What is a Sudoku?

      Sudoku is a logical puzzle game, originally created in puzzle books and then made available in countless newspapers worldwide.

      Many people are put off by seeing a grid with numbers in it, but in fact the puzzle doesn't require any arithmetic at all - just deduction and logic.

      There's plenty of discussion about what consitutes a Sudoku puzzle, but many Sudoku fans agree:

      A Sudoku should have 30 or less initial values filled in out of the 81 total
      Sudoku should be solvable by entirely logical deduction - no guesses should be needed. (That doesn't mean that you can't use guesswork, just that you shouldn't have to.
      For aesthetic reasons, a Sudoku should have rotational symmetry - the positions of the initially filled in cells should be the same if you were to turn your page round.
      The Sudoku must only have one solution!

      Of course, for beginner puzzles, often there are more than 30 values filled in - this is just to give you a head start while you're learning!

      Many people think that harder Sudoku puzzles are the ones with less values filled in to begin with. While this is often the case, there are plenty of frustratingly difficult puzzles available with 28 or more cells filled in - difficult because they really require you to use lots of different solving techniques to complete them.

The Basic Rule
There is really only one rule:
     Fill in the grid so that  every row,  every column, and every 3 x 3 box contains the digits 1 through 9.

Solving Sudoku : Guessing
      If you've tried everything else you can think of, and a few quick Nishio attempts haven't yielded a result (or completed the grid), then you may need to break down and make a guess. Most good Sudoku puzzles won't require you to guess, but it may just be that there's another logical technique out there you haven't used, or it might just be a puzzle which really does require a guess!
First of all, if you have to make a guess, at least try to make a guess in a place with limited options, that will open up a whole new set of cells for you.
      Next, be aware that even after making your guess, you might still have lots of hard work ahead of you before you get close to either completing the puzzle, or knowing that it was the wrong guess!
      Finally, and here's the worst part, one guess might not be enough! It might be that along the route to completion you have to make several guesses, each one leading you down a different path with different choices to make. Better have an eraser handy!
If multiple guesses are required, you'll find yourself needing to track back if you find you did make a wrong turn (and end up in a dead end). For that reason, a guess-based technique that follows from Nishio is known as "Ariadne's Thread" - meaning following guesses, but each time you find an error backtrack to your last choice, and take a different path, like Ariadne of legend! Yes, you'll eventually get to the end of the Sudoku, but it could take a very long time with a great deal of wrong turns! Working things out with logic is much simpler when you can! (Ariadne was the daughter of the Cretan King Minos, who helped Theseus by giving him a sword with which to kill the Minotaur, and a thread which he used to find his way back out of the labyrinth, winding the thread back up every time he made a decision ending in a dead-end, and taking a different path.)
      The technique of guessing (or trial and error) is also known as bifurcation - and many computer based solvers only include this technique! That may seem strange, but it is very easy for a computer program to brute-force run through each of the guesses to complete the puzzle, and trivial for it to backtrack to a previous choice - humans just don't work this way! (But then, we can make deductive leaps of logic that computers can't... yet!)

Linkus