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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:

  • each row has digits 1 through 9, with no duplicates;
  • each column has digits 1 through 9, with no duplicates;
  • each 3x3 box has digits 1 through 9, with no duplicates.

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:

  • Box nine must have a 4 in it somewhere, but it can't be in the top row of the box, because row seven already has a 4 in it.
  • Likewise, it can't be in the bottom row of the box because row 9 already has a 4 in it.
  • It must therefore be in row eight, but in box nine there is only one free cell in row eight, so this must be where the 4 goes.

Here's another example: cell 8,5 must be 5. Here's why:

  • This cell cannot be 1, 3, 4, 7, or 9 because box eight already contains these values, and we can't have any duplicates in the box.
  • This cell cannot be 3, 6, 7, or 8 becaue row eight already contains these values, and we can't have any duplicates in the row.
  • This cell cannot be 2, 4, 6, 7, or 9 because column five already contains these values, and we can't have any duplicates in the column.
  • The only value that is left is 5, so cell 8,5 must contain a 5.

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.

Advanced Strategies

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.

Guesswork

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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