# Sudoku Variants

### From PuzzleWiki

A Sudoku Variant is a puzzle that is a Variant of Sudoku.

## Contents |

# What is a Variant?

It is debatable what constitutes a Sudoku variant and what is simply a Latin Square-related puzzle, such as Skyscrapers. In their book Sudoku Masterpieces, Thomas Snyder and Wei-Hwa Huang put forth the theory that for a puzzle to be a Sudoku variant, all of the cells (or a large majority of at least 90%) should be contained in at least three "Sudoku-ruled" regions. A "Sudoku-ruled" region is one where the region either has a constraint that no digit can appear more than once in the region, or each digit has to appear at least once in the region, or both (the most common type of "Sudoku-ruled" region).

# Isomorphic

Arguably not true variants, these puzzles are mathematically equivalent to Sudoku.

# Size

These are variants that change the size of the grid in a trivial way. One could consider all of these Irregular Sudoku, as none of them use the standard 3x3 box as regions.

# Mathematics

These are variants that require the solver to understand mathematical properties of the digits.

- Addition
- Killer Sudoku
- Arrow Sudoku
- Magic Sum Sudoku
- Edge Sum Sudoku
- Corner Sum Sudoku (Group Sum Sudoku)
- Partial Sum Sudoku (sum of first three)
- Triangles Sudoku
- Little Killer Sudoku (sum partial diagonals)
- Mini-Diagonal Sudoku (3-diagonals)
- Fixed sums
- 12345-6789
- 1234+567+89
- Split Sudoku (use "split" instead of 9, sums given)
- Sums on Line Sudoku
- Summing across multiple grids
- Scale Sudoku

- Other arithmetic operations
- Difference Sudoku (gray - white)
- Edge Difference Sudoku
- Kropki Sudoku
- Product Sudoku
- Product Last-digit Arrow Sudoku
- Integer Division Sudoku
- Selected Product Sudoku
- Ratio Sudoku
- Factor Sudoku
- LCM Sudoku
- Arithmetic Sequence Sudoku
- Multiplication Sudoku
- Multiplication Table Sudoku (2x2 is multiple)
- Mathdoku (unknown operator)

- Comparison (greater-than/less-than)
- Consecutive
- Arbitrary Subsets
- "View" Constraints
- Frame Sudoku
- Odd-Even/View Sudoku
- Letterraam Sudoku (A through G, "F3" means "3rd is F")
- Where is Max? Sudoku

- Shape Sudoku
- Pencil Marks Sudoku
- Odd-Even Sudoku
- 147 Sudoku
- Star Subset (Starry Sky) Sudoku
- Points to nearest
- Adjacent Odd-Even-Count Sudoku
- Nearest Sudoku (sometimes points to biggest neighbor)
- Pusula (always points to bigger odd neighbor)
- All cells with repeated neighbors are marked
- all cells with neighbors sum to 16 are marked

- Quad Sudoku (same 4-digit "string")
- Main diagonal contains only 3 digits
- Circle Sudoku (4-digit "rotatable" circles)
- 2x2 set Sudoku

- "View" Constraints

# Constraint Count Relaxation

These variants come from relaxing some of the fundamental rules of Sudoku

- "No cell can hold more than one digit"
- 0-9 Sudoku -- first puzzle
- Tight Fit Sudoku
- Double Cairo Sudoku

- "Each cell must be filled with a digit"
- "Each region must have at least one of each digit"
- "No region can have the same digit appear more than once"
- Surplus Sudoku (Ssudoku)

- "Each cell only belongs to one row/column"

# Additional Regions

These variants add additional "sudoku-like" regions.

- 9x9 Grids
- Overlapping 9x9 Grids
- Other "Combined" grids
- Non-9x9 Quadrilateral grids
- Non-quadrilateral grids

# Encodings

These use different encodings of the digits 1-9, allowing for different set-theoretic constraints on what can be in a cell.

# Geometry

These use different geometric connections.

- Standard 9x9 grid, altered regions
- Standard 9x9 grid, extra adjacency constraints
- No-Touch Sudoku
- Knight-Move Sudoku
- Figure Sudoku (Same-Set Sudoku, as seen in Forsmarts)
- Diagonal-same-number Sudoku
- Odd-Labyrinth Sudoku
- Distance Sudoku (distance in row of two digits are given)
- Pairs Sudoku (yellow cells show diagonal matching pairs of distance)

- Square grid, relaxed row-column constraints
- Non-rectangular quadrilaterals
- Isometric Sudoku (Isodoku)
- Penrose Tiles
- Tricorn Sudoku
- Hexacorn Sudoku

- 120-degree-angled rows
- Cylindrical Topology
- Toroidal Topology
- Multi-Dimensional
- Other

# Jigsaw

These use elements of Jigsaw Puzzles.

# Meta

These involve some form of meta-puzzle solving.

# Other Puzzles

These variants cross over with other puzzles.