Mind Twisters Sudoku

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9×9 Sudoku

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.

There are two main approaches to analysis:

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.