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Example

Solution
History
The modern puzzle was invented by an American architect, Howard Garns, in 1979 and published by Dell Magazines under the name "Number Place". It became popular in Japan in 1986, after it was published by Nikoli and given the name Sudoku, meaning single number. It became an international hit in 2005.

Strategies
The strategy for solving a puzzle may be regarded as comprising 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.


The top right region must contain a 5.
By hatching across and up from 5s elsewhere,
the solver can eliminate all
the empty cells in the region which
cannot contain a 5. This leaves only
one possibility (shaded green).
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.

Logically, every sudoku puzzle, regardless of difficulty, is solved via scanning heuristics. In a true sudoku puzzle, every number has a necessary position in each part of the grid which can be deduced from the description or if you prefer definition of what a "true" sudoku is. The only difference between solving advanced puzzles and simpler puzzles is not the techniques used to solve the puzzle but recognizing the logical implications of the scanning heuristic. One such implication would be recognizing logical "contingencies" which just basically means narrowing down the possibilities of a given square via the relations between every other square.






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