were counting the numbers one through nine from left to right. You do this to leave room if you position other numbers in the middle of that cell later on.

Good hint, Crème Puff! Now let’s move on to the bottom three squares. The 2 in Square 7 and the 2 in Square 9, result in a 2 being forced into cell 8/2. Additionally, in Square 8, the 9 together with the 9 in Square 9 mean that a 9 must inhabit cell 7/1. The horizontal scanning is now complete (see Exhibit 3c).

Similar to the testing that we just accomplished, we will now take three squares at a time vertically. So, scanning Square 1 through Squares 4 and 7, we find that the 3’s in Column 2 (cell 1/5) and in Column 1 (cell