SHARING ZONE: Sudoku Strategy

There are different levels of Sudoku offer from each publishers, basically from easy until extreme difficult. Not only that, you Sudoku skill also measure from how fast you solve the game. Thus, many publisher not only provide the games format, but also strategies on solving the puzzle.

Basically, the strategy is focused on a combination of three processes, Scanning, Marking Up, and Analyzing. The approach to analysis may vary according to the concepts and the representations on which it is based.

Scanning
Scanning is performed at the outset and throughout the solution. Scans need be performed only once between analyses. Scanning consists of two techniques:

Cross-hatching: The scanning of rows to identify which line in a region may contain a certain numeral by a process of elimination. The process is repeated with the columns. It is important to perform this process systematically, checking all of the digits 1–9.
Counting 1–9 in regions, rows, and columns to identify missing numerals. Counting based upon the last numeral discovered may speed up the search. It also can be the case, particularly in tougher puzzles, that the best way to ascertain the value of a cell is to count in reverse—that is, by scanning the cell's region, row, and column for values it cannot be, in order to see what remains.
Advanced solvers look for "contingencies" while scanning, narrowing a numeral's location within a row, column, or region to two or three cells. When those cells lie within the same row and region, they can be used for elimination during cross-hatching and counting. Puzzles solved by scanning alone without requiring the detection of contingencies are classified as "easy"; more difficult puzzles are not readily solved by basic scanning alone.

Marking up
Scanning stops when no further numerals can be discovered, making it necessary to engage in logical analysis. One method to guide the analysis is to mark candidate numerals in the blank cells.

Subscript notation
In subscript notation, the candidate numerals are written in subscript in the cells. Because puzzles printed in a newspaper are too small to accommodate more than a few subscript digits of normal handwriting, solvers may create a larger copy of the puzzle. Using two colours, or mixing pencil and pen marks can be helpful.
Dot notation
The dot notation uses a pattern of dots in each square, where the dot position indicates a number from 1 to 9. The dot notation can be used on the original puzzle. Dexterity is required in placing the dots, since misplaced dots or inadvertent marks lead to confusion and may not be easily erased.
Another technique is to mark the numerals that a cell cannot be. The cell starts empty and as more constraints become known, it slowly fills until only one mark is missing. Assuming no mistakes are made and the marks can be overwritten with the value of a cell, there is no longer a need for any erasures.

Analysis
The two main approaches to analysis are "candidate elimination" and "what-if".

Candidate elimination
In "candidate elimination", progress is made by successively eliminating candidate numerals to leave one choice for a given cell. After each answer is found, another scan may be performed—usually checking to see the effect on contingencies. In general, if entering a numeral prevents completion of other empty cells, then the numeral can be eliminated as a candidate.
One method of candidate elimination works by identifying "matched cell groups". For instance, if precisely two cells within a scope (a particular row, column, or region) contain the same two candidate numerals (p,q), or if precisely three cells within a scope contain the same three candidate numerals (p,q,r), these cells are said to be matched. The placement of those candidate numerals anywhere else within the same scope would make a solution impossible, allowing the numbers to be eliminated as candidates from those other cells.
What-if
In the "what-if" approach (also called "guess-and-check", "bifurcation", "backtracking" and "Ariadne's thread"), a cell with two candidate numerals is selected, and a guess is made. The results are followed until a duplication is found or a cell is left without a candidate, in which case the alternative must have been the solution. For each cell's candidate, the question is posed: 'will entering a particular numeral prevent completion of the other placements of that numeral?' If 'yes', then that candidate can be eliminated. If the "what-if" exercises show that either candidate is possible, then another pair should be tried. Alternatively, if the "what-if" exercises for both candidates imply an identical result, then that result is known. The what-if approach requires a pencil and eraser or a good layout memory.
There are three kind of conflicts, which can appear during puzzle solving:
1. Basic conflicts - there are only N-1 different candidates in N cell in the area
2. Fish conflicts - when eliminating number from N rows/columns, it will disappear also from N+1 columns/rows.
3. Unique conflicts - this pattern means multiple solutions, all numbers in the pattern exist exactly two times in every area, row and column. If there is only one candidate in the cell, any virtual candidate can be added.
Encountering any of those would indicate that the puzzle is not uniquely solvable. Encountering any of them as a consequence of "what-if" indicates that an untried alternative is correct.