# List of Sudoku variants

Thanks to an explosive surge of Sudoku popularity in the late 2000s, there are a lot of Sudoku variants. Now they have a separate competition called World Sudoku Championship. Since naming everything is probably impossible, here the list of Sudoku variants that have appeared in the WPC is shown. If not noted, rules are from WPC IBs.

Most of the examples are not in penpa form because the author is too dull to type 81 numbers. *Warning: this article is very long, due to large image files for examples.*

### Irregular Sudoku[edit]

Origin unknown. Existed in the 1990s in Japan under the name 幾何学ナンプレ (Geometry Number Place).

Place a digit from 1-9 in each empty cell in the grid such that each row, column and marked **9-celled regions** contains each digit exactly once.

(Example from LMI SM 2021 IB)

### Extra Regions Sudoku[edit]

Origin unknown. Existed in the 1990s in Japan under the name 特別エリアナンプレ (Special Area Number Place).

Place a digit from 1-9 in each empty cell in the grid such that each row, column and marked 3x3 box contains each digit exactly once. Additionally, each marked extra region must contain digits from 1-9.

(Example from LMI SM 2018 IB)

### Killer Sudoku[edit]

Invented by Misawa Miyuki (Japan) in 1994. First appeared in Sep 1994 issue of *Nankuro* magazine under the name サムナンプレ (Sum Number Place).

Place a digit from 1-9 in each empty cell in the grid such that each row, column and marked 3x3 box contains each digit exactly once. The digits placed in each marked cage must sum to the total given in its top-left. Digits must not repeat in cages.

(Example by EctoPlasma)

### Skyscrapers Sudoku[edit]

According to Wei-Hwa Huang, the puzzle exists in the 2004 Japanese Finals.^{[1]} Probably predates it.

Place a digit from 1 to 9 into each of the empty cells so that each digit appears exactly once in each row, column and 3x3 outlined box. Each digit inside the grid represents the height of the skyscraper in that cell. Each number outside the grid represents the number of skyscrapers that can be seen in the corresponding row or column. Taller skyscrapers hide shorter ones.

### Word Search Sudoku[edit]

Invented by Uwe Wiedemann (Germany) in 2006.^{[2]}

Place a symbol from the given set into each of the empty cells so that each symbol appears exactly once in each row, column and 3x3 outlined box. Each given word must appear horizontally, vertically, or diagonally - forward or backward, in the grid.

### Frame Sudoku[edit]

Origin unknown. Existed in 2007 Japanese Qualifier under the name フレームナンプレ (Frame Number Place), but probably predates this.

Place a digit from 1-9 in each empty cell in the grid such that each row, column and marked 3x3 box contains each digit exactly once. Additionally, the clues outside the grid indicate the sum of the first three digits in that direction.

Sometimes (often in a smaller puzzle), "first three digits" is altered to "first two digits".

### Irregular Math Sudoku[edit]

Appeared on WPC 2018. Can be treated as a hybrid with Irregular and Frame.

### Easy as Sudoku[edit]

Or, Regional Easy as. Possibly re-invented many times. Appeared on 2004 Japanese Qualifier.^{[3]}

Place a digit from the given set into each of the empty cells so that each digit appears exactly once in each row, column and 3x3 outlined box. The remaining cells are blank. Each digit outside the grid is the first digit seen from the corresponding direction.

(Rules and example from WPC 2017 IB)

### Sudo-Kurve[edit]

The idea of bent row originates from "Cube Sudoku" by Steve Schafer (USA), first appeared on his website (not available anymore, can be seen here) in 2005. The name was given by Adam R. Wood (USA).^{[4]}

Place a digit from 1-9 in each empty cell in the grid such that each "row" and marked 3x3 box contains each digit exactly once. "Row" here is bent and runs along the curved line.

(Example from Sudokucup 3 IB^{[5]})

### Battleships Sudoku[edit]

There are two different hybrid puzzle types between Sudoku and Battleships.

#### Older version[edit]

Thomas Snyder (USA) published this type on his website in 2006. ^{[6]}

Place a digit from 1 to 9 into each of the empty cells so that each digit appears exactly once in each row, column and 3x3 outlined box. The given fleet of ships must appear in the grid such that ships do not touch each other, even diagonally. Rotation and reflection are allowed but the orientation of digits in the ships remain the same. Ship segments without a digit can contain any digit. Each number outside the grid is the number of ship segments in the corresponding row or column. Cells with given digits are not part of any ship.

(Rules and example from WPC 2017 IB)

#### Newer version[edit]

First appeared on 2014 Moscow Cup. The puzzle was written by Andrey Bogdanov (Russia).

Place a digit from 1 to 9 into each of the empty cells so that each digit appears exactly once in each row, column and 3x3 outlined box. The given fleet of ships must appear in the grid such that ships do not touch each other, even diagonally. Clues outside the grid show the sum of digits occupied by ships in the corresponding row or column.

