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Dragon

Theme and Variations

There are many different forms of Sudoku that have developed over the last few years. Some of them are straightforward extensions on the original idea of Sudoku and others take a radical turn.

Minor Variations

Grid Size

It turns out there is nothing special about the regular 9x9 puzzle, the grid size can be any old size. You can make it smaller and simpler or larger and harder to solve. Commonly used grid sizes are 2x3 regions rather than 3x3 so there are six numbers to place in the squares and 4x4 where there are sixteen numbers. Our theory page goes into more detail; there is no theoretical limit on how large the grid can be. All the same strategies apply, you can use them to solve different sized puzzles.

Variations of region size examples of 2 by 3; 2 by 7; and 4 by 5 grids.

Sudoku Dragon can generate and solve puzzles of all these sizes.

Colors, Words, Pictures and Symbols

Sudoku is about placing things in the correct order; it has nothing to do with arithmetic. The familiar numbers 1 to 9 can be replace these with anything at all as long as each is different from each other. So the puzzle can use a set of nine different colors, nine letters or pictures. If it uses fragments of a completed picture then one of regions (usually the central one) will show the picture in full. However you really need a program to help you play these picture puzzles as you can't all that easily pencil in sketches for the missing squares!

Word Sudoku

If letters are used rather than numbers then 'hidden' words can be included in the grid, often this is a nine letter word in a row or column. Here's an example of a puzzle with its solution alongside, the hidden word wordgames is in the rightmost column.

In this second example puzzle generated by Sudoku Dragon the hidden word is in the second row. The hidden word is Diplomats.
Word Sudoku

Sudoku Dragon fully supports this variation of Sudoku. Currently only grid size 9x9 is supported with a hidden nine letter word.

Jigsaw or Squiggle Sudoku

In regular Sudoku all the regions in the grid have an identical shape - a square or a rectangle. If instead you allow the regions to be any old shape, as long as each shape is contiguous and has the same number of squares as all the other regions. The strategies have to change a bit. The two-out-of-three strategy, which is so useful for regular puzzles, has to be overhauled and the shared subgroup exclusion rule needs to account for the individual overlaps of the particular patterns.

In this second example puzzle generated by Sudoku Dragon the irregular regions are highlighted with different colors. The pattern of regions is symmetric.
Squiggle Sudoku

Sudoku Dragon fully supports this variation of Sudoku for grid sizes up to 10x10.

Extra twists

The minor variations do not change or extend the rules one iota; they are still all essentially the same puzzle. In this next category are puzzles that add some other rule or hint on top of the normal Sudoku rules.

Neighbor Order

This is a neat idea of adding extra information that is easy to see and use. The border between two squares is used to give a hint as to which neighbor is larger. It includes a pointer to the smaller number. It is also known as 'Greater than Sudoku'. A row of 9; 8 ;7; 2; 4; 1; 6; 5; 3 has the ordering 9 > 8 > 7 > 2 < 4 > 1 < 6 > 5 > 3. This extra hint introduces a new way to solve squares. If you have a 2 and a neighbor that is smaller than this then it must be a 1, similarly an 8 with a higher square must be a 9.

Here is an example puzzle with all the orderings shown in each square's border. In this case the square Bb can be immediately be solved by ordering as it has 6 > x > 4 and so x must be 5.

To make solution a little harder only some of the neighbor borders can be indicated. Often the initial grid is empty except for the neighbor ordering. This is a puzzle with the addition of number ordering and so it is not strictly Sudoku any more, a picture or color Sudoku puzzle doesn't have a concept of order of neighbors so to a purist it's not quite the real deal.

Stripe

We at Sudoku Dragon have added our own little extension to Sudoku. Optionally one group in the grid will contain the numbers in order 1 to 9 or reverse order. The stripe can be wrapped up into a region which makes it sometimes hard to spot. We have a whole page devoted to describing the stripe.

X Sudoku

Going back to Euler and the origins of Sudoku the original Magic Numbers and Latin Squares had constraints on the diagonals as well as the rows and columns. So there is a variety of Sudoku that always has the numbers 1 to 9 occurring in both the diagonals as well as the rows and columns. You can use this extra constraint to solve squares.

In this second example puzzle generated by Sudoku Dragon a grid size of 2x5 is used (ten squares per group). The diagonal nature of the puzzle is indicated by the small diagnonal mark in the corner of the puzzle.

Diagonal Sudoku

Sudoku Dragon fully supports this variation of Sudoku. All ten grid sizes can optionally have the diagonals as an extra group.

Killer Sudoku

A popular variation of Sudoku is to add some arithmetic on top of the basic rules. In Killer Sudoku the standard grid is divided up into collections, in the top left square of the collection is the sum of the numbers that go in the squares making up the group. This lets you solve squares in new ways, in the simplest case you could have a collection of only two squares, if the sum is 3 then you know one square in 1 and the other 2, or if the sum was 17 then they must be 8 and 9. So the sum is giving extra information about the numbers in the squares quite apart from the standard 'number unique to a group' coming from Sudoku. A key starting point is to look for collections with a low average (e.g. a total of 6 for 3 squares, average 2, means can only be {1, 2, 3}) or a high average (e.g. a total of 30 for 4 squares, average 7.5 means can only be {6,7,8,9}) Usually the extra information from these additions is sufficient to start off with an empty grid and yet still be able to solve it.

Other Variations

There are a host of other variations on the basic theme and new ones are being invented all the time. If you have found one that you like let us know about it.

Give our SudokuDragon puzzle solver a free 23 day trial by visiting our download page. All the main Sudoku strategies have clear, easy to follow guide tutorials. It can selectively help you quickly identify possibilities and exclude the ones that actually are impossible.

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