What is Sudoku, Anyway?
Sudoku is the new puzzle that is taking the world by storm. Its rules are very simple, but the puzzles themselves can be anything from simple to sadistic.
The Rules of Sudoku
Sudoku is played on a board of 81 cells arranged in nine rows and nine columns. Additionally, there are nine 3x3 "boxes" containing nine cells each. The game uses the digits 1 through 9, but no mathematical skills are needed to play.
The board will start with some numbers already shown. The object of the game is to put digits 1-9 into the empty cells so that:
Here is a sample Sudoku puzzle:
We identify the rows as one through nine, from top to bottom, and the columns as one through nine, from left to right. The heavy lines outline the 3x3 boxes, which are identified as one through three along the top, four through six in the middle, and seven through nine along the bottom.
Solving Sudoku Puzzles Using Logic
No mathematical skills are needed to play Sudoku--all you need to do is to not put duplicate digits in any row, column, or box. Of course, it isn't as easy as it sounds (if it were that easy, it wouldn't be any fun).
Solving Sudoku puzzles calls for logic. For example, cell 8,9 (that's row eight, column nine) must be 4. Here's why:
Here's another example: cell 8,5 must be 5. Here's why:
These two strategies (called Hidden Singles and Naked Singles, respectively), are the basic strategies for solving Sudoku puzzles. The work of figuring out which values are legal in each unsolved cell is, as you can imagine, tedious and error-prone. SudoKoach does this work for you. By eliminating the boring work, SudoKoach makes solving Sudoku puzzles easier and more fun.
The two basic strategies are used in solving almost all Sudoku puzzles, however only the simplest of puzzles can be solved using only these strategies. The harder puzzles require more advanced strategies to solve. These strategies include Naked Pairs, Hidden Pairs, X-Wings, XY-Wings, XYZ-Wings, Box/Line Eliminations, Singles Chains, Pairs Chains, and many more.
SudoKoach currently implements 26 different solving strategies. The accompanying Help describes them all in detail, gives examples, and gives hints on how to find them in puzzles.
If you get stuck in a puzzle, you can try solving it with guesswork. To do this, just pick some cell and then pick some legal number for it (legal in that the number you've picked does not duplicate any numbers already in the row, column, and box which contains the cell you picked). Then continue solving. If you reach a dead end, such as an unsolved cell in which every digit would be a duplicate, then your initial guess was wrong. Now you've got to erase all of the moves you made after your initial guess, and then try again with a different number.
Solving by guesswork is a legitimate approach, but it is error-prone. Just remembering which moves you've made after the initial guess is difficult enough, but you've got to remember them so you can erase them if you reach a dead end. And your first initial guess may lead you to a point where you're stuck again and have to guess at another cell--and maybe another one after that. There's lots to keep track of with this approach.
Solving Puzzles Using Logic
Solving Sudoku puzzles using logical strategies does not involve any guesswork. Plus, using logic is great mental exercise, and it is very rewarding to recognize an obscure pattern in the puzzle.
My hypothesis is that all Sudoku puzzles can be solved without guesswork. I cannot prove this yet, but so far SudoKoach can solve 99.5% of all Sudoku puzzles using its built-in strategies.
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