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Online Sudoku Puzzles - Click to enlargeSudoku Puzzle Games coming soon to Stop2Shop.com.

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Sudoku, sometimes spelled Su Doku, is a logic-based placement puzzle, also known as Number Place in the United States. The aim of the canonical puzzle is to enter a numerical digit from 1 through 9 in each cell of a 9×9 grid made up of 3×3 subgrids (called "regions"), starting with various digits given in some cells (the "givens"). Each row, column, and region must contain only one instance of each numeral. Completing the puzzle requires patience and logical ability. Its grid layout is reminiscent of other newspaper puzzles like crosswords and chess problems. Although first published in 1979, Sudoku initially became popular in Japan in 1986 and attained international popularity in 2005.

Introduction
The term Sudoku implies "numbers singly" 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.

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.

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.

Rules and terminology
The 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.

Solution methods
The strategy for solving a puzzle may be regarded as comprising a combination of three processes: scanning, marking up, and analyzing.

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.

Marking up
Scanning comes to a halt when no further numbers can be discovered. From this point, it is necessary to engage in some logical analysis. Many find it useful to guide this analysis by marking candidate numbers in the blank cells. There are two popular notations: subscripts and dots.

In the subscript notation the candidate numbers are written in subscript in the cells. The drawback to this is that original puzzles printed in a newspaper usually are too small to accommodate more than a few digits of normal handwriting. If using the subscript notation, solvers often create a larger copy of the puzzle or employ a sharp or mechanical pencil.

The second notation is a pattern of dots with a dot in the top left hand corner representing a 1 and a dot in the bottom right hand corner representing a 9. The dot notation has the advantage that it can be used on the original puzzle. Dexterity is required in placing the dots, since misplaced dots or inadvertent marks inevitably lead to confusion and may not be easy to erase without adding to the confusion. Using a pencil would then be recommended.

An alternative technique that some find easier is to mark up those numbers that a cell cannot be. Thus a cell will start empty and as more constraints become known it will slowly fill. When only one marking is missing, that has to be the value of the well.

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