# Rules for Sudoku and Sudoku Puzzle Variants

## Sudoku (Standard 9 x 9)

The rules for the standard 9x9 Sudoku puzzle are simple:

- The puzzle is a 9x9 grid of cells. This grid is made up of 9 rows and columns but is also sub-divided into a 3x3 grid of 'sub-grids', each with 3x3 cells in. These 'sub-grids' are variously known as subgrids, boxes, nonets, regions and numerous other names;
- Each cell must contain a digit 1 through to 9;
- No digit can be repeated in any row, column or subgrid.

Standard Sudoku puzzles must have some cells set (sometimes called *givens*) in the puzzle for you to be able to complete it using logic alone.

Although it is not a rule of *solving *a Sudoku puzzle, it is generally considered bad-form to have a puzzle that does not have a *unique *solution, nor one that involves a trial-and-error approach.

Sudoku is also sometimes known as 'Number Place'. *Sudoku Assistant *currently assists in training you and solving the standard 9 * 9 grid, with plans to support alternative puzzle sizes in the near future.

### Standard 9 x 9 - with Letter Symbols

There is a growing number of standard Sudoku puzzles supplied with letters used instead of the digits 1 - 9. As long as these puzzles can be solved entirely by logic, they may still safely be considered a standard Sudoku puzzle. However, some puzzles may rely (Pop-quiz or crossword style) on certain highlighted cells being recognised as a particular word or famous name, or similar 'textual' identification of a particular cells value. In these cases, the puzzle is not really considered to be a standard Sudoku puzzle any more.

### Other Sizes

Variants of the Sudoku puzzle are possible in almost any (square grid) size; although practical limits are probably about the 16x16 (4x4 subgrids) or 25x25 (5x5 subgrids). Personally, I'm surprised the 16x16 grid has not caught on more, especially amongst computer types, where the symbols of 0-9 and A-F are commonly used to represent hexadecimal numbers. I personally call such puzzles hexdoku, but they often seem to be referred to as Monster puzzles.

The following grid sizes have also been used:

- 12x12 with 4x3 cell subgrids, typically with symbols 1-9 and A-C;
- 8x8 with 4x2 cell subgrids, typically with symbols 1-8;
- 6x6 with 3x2 cell subgrids, typically with symbols 1-6;
- 5x5 with no subgrids (i.e. no subgrid constraints, just rows and columns) - digits 1-5 or picture symbols etc.;
- ...and so on.

## Sudoku X

As per standard 9x9 Sudoku, the grid has the same layout with one additional set of constraints:

- No digit must be repeated in either of the long diagonals.

The cells on the diagonals will often be highlighted with a different colour border or similar. These puzzles have also been seen in 6x6 variants.

## Killer Sudoku (S**amunamupure**)

Based on the grid of standard 9x9 Sudoku, Killer Sudoku puzzles typically do not have any *givens*. However, the grid has further sub-divisions typically indicated by dotted lines that isolate several cells, along with a number indicating the sum of the values of the cells enclosed. The additional rule* is that no number is to be repeated within any linked cells, and that the sum of numbers in those 'cages' must equal the given sum.

In this way, Killer Sudoku very much maintains the spirit of the original Sudoku, whilst adding a phase of analysis of the dotted regions.

My personal experience with Killer Sudoku is limited, but I am sceptical that this puzzle quite fits the Sudoku bill. It certainly is true that a well-formed Killer puzzle will be solveable by logic and clever analysis... but it is also true that tables of possible digits to make up the sums in cages are really very useful. If one considers this to be such a necessity that it is effectively *required *for solving these puzzles, then we have moved away from that great simplicity of the initial Sudoku puzzle! Additionally, where Sudoku does *not *require you to do any addition or subtraction, the very nature of Killer Sudoku will be much more mathematic (not necessarily a bad thing, but another step away from that pure-logic aspect of the original).

* There is apparently some history over the use of this rule - originally The Times did not specify this, although almost all of it's puzzles adhered to it especially when a cage crossed subgrids. This rule is now typically specified with most problems described as Killer Sudoku.

## Samurai Sudoku (Gattai 5)

Samurai Sudoku is a set of five standard 9x9 grid Sudoku puzzles; four interlocked around one central grid. The puzzles are set in such a way that each seperate puzzle needs to be analysed in turn to find values in the overlapping subgrids, which may then be useful in analysis of the neighbouring puzzle.

#### References

We found the Sudoku entries at Wikipedia to be useful in the preparation of this page, especially in relation to the original Japanese names for some of the puzzles.