What is Sudoku?
Sudoku is a number placement puzzle based on logic rather than mathematics. Sudoku gained worldwide popularity in early 2005 and began selling in the form of puzzle books, handheld electronic versions and board games, as well as appearing in thousands of daily newspapers.
The concept of Sudoku is simple. The puzzle consists of a 9x9 square grid that is divided into nine 3x3 squares, resulting in nine rows and nine columns, for a total of 81 small squares. The unsolved Sudoku puzzle supplies only a few numbers in random squares. To solve the puzzle, the remaining squares must be filled in with the numbers 1 through 9, each appearing only once in each row, column and 3x3 square.
This might be the most common and basic technique to start with while solving a Sudoku puzzle. When trying to determine where a digit should be placed in a row, a column or a 3x3 box, we may find that there is only one cell this digit can go and therefore it has to be in that cell.
This is another very basic technique for solving Sudoku puzzles. While considering what digits from 1 to 9 are possibly placed in an empty cell, one would first find out what digits have appeared in the common row, column and the 3x3 box with this cell. If eight out of nine digits have been used, then the other one digit left must be in this cell.
When examining a 3x3 box, one might find that one digit is locked in a specific row (or column) of that box although the exact position cannot be determined yet. This information leads us to confirm that such digit cannot appear in other positions of the same row (or column).
In a Sudoku puzzle, if two cells in the same row have exactly the same two digits as possibilities, then such two digits must be in either one of these two cells and cannot be candidates in any other cells of that row. The same reasoning can be used for any columns and any 3x3 boxes. The technique is called naked pair.
This technique can be applied to more than two digits. It is called naked triplet if three digits are involved and naked quad if four. The number of cells must be the same as the number of digits. But each of the digits involved need not be a candidate of all cells. In other words, each cell has a subset of the digits involved as candidates for that cell.
In a Sudoku puzzle, if two digits are candidates for the same two cells in the same row and not for any other cells of that row, then such two digits must be in either one of these two cells and other candidates in those two cells can be eliminated. The same reasoning can be used for any columns and any 3x3 boxes. The technique is called hidden pair.
This technique can be applied to more than two digits. It is called hidden triplet if three digits are involved and hidden quad if four. The number of cells must be the same as the number of digits. But each of the digits involved need not be a candidate of all cells.