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# Sudoku Variants: How Many Are There?

It is probably impossible to come up with a definitive list of sudoku variants because the number of them is truly mind-boggling. And there are new types being created all the time. There is also some ambiguity about what counts as a sudoku variant: for instance must a sudoku variant keep the three key constrants such as no number may repeat in a row, column and box, or can one of those constraints (typically the box constraint) be dropped? The answer to that question will either allow a puzzle like futoshiki to be counted as sudoku or not - since futoshiki has no box rule.

The list below looks at several different sudoku variants - how many of these have you come across? It also links to various books where you can play more of each puzzle type, if so inclined. These are in alphabetical order, not in order of popularity!

## List of Sudoku Variants

Consecutive Sudoku

Consecutive sudoku is a fun variant of the standard sudoku puzzle that contains bars between squares of the grid. These bars indicate that squares contain values that are one-more or one-less than each other. For instance, a bar at the edge of a square that contains a 2 means that the neighbour must contain either 1 or 3.

Consecutive sudoku puzzles virtually always mark ALL instances of consecutive digits in the grid. This means that there is also a negative constraint implicit in the puzzle: if the bar is not there, then two squares are NOT consecutive in value: thus if the 2 does not have a bar above it than its neighbour above does NOT contain 1 or 3. Sometimes remembering this constraint is key to solving consecutive sudoku puzzles: it all depends how they are created.

Here's a link to a book we have created that contains 36 consecutive sudoku, along with lots of other sudoku variants: it's our book of Sudoku and Variants 2023.

Jigsaw Sudoku

One of the most common sudoku variants, and also a very popular variant, is jigsaw sudoku. These puzzles contain exactly the same ruleset as standard sudoku, the difference is that the orderly 3x3 box regions are replaced with squiggly shaped regions that join together, like a jigsaw (it is also sometimes called irregular sudoku).

Although the rules are the same, these puzzles are usually harder for humans to solve as it's easier for the eye to keep track of the digits with the orderly 3x3 regions than it is with the weird and wonderful region shapes that can appear with jigsaw sudoku.

Another noted difference with jigsaw sudoku is that every grid pattern is different and thus leads to a different solving experience, this compares to standard sudoku where the grid itself is always the same so purely the numbers and their placement leads to a point of difference.

Like jigsaw sudoku? Here's a book that contains 500 Killer Sudoku puzzles - that's a lot to get through!

Sandwich Sudoku

Sandwich sudoku is a rarely seen variant, and in this version of the game you are given some digits around the edge of the grid outside each row and column. These tell you the sum total of the digits between the 1 and the 9 in the grid, ie the total of the cells that are sandwiched between the 1 and the 9 - hence its name.

For instance, if there is a 0 at the end of a row then you know the 1 and 9 are adjacent in that row with nothing between them. The maximum value possible at the end of a region in a 9x9 grid is 2+3+4+5+6+7+8 = 35, therefore if you see a 35 then you know the 1 and the 9 are pegged to the start and end cells in that region.

Although the rule may not immediately sound interesting, this is actually a variant with a lot of subtlety and depth, and solves quite differently to a standard sudoku puzzle. In fact with most sandwich sudoku puzzles, the puzzle starts with trying to locate the 1 and the 9 in each row and column, so using a shaded pencil (or solving online) to try to locate the 1 and the 9 is an essential element of solving these puzzles. Once they are located, then the puzzle solves more like a standard sudoku.

Intrigued by sandwich sudoku? Then you might like to try the puzzles in our Sandwich Sudoku puzzle book.

Arrow Sudoku

Arrow sudoku is a tricky but visually appealing variant of sudoku, in which the grid contains various arrows (hence the name). With an arrow sudoku the value that is placed in the circled cell of the arrow is the sum of the digits that appear along the body of the arrow. For instance if the circled cell contains 9 and the body contains three cells, then those cells might contain 1,3,5 for instance.

With arrow sudoku digits CAN repeat along the body of the arrow, so long as doing so does not break the standard sudoku rules (thus if all the cells along an arrow are within the same 3x3 box, for instance, then there will be no repetition of values).

