Introduction to Sudoku

A puzzle is a 9x9 grid made up of 3x3 regions. Initially, some cells already contain a number. These numbers are called givens.

The aim of Sudoku is to fill in the partially-completed grid so that every row, every column, and every 3x3 box contains the digits 1 through 9 exactly once.

Single-player game

To begin a single-player game:

On the difficulty menu, the Custom option allows a puzzle to be entered by hand (e.g. from a newspaper), rather than using a system-generated puzzle. Further instructions are displayed if this option is chosen.

Competition mode

To be the host of a competition:

To join a competition for which there is already a host:

The same puzzle is given to both players in a competition. The aim is to be the first player to complete the puzzle.

Each player can see their position relative to their opponent’s. There is an interesting twist, however: a player is informed, by the colour of the progress bar, whether their opponent has made any errors!

During a game

Clicking the left mouse button on a cell selects that cell, and the keyboard is used to enter a digit into it. To clear the contents of a cell, use the backspace key when it is selected.

It is possible to ‘scribble’ into any cell to make a note of the digits thought to be possibilities. This mode is accessed by selecting a cell using the right mouse button. Then, the numbers on the keyboard toggle each digit on and off.

Every occurrence of a particular digit can be highlighted by double-clicking on any instance of it.

Hints can be requested at any time during a game by pressing the Hint button. In competition mode, each player is restricted to 5 hints.

The current puzzle may be reset by clicking the Reset Grid button. This clears any digits which have been entered since the puzzle began.

A game can be saved by clicking the Save Game button. Any digits which have been entered into the grid are saved with the game so that it can be continued at a later date.

Hints

A hint can be requested at any point in the game, however some of the hints given will not be entirely easy to understand unless the techniques to which they refer are known. In order to guide you through the puzzle in the most simple logical way the hint system will make reference to the following well-known solving techniques:

(N.B. Difficulty rating for each technique is in parentheses following its name.)

Naked single (Easy)
Naked single is the name given to a cell that, after considering cells in the same block/column/row, can contain only one value. In the following example the highlighted cell can only be a 6 as all the other 8 digits have already been used.


Hidden single (Mild)
Hidden single is the name given to a cell that, although after considering cells in the same block/column/row, may contain more than one value, can be the only cell of it's given row/column/block that can contain a specific value. In the following example the highlighted cell is the only one in it's row, column, and block that can be a 7 (N.B. It would have been enough to be the only cell that could contain a 7 in either the row, column OR block)


Block-Row/Column (Tricky)
In many cases when considering a block, a value may not be able to be placed exactly however can be confirmed as in a particular row/column. In this case it is possible to eliminate the value from all other cells in the relevant row/column. In the following example the value 8 within the highlighted block is forced to be in the middle column. This being the case the scribbles in the lone highlighted cell can have their 8 eliminated.


Block-Block (Tricky)
In many cases when considering two blocks in the same plane it is possible to notice that a value does not appear in one of the rows/columns shared by both. If this is the case then the value must reside in the relevant row/column of the final block in that plane. The value can therefore be removed from the other rows/columns in the third block. In the following example the central column of the two highlighted blocks does not contain a 5 as a possibility. Therefore the 5 must reside in the central column of the bottom block, meaning that the scribble can be eliminated from the lone highlighted square.


Naked pair, triple (Tricky)
A naked pair is a pair of cells in the same row/column/block in which only the same two values can be placed. Given that only these two values can occur in both cells we can deduce that the two values MUST occupy both cells and as such can be eliminated from any cells sharing the same row/column/block. A naked triple is the same however using three cells and three values. In the following example the first, third and fourth highlighted cells contain only the values {2,3,7}. Given that these values must be used only once each then they MUST fill those three cells (a naked triple), and the 2 and 3 scribbled in the fourth cell can be eliminated.


Naked quad, subset (Difficult)
These are the same as with the naked pair/triple except that the number of cells/values is larger and hence the difficulty rating has increased. This technique can be applied to the following puzzle:


X Wing (Difficult)
An X Wing can be found when there exists only 2 cells in both of a pair of rows/columns that can contain a particular value. In addition the cells must lie in the same columns/rows, so will form a rectangle. Given this arrangement it is possible to see that the value in question will reside in opposing corners of the rectangle, allowing us to eliminate the value from the scribbles of cells in the same rows/columns. In the following example the value 6 is used to find two rows that can contain a 6 in only two places, and these fall in the same two columns producing the rectangle. Now the 6 can be eliminated from the other highlighted square as it lies in one of the columns.


XY Wing (Difficult)
An XY Wing occurs when there exists a unit (row/column/block) with two cells allowing possibilities {x,y} {x,z}. Further, another unit is needed that is connected to the first cell ({x, y}) with a cell of possibilities {y, z}. From this we can deduce that whichever x or y is in the first cell then z will be in one of the other two. This allows us to eliminate z from the scribbles of any cell that lies in a unit with both these two cells. In the following example we have cells {5, 7}, {7, 8} and {5, 8} (the lower one). This ensures that an 8 will occur in one of the two latter cells, and any cells lying in a unit with both of them (like our final cell) can have the 8 scribble eliminated. If you work through the example below using the upper {5,8} instead then you will be able to eliminate the 5 from the lower.


Forcing chains (Insane)
A chain is made up of pairs of cells that are strongly connected (i.e. if cell A is a 1, then cell B must be a 2 etc.). Such a pair must be in the same unit and both the cells will always contain only two possible candidates. A chain may be composed of many different pairs from different units. A forcing chain is one that, given a starting cell, if EITHER possibility is entered then some cell further down the chain still ends up as the same value. If this is true then we know that the latter cell will contain this resulting value independent of the value given to the initial cell. The following example has two chains marked, and both result in a 6 in the final cell.


Colouring (Insane)
Using similar chains to the above technique, this one focuses on a particular value, and looks for a unit in which there are only two possible cells for it. Obviously one of the two cells will have the value and the other will not. Linking these pairs together leads to an alternating sequence of cells where every other cell has the value and the subsequent will not. If one then considers cells in the same unit as two members of the chain that are apart by an odd number of links then it is apparant that exactly one of the two cells will have the value, and the cell in question may have its scribble eliminated. In the following example a chain has developed based on the value 5. The two end cells of the chain are 3 links apart and hence the final highlighted cell, being in a unit with both, can have its scribble eliminated.