Introduction: The One and Only Rule
This type of number puzzle follows only one single rule:
Each row, each column and each block must contain each digit exactly once.
Count if you like!
Blocks are the internal 3x3 squares.
This kind of puzzle has dimension (size) and it has a character set. This character set comprises exactly dimension character. These are typically the numbers from 1 to 9, but they don't have to be. You could choose colors or strange symbols for the fields. As long as there are exactly dimension symbols, the logic is the same.
We'll talk a lot about "logical units". Logical units are all possible subunits: rows, columns and blocks - exactly those subunits within which each symbol must occur exactly once.
The picture above shows the typical and widely used standard puzzle. In rare cases, there are puzzles with different side lengths, or ones which include the diagonals as logical units. Including the diagonals makes solving the puzzle much easier.
The procedures for solving the puzzles can be roughly subdivided into three groups. First there are the two basic methods Naked One and Hidden One. These two are fundamental because they always lead to a filled-in field.
Then there are the higher methods. They are based on patterns which can be found in the puzzle, and may allow you to draw certain conclusions. Higher methods do not necessarily have an effect. But if they do, they will eliminate individual candidates from the candidate lists of one or more fields. This process will only lead to a filled-in field when a candidate is eliminated from a list of candidates that only had two candidates. In other words, when the elimination results in a Naked One.
The third "group" is really only one method. It is generally called the Brute-Force method - simply trying out different variations. One could argue, with some justification, that the idea of Chains and Loops is ultimately nothing more than an application of the Brute-Force method. Other authors may have differing views.
An inconsistent state can be diagnosed when one of three possible situations exists:
- Two or more fields In a logical unit contain the same symbol.
- A symbol does not yet occur in a logical unit, and also no longer exists in the candidate lists for empty fields. The candidate is "lost".
- The candidate list for empty field has shrunk to zero candidates.
In addition, a valid puzzle should have only one possible solution. Ambiguity is generally an undesirable characteristic in puzzles - it is here too.
The list of solution methods described here does not claim to be irrefutable or complete. Please excuse any mistakes or errors.