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Welcome to sudoku Sudoku (or su doku) is a contraction of the Japanese phrase suji wa dokushinsha ni kagiru which may be translated as meaning digits by themselves. Worldwide, the most popular sudoku puzzle grid is made up of nine cells (or boxes), each cell containing nine squares and arranged to form nine rows and nine columns. The challenge is to complete the grid so that every cell, row, and column displays the digits 1 to 9, in whatever necessary order. A few squares are filled in by the puzzle's setter. Typically, an 'elementary' puzzle may have some thirty digits supplied, though the number of squares filled does not necessarily determine the level of difficulty. The elimination method
The elimination method is a good way for the newcomer to sudoku to gain confidence. It also aids the experienced solver when tackling stubborn puzzles. At any level, the technique offers an insight into the sudoku process.
Let the solving begin
Within each cell, eliminate from the unpromoted arrays the value of any promoted array. For example, if the setter has supplied a 5, and the corresponding array has been promoted, then 5 is no longer a possibility for the other arrays in the same cell, and all the digits 5 can be deleted. The same logic applies for rows and columns: 5 can be removed from arrays in the same row across the grid, and in the same column down the grid. Once the procedure has been completed for all the values given by the setter, the number of available digits on the elimination grid (which is essentially a statement of possibilities) will be substantially reduced.
Some advanced solving Occasionally, the elimination process may seem to stall, there being no obvious digit on its own anywhere on the grid. The situation calls for the application of a little more reasoning. Consider the arrays filling the band of cells in the following diagram. (A band is a horizontal grouping of three cells - one third of the full grid. A vertical grouping of cells is called a stack.)
Because the digit 1 has been eliminated from the middle and bottom arrays of Cell 3, the digit can only promote in one of the cell's top arrays. Taking the top row as a whole (across the band), the digit 1 can therefore be eliminated from the top arrays of Cell 1.
Couples and Threesomes
As the solving of the puzzle continues, couples (sometimes called doubles or twins) are bound to occur. Within the same cell, row or column, two arrays will contain just two digits, each array mimicking the other. Since the arrays must be home to both digits and to no other, then the digits can be eliminated from other arrays in the associated cell, row and column. (A couple can be seen on the primed elimination grid for the worked example: see r1c5 and r1c6 .)
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