# CLASSIC SUDOKU

Sudoku is a popular logic-based number puzzle game where the objective is to fill a 9x9 grid with digits so that each column, each row, and each of the nine 3x3 subgrids contain all of the digits from 1 to 9 without repetition.

# Terms

## Cell

Classic Sudokus in size 9x9 contain 81 cells that can have a value between 1 and 9. Some of these cells are predetermined and therefore visible. Others must be discovered by the player through logical considerations.

Even though numbers have become the most common variant, they can also be replaced by letters, symbols or similar. The only requirement is that they are distinguishable alternatives.

## Cell

Classic Sudokus in size 9x9 contain 81 cells that can have a value between 1 and 9. Some of these cells are predetermined and therefore visible. Others must be discovered by the player through logical considerations.

Even though numbers have become the most common variant, they can also be replaced by letters, symbols or similar. The only requirement is that they are distinguishable alternatives.

## Boxes

A 9x9 Sudoku is divided into nine subfields, also known as boxes, containing nine cells on a 3x3 grid. Each number can only appear once in each box. For other Sudoku sizes, the size of the subfield also changes. For example, for a 16x16 Sudoku this is 4x4.

## Boxes

A 9x9 Sudoku is divided into nine subfields, also known as boxes, containing nine cells on a 3x3 grid. Each number can only appear once in each box. For other Sudoku sizes, the size of the subfield also changes. For example, for a 16x16 Sudoku this is 4x4.

## Columns and Rows

For easier navigation, a Sudoku is divided into rows that are labeled with numbers and columns that are assigned letters. This makes it easy to find cells in solution aids, for example.

In the example, column G and row 4 are highlighted. This marks the cell with the coordinates G4.

## Columns and Rows

For easier navigation, a Sudoku is divided into rows that are labeled with numbers and columns that are assigned letters. This makes it easy to find cells in solution aids, for example.

In the example, column G and row 4 are highlighted. This marks the cell with the coordinates G4.

## Pairs

In Sudoku the term pair is used when there are only two possibilities for a number in a box left and they are on the same row or column. If such a pair is known, it excludes the corresponding number for all other cells in the same column or row.

## Pairs

In Sudoku the term pair is used when there are only two possibilities for a number in a box left and they are on the same row or column. If such a pair is known, it excludes the corresponding number for all other cells in the same column or row.

## Givens and revealed cells

On a Sudoku board, the numbers in the cells are either given or have to be revealed by the players.

## Givens and revealed cells

On a Sudoku board, the numbers in the cells are either given or have to be revealed by the players.

# Variants

One Sudoku contains classic Sudoku puzzles in sizes 4x4, 9x9 and 16x16.

Note: 16x16 Sudokus are not available on devices with small screens (for example Example mobile phones).

One Sudoku contains classic Sudoku puzzles in sizes 4x4, 9x9 and 16x16.

Note: 16x16 Sudokus are not available on devices with small screens (for example Example mobile phones).

# Rules

In every Sudoku, each number can only appear once in all boxes, columns and rows. In the example of a 9x9 Sudoku, this means that the numbers 1 to 9 can only be used once in the 3x3 boxes, the rows and columns, each with nine number fields (the cells). If a number has already been given or has been revealed by the player, it can be excluded from all other cells in the column, row or box.

In every Sudoku, each number can only appear once in all boxes, columns and rows. In the example of a 9x9 Sudoku, this means that the numbers 1 to 9 can only be used once in the 3x3 boxes, the rows and columns, each with nine number fields (the cells). If a number has already been given or has been revealed by the player, it can be excluded from all other cells in the column, row or box.

# Solving Steps

## Step 1

In this example, we solve a 4x4 Sudoku puzzle together. All strategies discussed can easily be transferred to other sizes and Sudoku variants. If you have never solved a Sudoku before, the 4x4 variant is a good starting point into the exciting world of this logic puzzle.

In the example, four of 16 numbers are given. The remaining hidden numbers can be found through elimination and other strategies.

## Step 1

In this example, we solve a 4x4 Sudoku puzzle together. All strategies discussed can easily be transferred to other sizes and Sudoku variants. If you have never solved a Sudoku before, the 4x4 variant is a good starting point into the exciting world of this logic puzzle.

In the example, four of 16 numbers are given. The remaining hidden numbers can be found through elimination and other strategies.

## Step 2

Let us first turn our attention to the given 2 in cell D4. Because of this 2, there is only one possibility for B3 to enter the 2 in the neighbouring box on the left. Furthermore, there is also only one possible cell for the 2 in line 3, because the given number at D4 prevents us from entering the 2 in line 3 in the cell C3 or D3.

## Step 2

Let us first turn our attention to the given 2 in cell D4. Because of this 2, there is only one possibility for B3 to enter the 2 in the neighbouring box on the left. Furthermore, there is also only one possible cell for the 2 in line 3, because the given number at D4 prevents us from entering the 2 in line 3 in the cell C3 or D3.

## Step 3

By the newly found 2 at B3 we can furthermore enter the 2 by the same technique at A2 and C1. With this, all twos are already uncovered.

## Step 3

By the newly found 2 at B3 we can furthermore enter the 2 by the same technique at A2 and C1. With this, all twos are already uncovered.

## Step 4

None of the given numbers is a 4. Nevertheless, we can already uncover the first 4. In the upper left box, the numbers at B1 and B2 are hidden. Since the 3 and 2 are already visible in this box, we know that the cells mentioned must contain a 1 and a 4. Thus, we can already rule out the possibility that there is a 4 in column B at another position. To fulfill the rule that all numbers from 1 to 4 must occur exactly once in each box, only cell A4 remains for the 4 in the lower left box.

## Step 4

None of the given numbers is a 4. Nevertheless, we can already uncover the first 4. In the upper left box, the numbers at B1 and B2 are hidden. Since the 3 and 2 are already visible in this box, we know that the cells mentioned must contain a 1 and a 4. Thus, we can already rule out the possibility that there is a 4 in column B at another position. To fulfill the rule that all numbers from 1 to 4 must occur exactly once in each box, only cell A4 remains for the 4 in the lower left box.

## Step 5

By a similar technique we can find the last possibility of all ones. If we follow the only currently revealed 1 at C1, we find the last possible position for the 1 at C4 in the bottom right box. With this 1, we can go up column 3 and find only one possible cell for the 1 in the upper right box at D1. And with this we can also uncover for the box on the left the position of the 1 at B2.

## Step 5

By a similar technique we can find the last possibility of all ones. If we follow the only currently revealed 1 at C1, we find the last possible position for the 1 at C4 in the bottom right box. With this 1, we can go up column 3 and find only one possible cell for the 1 in the upper right box at D1. And with this we can also uncover for the box on the left the position of the 1 at B2.

## Step 6

For column D and the rows 2 and 4 we now have only one possible number left, since all other cells in this column or row are already uncovered. Thus we can enter 4 for D3, 4 for C2 and 3 for B4.

## Step 6

For column D and the rows 2 and 4 we now have only one possible number left, since all other cells in this column or row are already uncovered. Thus we can enter 4 for D3, 4 for C2 and 3 for B4.

## Step 7

To finally solve the Sudoku, we can now determine that a 4 is missing for the upper left box and a 3 for the lower right box. By entering these two numbers, the Sudoku is completely revealed and thus solved.

## Step 7

To finally solve the Sudoku, we can now determine that a 4 is missing for the upper left box and a 3 for the lower right box. By entering these two numbers, the Sudoku is completely revealed and thus solved. 