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sudoku

Sudoku – A single solution, a symmetric sudoku grid

Introducing Sudoku
This fun, easy-to-understand puzzle game has captivated people for nearly 3,000 years.

The object of the game is to fill the Sudoku grid with a sequence of single-digit numbers, each of which appears only once in a given row, column, or 3×3 block. At the start, there are a number of pre-populated cells in the Sudoku grid that act as clues to help the player gradually solve the whole puzzle.

Anyone can play Sudoku. Not involved in the calculation; This is purely a logic game, so you don’t need to be a mathematician to solve Sudoku grids. This explains why Sudoku has become a truly global phenomenon. Millions of people play Sudoku every day!

By definition, a valid Sudoku grid must have one (and only one) solution. We make sure that all our Sudoku grids have a unique solution. While it is easier to design a grid with multiple solutions (or no solutions at all), that cannot be considered a real Sudoku puzzle. As in the case of many logic games, there can be only one answer. Therefore, great care should be taken when designing as even a misplaced number will render the puzzle unsolvable.

There is also an unwritten rule that the beauty of the Sudoku grid lies in the symmetrical distribution, on either side of the two diagonals of the grid, the numbers are pre-filled at the start. This visual harmony is sought after by many of the most avid Sudoku players. Although it is extremely complicated to create symmetric grids, especially ones that are guaranteed to have a single solution, we only designed Sudoku grids with this symmetry. Some of our grids take weeks of computation to develop and we are therefore proud to be able to offer you these single-solver symmetric puzzles. After all, Sudoku isn’t just a game; it’s a philosophy and a way of life where beauty and harmony come first!

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The numbers in Sudoku puzzles are used for convenience only; Arithmetic relationships between these numbers are not relevant. Any distinct set of icons will be; letters, shapes or colors can be used without changing the rules of the game.

The attraction of the game is that the rules are simple, but the line of reasoning to solve the puzzle is complicated. The grids we publish are ranked by difficulty from 1 (easiest) to 5 (hardest). In general, the more numbers given at the beginning, the easier the puzzle will be to solve, and vice versa, although there are some exceptions.

In recent years, Sudoku’s amazing popularity and quick introduction in international newspapers have made Sudoku the favorite puzzle game of the 21st century. Furthermore, many governments encourage people to play Sudoku because the game is considered to have an important role in preventing age-related diseases (especially Alzheimer’s disease).

The Basic Method for Solving Sudoku Puzzles
Rule
Start by snapping a Sudoku grid for each number from 1 to 9. In each block:

Check if the number appears or not;
If a number appears, determine which other squares in the same row or column cannot accept the number;
If the number does not appear, determine which other squares cannot accept the number, with a different occurrence of the same number in other blocks in the same row and column.
When there’s only one possible value for a row, column, or block, this is where the numbers come in. With a little experience, you should be able to visualize the squares where the number might appear as if the number were “lit” on the Sudoku grid. This will allow you to detect more advanced configurations.

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If Sudoku can be solved with just basic strategies, experienced players may not need to write down the squares.

Unique number
A “unique number” is the usual case where there is only one blank cell in an “area” (row, column, or block). In this case, the numeric value of that cell should be the missing number in the range: that is the only place where the missing number can be filled (unknown number) and the only value that a blank cell can accept (the number of only obvious).

This configuration occurs most often near the end of a puzzle, when nearly all the Sudoku tiles are filled.

More generally, the term “unique number” refers to a situation in which there is only one solution for a particular square, even if that cell can only accept a single value (the unique number displayed). course) or because a value can only be in a single square (unique unknown), since any other choice would lead to an immediate mismatch. Unique numbers differ from “pair of numbers,” “triple of numbers,” and “triple of numbers,” in that there can be several potential values ​​of the same match.

Knockout: Hide Unique Numbers
When searching for a “unique unknown”, the question to ask is: “In this region (row, column or block), which square is likely to accept 1 (2, 3 … 9)?” If a response appears only once in the search range, the number must be the value for the cell.

The more often the value appears in the Sudoku grid, the easier it is to find the unique unknowns; as location restrictions increase, the number of possible locations decreases.

Marking potential values ​​in cells is of limited help when searching for unique unknowns; you will still need to capture the entire “region” to check that the value you are looking for only appears as a potential value once. This is why these unique numbers are called “hidden.”

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In contrast, the “unique unknown” is often easy to find by capturing all the numbers and blocks, since the position depends only on the position of the number to be found in the neighboring blocks and on whether the squares of the required block search is available or filled in.

Indirect Type:
Indirect type is an extension of knockout.

While snapping a Sudoku grid to locate potential squares for a particular answer, you may find that all the available squares in a block are in the same row (or column). In that case, regardless of the final position of the potential value in the block, the value cannot appear in any other available squares in the same row (or column) in other blocks. In other words, if the squares in a block are all in the same row, that value can be excluded from the other available squares in the whole row.

Similarly, when the coefficients are limited to two rows (or columns) in two adjacent blocks, the potential values ​​of the third block can appear only in the third row (or column).

This limit can help determine the unique unknown. In a more subtle way, it can also be concluded that, in another block along the same row (or column), potential values ​​can only be placed in one row or one column. This will create an indirect chain reaction. Thus, this initial indirect removal can be performed without marking the squares; However, this requires more logical thinking.

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