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## @kevingreen

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**History of Sudoku**

Sudoku (Japanese 数 独 su: doku, pronunciation (inf.)) Is a puzzle with numbers. Sometimes Sudoku is called the magic square, which is generally incorrect, since Sudoku is a 9th order Latin square. Sudoku is actively published by newspapers and magazines from around the world, collections of Sudoku are published in large circulations. Sudoku solving is a popular leisure activity.

**Rules**

The playing field is a 9 × 9 square, divided into smaller squares with a side of 3 cells. Thus, the entire playing field consists of 81 cells. At the beginning of the game, they contain some numbers (from 1 to 9), called hints. The player is required to fill the empty cells with numbers from 1 to 9 so that in each row, in each column and in each small 3 × 3 square, each number would appear only once.

The difficulty of Sudoku depends on the number of initially filled cells and on the methods that need to be used to solve it. The simplest ones are solved deductively: there is always at least one cell where only one number fits. Some puzzles can be solved in minutes, others can take hours.

A correctly formed puzzle has only one solution. Nevertheless, on some sites on the Internet, under the guise of complicated puzzles, the user is offered Sudoku options with several solutions, as well as branches of the solution itself.

**Origin**

In the 18th century, Leonard Euler invented the game "Carré latin" (Latin square). Based on this game, special number puzzles were invented in North America in the 70s of the last century. So, in the USA Sudoku appeared for the first time in 1979 in Dell Puzzle Magazine. Then it was called "Number Place". Sudoku gained real popularity in the 1980s and 1990s, when the Japanese magazine Nikoli began to regularly publish this puzzle on its pages (since 1986). Sudoku is a must-have feature in many newspapers today. Among them there are many publications with multimillion circulation, for example, the German newspaper "Die Zeit" [, the Austrian "Der Standard". The Russian newspaper Trud also publishes Sudoku.

**Mathematical basis**

The generalized sudoku problem on the {\ displaystyle N ^ {2} \ times N ^ {2}} [{\ displaystyle N ^ {2} \ times N ^ {2}}] field is NP-complete because it reduces the problem about filling the Latin square.

For a long time, the question of the minimum number of clues required for an unambiguous solution to Sudoku has remained open. In particular, it was not known if there was a uniquely solvable 16-clue Sudoku. The distributed computing project Sudoku @ vtaiwan on the BOINC platform was looking for such a Sudoku. In January 2012, evidence emerged that there were no uniquely solvable 16-clue Sudoku.

**Varieties**

There are many variations of Sudoku:

Irregular Sudoku (also called Sudoku online, free Sudoku easy, Areas). This puzzle uses freeform regions instead of the standard 3x3 areas. The numbers should not be repeated in every such area. Sudoku in different sizes. There are sudoku sizes from 4x4 (such smaller puzzles are called "Shidoku" from Japanese shi - four) to 25x25. The most common Sudoku for children is small.

Sudoku with additional areas. In these tasks, in addition to standard areas (verticals, contour lines and blocks), additional areas are set in which numbers cannot be repeated. The most common are diagonal sudoku. Sudoku with additional conditions. In such problems, in addition to the standard condition for the non-repeatability of digits, additional conditions are set on the values. For example: Sudoku "Sums" and many of its variations ("Sudoku-Works", "Sudoku-Arithmetic", "Quadrudoku", "Sums-side", "Diagonal Sums", etc.), where the whole field is divided into blocks, for which the sum (product, difference, etc.) of all the digits included in it is reported.

Odd and Odd Sudoku. In them, some cells are initially highlighted in color, in these cells there are either only even or only odd numbers.

Over-less Sudoku. For some neighboring cells, a sign is indicated, indicating which of the cells has a higher number. Sudoku "Points", where a point of white or black color is displayed between adjacent cells, when adjacent numbers differ by 1 or 2 times.

Sudoku "Partitions" ("Sudoku-Neighbors"), where all places with numbers in neighboring cells differ by 1 are marked. Sudoku of a different form. The puzzle does not use a square grid, but a triangular, hexagonal or more sophisticated shape.

Linked Sudoku. "Sudoku-Samurai" ("Sudoku-Combo", "Sudoku-Constructions", "Tudoku", etc.), in which several separate Sudoku have common blocks and are solved interdependently.

**Useful Resources:**

Is it useful to solve Sudoku?

The benefits of Sudoku and crosswords have been proven! Regular puzzle solving rejuvenates the brain by 10 years

Sudoku - history, tactics, description and interesting facts.

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