These can be tough puzzles, particularly to get started, and typically have few givens. You get really interesting logic too as the possible values for the head constrain the values along the body, and vice versa, so there is a nice back-and-forth possible. This is a puzzle type that really rewards sticking at it and solving various puzzles as you notice more and more logic that can help you make progress the more puzzles you solve.

Interested? Then why not take a look at our book of Arrow Sudoku puzzles that features some 366 puzzles - that will keep you going for a while!

3D Sudoku

There are various types of 3D sudoku puzzles. As the name suggests, these add another dimension to the sudoku-solving experience, although they are still played on a 2D surface - paper. With this version of the puzzle there are regions that bend around the faces of a cube (or on a snowflake), so it helps if you can visualise 3D surfaces whilst solving them.

They also tend to be quite a bit bigger than standard sudoku so although the rules are the same the size combined with the way they are displayed makes them harder to solve. However they are a popular puzzle with those who like an added challenge!

Interested? Take a look at our book of 3D Sudoku Puzzles.

Samurai Sudoku

Samurai Sudoku refers to sudoku puzzles that are composed of two-or-more overlapping grids. These puzzles are obviously larger than standard sudoku puzzles and therefore also typically harder to solve since they can require a lot of searching around the large grid to find out where to make progress.

The size of the samurai grid is in theory unlimited as you can overlap as many grids as you like - the most common size of grid is probably a five-grid samurai sudoku with the five grids forming the shape of a quincunx. However there are puzzles with 2,3,4,5,7,9,11,13 and indeed even more grids overlapping - there is no limit. Some samurai patterns are more squashed together than others, for instance there is another five-grid puzzle called samurai star that has the grids overlapping to such an extent that one grid is fully-formed from regions of the other four grids.

Solving samurai sudoku takes patience and careful thought as to where the regions of one grid end and another start so that you don't accidentally make deductions you are not entitled to do so, or vice versa.

Intrigued by samurai sudoku? Our book of Colour Samurai Sudoku contains 50 fantastic mixed samurai sudoku puzzles: these involve the five overlapping grids in the shape of an X but also contain various other rules, for instance sudoku X, extra regions and so forth.

Border Sum Sudoku

Border Sum sudoku, also sometimes called Frame Sudoku, contains a series of digits around the edge of the grid - hence the descriptive name 'Border Sum'. These sums state the sum value of the first/last three digits in each row/column, so introduce a killer sudoku style element to the solving.

If you'd like to try some border sum sudoku, then you might like to take a look at our Border Sum Sudoku puzzle book.

Killer Sudoku Uncaged

Building on killer sudoku puzzles, comes an even-harder variant of sudoku: killer sudoku uncaged!

With these tricky puzzles the cages themselves have been removed from the grid but the totals remain, so the solver must work out the shape of the cage that contains cells that sum to each digit given, in addition to solving the sudoku puzzle.

These can be tough puzzles to solve, but very rewarding when you manage to get them over the line. Recommended for those who like a tough solving experience - if you think you'd like to give them a go, take a look at our book of Killer Sudoku Uncaged puzzles.

Eliminate Sudoku

Eliminate sudoku is a novel variant of sudoku which does some of the work for you! Rather than starting with an empty grid, apart from some given digits, every square in eliminate sudoku starts with four candidates in it.

You must then decide which of the candidates given for each square is the correct one, and gradually solve the puzzle bit-by-bit making progress as you go along through eliminations: for instance you know that the number 1 must appear once in each row and column and box, so if you find a box that only contains 1 as an option for one of its cells, then you know that cell must contain the 1 - and so on.

Intrigued and like to give it a go? Then check out our book of sudoku | Keywords: sudoku | sudoku variants | arrow sudoku | jigsaw sudoku | killer sudoku | sandwich sudoku | logic puzzles

### Puzzle Videos: Learn to Solve

Sandwich Sudoku Rules
A lovely sudoku variant, sandwich sudoku gives you hints around the edge of the grid as to the location of the 1 and 9 in each row and column. This video explains the rules so you can have a go at this fun but tricky variant...

If you'd like to try this puzzle before watching the video then you can do so here: Sandwich Sudoku Puzzle

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