Sudoku (Japanese su: doku ?, pronunciation (inf.) - "lonely number") is a popular number puzzle. Translated from Japanese "su" means "digit", "dook" means "standing apart". Sometimes Sudoku is called the "magic square", which is generally not true, 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 9x9 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 free 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 online Sudoku does not depend on the number of initially filled cells, but 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 crosswords 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 puzzles problem on an N² × N² field is NP-complete, since the problem of filling a Latin square is reduced to it.

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 was no uniquely solvable 16-clue Sudoku.

Solution search methods

It is recommended to use a pencil for solving Sudoku as the pencil can be easily erased in case of a mistake. Puzzle-solving skills come with practice gradually.

The best solution is to write down the candidate numbers at the top of the left corner of the cell, and then cross out the impossible numbers from this cell. After that, you can see exactly the numbers that can occupy this cell. It is recommended to play Sudoku slowly as it is a relaxing game. Some web Sudoku puzzles can be solved in minutes, but others can take hours or, in some cases, even days. A correctly formed puzzle has only one solution. (However, there are cases where cyclic permutations among some numbers are possible, in which the solution goes to another solution than the first. This is due to the fact that not enough numbers were given in the original puzzle.)

First, they look at the rows, columns and 3 × 3 blocks with the most filled squares: it is easier to solve where there are fewer options. When filling a cell, you need to check the column, row and 3 × 3 block. It is necessary to check that all other 8 numbers are not duplicated. It is easier to avoid mistakes early in the game than when there is a contradiction in a solved puzzle. If a column and a row have one blank cell, then fill it in. When filling in rows and columns, exclude numbers that have already been entered.

Useful resources:

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