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## IntroductionThe term Sudoku implies "numbers singly", or loosely translates to "all the numbers must remain unmarried", in Japanese; it is a registered trademark of puzzle publisher Nikoli Co. Ltd in Japan. Other Japanese publishers generally refer to the puzzle as Nanpure (Number Place), its original title. Sudoku is pronounced as the English words "SUE-dough-coo", with the first syllable accented.## Rules and terminologyThe puzzle is most frequently a 9×9 grid, made up of 3×3 subgrids called "regions" (other terms include "boxes", "blocks", and the like when referring to the standard variation). Some cells already contain numbers, known as "givens" (or sometimes as "clues"). The goal is to fill in the empty cells, one number in each, so that each column, row, and region contains the numbers 1–9 exactly once. Each number in the solution therefore occurs only once in each of three "directions", hence the "single numbers" implied by the puzzle's name. |

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The numerals in Sudoku puzzles are used for convenience; arithmetic relationships between numerals are absolutely irrelevant. Any set of distinct symbols will do; letters, shapes, or colours may be used without altering the rules (Penny Press' Scramblets and Knight Features Syndicate's Sudoku Word both use letters). Dell Magazines, the puzzle's originator, has been using numerals for Number Place in its magazines since they first published it in 1979. Numerals are used throughout this article.

The attraction of the puzzle is that the completion rules are simple, yet the line of reasoning required to reach the completion may be difficult. Sudoku is recommended by some teachers as an exercise in logical reasoning. The level of difficulty of the puzzles can be selected to suit the audience. The puzzles are often available free from published sources and also may be custom-generated using software.

The 3×3 region in the top-right corner must contain a 5. By hatching across and up from 5s located elsewhere in the grid, the solver can eliminate all of the empty cells in the top-right corner which cannot contain a 5. This leaves only one possible cell (highlighted in green).[edit]

Scanning

Scanning is performed at the outset and periodically throughout the solution. Scans may have to be performed several times in between analysis periods. Scanning consists of two basic techniques:

Cross-hatching: the scanning of rows (or columns) to identify which line in a particular region may contain a certain number by a process of elimination. This process is then repeated with the columns (or rows). For fastest results, the numbers are scanned in order of their frequency. 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 numbers. Counting based upon the last number discovered may speed up the search. It also can be the case (typically in tougher puzzles) that the value of an individual cell can be determined by counting in reverse—that is, scanning its region, row, and column for values it cannot be to see which is left. Advanced solvers look for "contingencies" while scanning—that is, narrowing a number's location within a row, column, or region to two or three cells. When those cells all lie within the same row (or column) and region, they can be used for elimination purposes during cross-hatching and counting (Contingency example at Puzzle Japan). Particularly challenging puzzles may require multiple contingencies to be recognized, perhaps in multiple directions or even intersecting—relegating most solvers to marking up (as described below). Puzzles which can be solved by scanning alone without requiring the detection of contingencies are classified as "easy" puzzles; more difficult puzzles, by definition, cannot be solved by basic scanning alone.