The puzzle grid consists of 9 rows (horizontally), 9 columns (vertically) and 9 3x3 blocks (also called boxes). Rows, columns and block are all kinds of unit. There are 27 units in a grid. Every unit contains 9 cells, and every unit must contain the digits 1 through 9. The numbers already in the grid are the puzzle’s clues. The numbers you add, as a player, are big numbers (as opposed to the small numbers you use temporarily, which are pencil-marks).
When you have an empty cell, the remaining numbers which could go into it according to the rules of the game are the empty cell’s candidates.
Rows are numbered 1 to 9, top to bottom. Columns are numbered 1 to 9, left to right. Blocks are numbered 1 to 9, in this layout:

How to play Sudoku

Sudoku Techniques

Single in Box

When there is only one cell in the box which can contain a certain value, this value can be safely assigned to this cell. This is the most common technique used to solve a puzzle.

In the example below every known value 8 is marked black. The black lines indicate some of the cells that cannot be 8 because there already is an 8 in the row or column. Therefore, the yellow marked cell must be 8 because this is the only possible 8 in the box.

Naked Single

It is often the case that a cell can only possibly take a single value, when the contents of the other cells in the same row, column and block are considered.

Block/Block Interaction

If a number appears as candidates for two cells in two different blocks, but both cells are in the same column or row, it is possible to remove that number as a candidate for other cells in that column or row.

Pointing pair

When a specific candidate value inside a box is restricted to one row or column, you can use the Pointing Pair technique. This means that you can exclude the same candidate value from other boxes in the same row or column.

Naked Subset

If two cells in the same row, column or block have only the same two candidates, then those candidates can be removed from other cells in that row, column or block. This technique can also be extended to cover more that two cells.

Scanning

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

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. For fastest results, the numerals are scanned in order of their frequency, in sequential order. 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.

Marking Up

Scanning comes to a halt 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.There are two popular notations: subscripts and dots.

·In the subscript notations, the candidate numbers are written in subscript in the cell. The drawback is that original puzzles printed in a newspaper are too small to accommodate more than a few digits of normal handwriting. To use the subscript notation, solvers often create a larger copy of the puzzle or use a sharp 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 can be used on the original puzzle. However, a lot of skill is required in placing the dots, since misplaced dots or accidental marks may lead to confusion and it may not be easy to erase them without adding to the confusion. Using a pencil would then be recommended.

History

The puzzle was designed by Howard Garns, a retired architect and freelance puzzle constructor, and first published in 1979. Although likely inspired by the Latin square invention of Leonhard Euler, Garns added a third dimension (the regional restriction) to the mathematical construct and (unlike Euler) presented the creation as a puzzle, providing a partially-completed grid and requiring the solver to fill in the rest. The puzzle was first published in New York by the specialist puzzle publisher Dell Magazines in its magazine Dell Pencil Puzzles and Word Games, under the title Number Place (which we can only assume Garns named it).

The puzzle was introduced in Japan by Nikoli in the paper Monthly Nikolist in April 1984 as Suuji WA dokushin ni kagiru , which can be translated as "the numbers must be single" or "the numbers must occur only once" (literally means "single; celibate; unmarried"). The puzzle was named by Kaji Maki, the president of Nikoli. At a later date, the name was abbreviated to Sudoku (pronounced SUE-dough-coo; su = number, doku = single); it is a common practice in Japanese to take only the first kanji of compound words to form a shorter version.

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