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Cross-hatching:

This is performed by the scanning of rows or columns to identify which line in a region may contain a certain number. This is done by process of elimination and for the fastest results the numbers are scanned in order of their frequency. It is important that this is performed systematically with all digits 1-9 being checked.

Counting 1-9 in regions, rows, columns to identify missing numbers:

Counting based on the last number discovered may speed up the process. With the more difficult puzzles especially it can often be the case that the easiest way to discover the number for a cell is by counting in reverse. That is by scanning the cell?s region, row and column to find the numbers it cannot be, to see which is left.

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As well as the popular 9×9 grid with 3×3 regions there are other forms the puzzle can take. Sample puzzles can be 4×4 grids with 2×2 regions; 5×5 grids with pentomino regions have been published under the name of Logi-5; the World Puzzle Championship has featured a 6×6 grid with 2×3 regions and a 7×7 grid with heptomino regions and a disjoint region.

12×12 Sudoku

There have been yet larger and more complicated shapes incorporated into the puzzle as well. Recently a 12×12 grid called Monster Su Doku was published and The Times have Dodeka Sudoku with 12 regions each 4×3. As well as numbers, the puzzle can contain letters, shapes or colours without altering the rules.

Candidate Elimination

One method of candidate elimination is to identify the ‘matched cells’. Cells are said to be matched within a particular row, column or region. If two cells contain the same pair of candidate numbers and no others, or if three cells contain the same three candidate numbers and no others. Placing these numbers anywhere else within that same region would make a solution for the matched cells impossible; thus the candidate numbers appearing in unmatched cells in the same row, column or region can be deleted.

A second related principle can also be true. If cells within a set of rows, columns or regions contain the same set of candidate numbers and the number of cells and numbers is equal to the quantity of candidate numbers, the cells and numbers the cells and numbers are matched. Only those numbers can appear in matched cells and other candidates in the matched cells can be eliminated.

What if

With the ‘what if’ approach, a cell with only two candidate numbers is selected and the player then guesses. The same method as above is used unless a duplication is found or there appears to be no possible candidate number for a cell. In logic terms this is known as: reductio ad absurdum
The ‘what if’ approach requires a pencil and eraser and is often frowned upon by logical pursuits as trial and error. However, it can arrive at solutions remarkably quickly

Ideally the player will find the method that suits him/her best and needs to find a combination of technique that avoids some of the drawbacks of the above elements. Writing candidate numbers into cells, the counting of regions, rows and columns can be time consuming and monotonous. The ‘what if’ approach to can be confusing to say the least and through practise the technique that works best for the individual will ultimately minimize counting, marking up and rubbing out.

Subscripts

In the subscript notation the candidate numbers can be written in subscript in the empty cells. If the original puzzle is too small to carry this out (most newspapers are printed with cells that are too small to accommodate more than a few digits of normal handwriting) it may be sensible to make a larger copy of the puzzle.

Dots

The other notation is where the player uses a series of dots to represent the numbers 1-9, with 1 being a dot in the top left hand corner of the cell and 9 being a dot in the bottom right hand corner. Using a pencil is recommended as misplaced dots can easily lead to confusion.

When using the marking system a couple of similar rules applied in a specific order will solve any Sudoku puzzle, with no need to backtrack.

• scanning
• marking up
• analysing

Usually the puzzle is a 9×9 grid, made up of 3×3 subgrids called ‘regions’. Some cells contain numbers and these are called ‘givens’. The object of the game is to fill in the empty cells so that each column, row and region contains the numbers 1-9 only once. In each of the three ’scopes’ or ‘directions’ each number occurs only once therefore, thus the ’single number’ implied by the name of the puzzle. There is no mathematical solution to the puzzle; it is completed more through logical reasoning. The level of difficulty has very little to do with the number of givens within a grid, it is more the positioning of the numbers as opposed to the quantity.

Other forms of the puzzle have included Channel 4’s teletext service having a daily Su Doku on page 391 and the Radio Times features a Super Sudoku. On Sky One, as a one-off, the world’s first televised Su Doku TV show was broadcast titled Sudoku Live. Nine teams, consisting of nine players in each, from regions throughout Britain took part by entering numbers with a hand held device with numbers corresponding to answers for four cells. The audience at home could take part through a separate interactive competition. As part of the publicity for the show an 84m square puzzle was carved into a hillside in Chipping Sodbury near Bristol in view of the M4 motorway. Claimed as the world’s largest Su Doku puzzle, it was found to have 1,905 correct solutions! There has even been a radio version on Radio 4’s Today programme.

St Louis hosts the worlds largest Sudoku event

Later this year in the US, the largest Su Doku tournament to date is scheduled to take place in St Louis. Participants from 32 regional tournaments will compete to become champions of their regions and then go on to play in the National Final with a prize of $50,000 at stake. Lucca in Italy will be host to the first world championship in March this year.

Other Sudoku versions

As well as the well-known numeric version, there are versions that use letters, two of which are the Penny Press’s Scramblets and Knight Features Syndicate’s Sudoku Word.