I use this blog as a soap box to preach (ahem... to talk :-) about subjects that interest me.

Sunday, May 29, 2011

Sudoku Explained

I have just released the book “Sudoku Explained”.

This book tells you in a very practical way how to solve Sudoku puzzles. First, it describes in detail and with examples fourteen solving strategies, from the very simple to the very complex. Then, it explains how to apply the strategies you have learned to forty puzzles of increasing levels of difficulty. No other book will teach you how to solve Sudoku puzzles as effectively as this one, but be warned: after reading it, you will discover that the puzzles in your local paper are not so challenging after all!

For now, it is only available on Lulu, either in print for US$9.99 or as an eBook in PDF format for US$4.99.

Welcome to Sudoku Explained. The purpose of this book is to help you become a Sudoku champion. Not everyone has the pattern-recognition abilities to become a champion, and I cannot guarantee that you will succeed, but I can point you in the right direction. The rest is up to you.

The WorldWide Web is full of explanations about Sudoku. You can find the description of many strategies and lots of examples. What I believe you will only find in this book is a systematic and consistent description of all significant strategies coupled with commented solutions of puzzles.

For this book, I have chosen forty Sudokus I generated with the program described in my first Sudoku book (Sudoku Programming). They all have thirty-three clues and look like medieval crosses, because the central row and the central column are always already solved.

Their difficulties range from easy to diabolical, measured as the number and complexity of the solving strategies they require. It is true that, in general, puzzles with fewer clues are easier, but what is true statistically, doesn't apply to each individual puzzle. I have seen very easy puzzles with only seventeen clues, while the last puzzles in this book, despite their thirty-three clues, are as challenging as they come.

Chapter 1 describes the terminology I use throughout the book.
Chapter 2 explains in detail fifteen strategies grouped in four levels of complexity, from 0 to 3.
Chapter 3 presents the Sudokus. Puzzles 1 to 10 can be solved with level 0 strategies; 11 to 20 require level 1 strategies; 21 to 30 are at level 2, and 31 to 40 are at level 3.
Chapter 4 provides the solutions of the puzzles shown in Chapter 3. For the puzzles at level 1, I also list a sequence of strategies capable of solving them, while for the puzzles at level 2 and 3, I explain the application of the more complex strategies in detail.

Have fun with Sudoku!

As an example of how I describe strategies, here is the description of ‘naked pair’
 If two cells in the same unit only contain the same two candidates, it means that one of those candidates will solve one of the two cells, and the other candidate will solve the other cell. Therefore, the same candidates can be removed from all other cells of the unit.
For example, suppose that box 3 has reached the point shown in Figure 2-2.
Figure 2-2: A naked pair

The two cells (4,0) and (4,2) contain the naked pair 8 and 9. If 8 solves (4,0), then 9 must solve (4,2). If, on the other hand, 8 solves (4,2), then 9 must solve (4,0). In either case, both 8 and 9 are used. Therefore, the 8s in cells (5,0), (5,1), and (5,2) as well as the 9s in cells (3,1) and (3,2) can be removed.

Example of how I explain a solution in detail (excerpt)
'unique': 5 in (2,8) is unique within the column
remove 3 and 6 from (2,8)
solved (2,8) with 5
'unique': 9 in (0,0) is unique within the row
remove 1 and 2 from (0,0)
solved (0,0) with 9
'unique': 6 in (0,5) is unique within the box
remove 3 from (0,5)
solved (0,5) with 6

At this point, 53 cells have been solved and many candidates removed, but it is not possible to proceed further with level 0 strategies. Applying ‘naked pair’ twice does the trick:
‘naked pair’: (1,3) and (1,5) in row 1 contain the pair 35
remove 3 from (1,1)
remove 3 from (1,2)
‘naked pair’: (1,1) and (6,1) in column 1 contain the pair 28
remove 2 from (7,1)
solved (7,1) with 1
'cleanup' of row 7: remove 1 from (7,7)
solved (7,7) with 2

Example of how I describe the application of a complex strategy
Puzzle 22 after level 1 strategies

To solve the puzzle, you can apply ‘Y-wing’ to the three cells (6,7), (8,6), and (8,5), containing respectively the pairs 81, 19, and 98. The cells (6,3), (6,4), (6,5), (8,7), and (8,8) are ‘visible’ from both (6,7) and (8,5). Therefore, the candidates for the digit 8 can be removed from them. This boils down to removing a single 8 from (6,5), but that is enough to ‘unlock’ the puzzle, which you can then solve by applying a series of ‘cleanup’s.

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