(Rules and example from WPC 2015 IB)

### Japanese Sums Sudoku[edit]

A hybrid with Japanese Sums. Thomas Snyder (USA) published this puzzle on his website in 2006. ^{[7]}

Place a digit from 1 to 9 into each of the empty cells so that each digit appears exactly once in each row, column and 3x3 outlined box. Shade some cells in the grid such that the numbers outside the grid represent sums of digits in white cells of the corresponding row or column. If there is more than one sum, the given order is valid and there must be at least one shaded cell between the sums. Some shaded cells may be given.

(Rules and example from WPC 2017 IB)

### Paint It Black Sudoku[edit]

A hybrid with Paint by Numbers. Probably first appeared on 2007 WSC at Prague.

Shade some cells such that the numbers outside the grid indicate the number of shaded cells in each shaded stretch in the corresponding row or column. If there is more than one number, the given order is valid and there must be at least one white cell between the stretches of shaded cells. Then transfer the digits from the white cells into the blank grid and solve it as classic Sudoku. Place a digit from 1 to 9 into each of the empty cells so that each digit appears exactly once in each row, column and 3x3 outlined box.

(Rules and example from WPC 2017 IB)

### Mastermind Sudoku[edit]

A hybrid with Mastermind. The earliest instance found is *Mock Test 16* held on Logic Masters India in 2010. ^{[8]} The test was written by Amit Sowani and Kshitij Sharma (India).

Place a digit from 1 to 9 into each of the empty cells so that each digit appears exactly once in each row, column and 3x3 outlined box. The black and white dots to the right of the grid compare the five marked cells in that row to the mastermind code. Black dots imply correct digits in the correct position while white dots imply correct digits in the wrong position. There must not be any repeating digits in the code.

(Rules and example from WPC 2017 IB)

### Sudokuro[edit]

Two puzzles with this name, both hybrids with Kakuro, exist.

#### Older version[edit]

The basic rules were invented by Mark Huckvale (UK) in 2005^{[9]}, though the regions were added later at some point.

Place a digit from 1 to 9 into each of the empty cells so that each digit appears exactly once in each row, column and irregular shaped outlined box. The sum of digits in each horizontal and vertical group of cells is given on its left and top respectively.

(Rules and example from WPC 2017 IB)

#### Newer version[edit]

First appeared on WPC 2010/Part 3 ("MARRIED PUZZLES"). Author of the puzzle was Jan Mrozowski (Poland).

(TBE!)

### Star Battle Sudoku[edit]

A hybrid with Star Battle. The earliest instance found is from 2011 French WPC Qualifier. Author of the puzzle was Denis Auroux (France).^{[10]}

Place a digit from the given set into some of the empty cells so that each digit appears exactly once in each row, column and 3x3 outlined box. All the remaining cells contain stars that do not touch each other, even diagonally.

(Rules and example from WPC 2017 IB)

## Appearances in the past WPCs[edit]

- WPC 2019/Round 9 (Killer Sudoku) by Ulrich Voigt
- WPC 2019/Round 11 (Sudo-Kurve) by Roland Voigt
- WPC 2018/Round 5 (Irregular Math Sudoku) by František Luskač
- WPC 2017/Round 19 (Star Battle, Paint It Black, Word Search) by Amit Sowani
- WPC 2017/Round 19 (Mastermind) by Deb Mohanty
- WPC 2017/Round 19 (Japanese Sums, Sudokuro, Skyscrapers) by Prasanna Seshadri
- WPC 2017/Round 19 (Easy as, Battleships (older)) by Rohan Rao
- WPC 2015/Round 5 (Battleships (newer)) by Andrey Bogdanov
- WPC 2015/Round 9 (Extra Regions) by Vladimir Portugalov
- WPC 2014/Round 10 (Tents-Sudoku-Slitherlink)
- WPC 2013/Part 2 (Sudoku +/-4)
- WPC 2013/Part 9 (Sudoku Snail)
- WPC 2012/Part 8 (Andy's Sudoku)
- WPC 2012/Part 12 (Easy as ABC + Sudoku + Skyscrapers)
- WPC 2011/Part 13 (Sudoku Snail)

## References[edit]

- ↑ http://www.mathpuzzle.com/Sudoku/WeiHwaSudoku.htm
- ↑ http://www.sachsentext.de/en/node/1248
- ↑ http://jpc.puzzler.ne.jp/images/mondai2004.pdf
- ↑ https://www.gmpuzzles.com/blog/sudoku-rules-and-info/sudo-kurve-rules-and-info/
- ↑ http://sudokucup.com/node/740
- ↑ https://motris.livejournal.com/18608.html
- ↑ https://motris.livejournal.com/23949.html
- ↑ https://logicmastersindia.com/lmitests/?test=mock16
- ↑ http://www.markhuckvale.com/games/kakuro/
- ↑ http://people.math.harvard.edu/~auroux/frwpc11/sol4-en.pdf