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Sudoku Variants


Although the 9x9 grid with 3x3 regions is by far the most common, numerous variations abound: sample puzzles can be 4x4 grids with 2x2 regions; 5x5 grids with pentomino regions have been published under the name Logi-5; the World Puzzle Championship has previously featured a 6x6 grid with 2x3 regions and a 7x7 grid with six heptomino regions and a disjoint region. Even the 9x9 grid is not always standard, with Ebb regularly publishing some of those with nonomino regions. Larger grids are also possible, with Dell regularly publishing 16x16-grid Number Place Challenger puzzles and Nikoli proffering 25x25 Sudoku the Giant behemoths. Another common variant is for the numbers in the main diagonals of the grid to also be required to be unique; all Dell Number Place Challenger puzzles are of this variant.

Five 9x9 grids which overlap at the corner regions in the shape of a quincunx is known in Japan as Gattai 5 (five merged) Sudoku. In The Times this form of puzzle is known as Samurai Su Doku.

A three-dimensional Sudoku puzzle was invented by Dion Church and published in the Daily Telegraph in May 2005.

Alphabetical variations, which use letters rather than numbers, have also emerged. The Guardian calls these Godoku and describes them as .devilish'. Others title them Wordoku. The required letters are given beneath the puzzle. Once arranged they spell out a topical word between the top left and bottom right corners. This adds an extra dimension to Sudoku as it may be possible to guess what the word is, indicating what some of the unfilled cells might be.

Other variants common in Japanese magazines include, but are not limited to:

  • Sequentially connected puzzles: several standard 9x9 puzzles are solved consecutively. Only the first puzzle has enough givens to be solved on its own; once the first puzzle is solved, one or more numbers are transferred from its solution to the starting grid of the second, etc. In some cases, the solver must work back and forth between partially completed puzzles.
  • Very large puzzles made up of multiple overlapping puzzles (usually, but not always, 9x9s). Puzzles made up of 20 to 50 or more standard grids are not uncommon. The region of overlap varies x two 9x9s may share 9, 18, or 36 cells. Often, there are no givens in overlapped areas.
  • Otherwise standard puzzles in which each cell is a member of four groups rather than the normal three (rows, columns, and regions): digits with the same relative location within their respective regions must not match. Such puzzles are usually printed in colour, with each disjoint group sharing one colour for clarity.
    The 2005 U.S. qualifier for the World Puzzle Championship includes a variant called Digital Number Place: rather than givens, most cells contain a partial given - a segment of a number, with the numbers drawn as if part of a liquid crystal display.
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