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A similar form, for younger solvers of puzzles, called "The Junior Sudoku", has appeared in some newspapers, such as some editions of The Daily Mail.
Another common variant is to add limits on the placement of numbers beyond the usual row, column, and box requirements.
Often, the limit takes the form of an extra "dimension"; the most common is to require the numbers in the main diagonals of the grid to also be unique.
The Killer Sudoku variant combines elements of Sudoku and Kakuro. Alphabetical variations have emerged, sometimes called Wordoku ; no functional difference exists in the puzzle unless the letters spell something.
Some variants, such as in the TV Guide , include a word reading along a main diagonal, row, or column once solved; determining the word in advance can be viewed as a solving aid.
A Wordoku might contain words other than the main word. Like the Wordoku, it presents no functional difference from a normal Sudoku, but adds the visual difficulty of using Roman numerals.
It is also known as Windoku because with the grid's four interior regions shaded, it resembles a window with glazing bars. This is one of many possible types of overlapping grids.
The rules for each individual grid are the same as in normal Sudoku, but the digits in the overlapping section are shared by each half. In some compositions neither individual grid can be solved alone — the complete solution is only possible after each individual grid has at least been partially solved.
Puzzles constructed from more than two grids are also common. Often, no givens are placed in the overlapping regions. Sequential grids, as opposed to overlapping, are also published, with values in specific locations in grids needing to be transferred to others.
A tabletop version of Sudoku can be played with a standard card Set deck see Set game. The Times also publishes a three-dimensional version under the name Tredoku.
Many other variants have been developed. One of these is "Greater Than Sudoku". In this variant all of the positions are filled in. Tiles are moved to the proper position to solve the puzzle.
This variant contains power-ups and a campaign mode. The relationship between the two theories is known, after it was proven that a first-order formula that does not mention blocks is valid for Sudoku if and only if it is valid for Latin squares.
A Sudoku puzzle can be expressed as a graph coloring problem. The fewest clues possible for a proper Sudoku is 17 proven January , and confirmed September The maximum number of clues that can be provided while still not rendering a unique solution is four short of a full grid 77 ; if two instances of two numbers each are missing from cells that occupy the corners of an orthogonal rectangle, and exactly two of these cells are within one region, the numbers can be assigned two ways.
Since this applies to Latin squares in general, most variants of Sudoku have the same maximum. This is roughly 1. The number of essentially different solutions, when symmetries such as rotation, reflection, permutation, and relabelling are taken into account, was shown to be just 5,,,  sequence A in the OEIS.
A minimal puzzle is one in which no clue can be deleted without losing uniqueness of the solution. However, statistical techniques combined with a puzzle generator  show that about with 0.
From Wikipedia, the free encyclopedia. For the disease with a similar name, see Sodoku. Logic-based number-placement puzzle. A nonomino or jigsaw Sudoku, as seen in The Sunday Telegraph.
Main article: Killer sudoku. Main article: Mathematics of Sudoku. New York. Retrieved March 4, The Christian Science Monitor.
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Retrieved March 29, The Sydney Morning Herald. Retrieved June 11, Retrieved August 27, Mutant Sudoku. We may also use analytics cookies to test new advertisements, pages, features or new functionality of the Website to see how our users react to them.
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