# COMPARSION SUDOKU

The Comparison Sudoku is an exciting and challenging variant of the classic Sudoku. Depending on the level of difficulty, there are no given numbers. Instead, the player receives greater-than or less-than symbols as clues, which determine the relationship to the neighboring cell.

Thus this variant differs in terms of the specifications and some solution strategies. However, all other rules of the classic Sudoku apply here as well.

# Terms

## Greater than and less than sign

The greater-than and less-than signs show the relation to the neighboring cell. If the open end of this symbol points in the direction of the neighbor, this means that the numerical value of the neighbor is greater than in the original cell. With the less-than sign, it is exactly the opposite.

## Greater than and less than sign

The greater-than and less-than signs show the relation to the neighboring cell. If the open end of this symbol points in the direction of the neighbor, this means that the numerical value of the neighbor is greater than in the original cell. With the less-than sign, it is exactly the opposite.

# Rules

Besides the mentioned markings between the cells, the Comparison Sudoku follows the standard rules for Sudoku puzzles. These can be found in the Classic Sudoku Game Guide. Before following the solution steps here, it is recommended that you first familiarize yourself with these rules and terms.

Besides the mentioned markings between the cells, the Comparison Sudoku follows the standard rules for Sudoku puzzles. These can be found in the Classic Sudoku Game Guide. Before following the solution steps here, it is recommended that you first familiarize yourself with these rules and terms.

# Solving Steps

## Step 1

For this sample comparison Sudoku, we have eight numbers already revealed. These are the numbers 1 and 9 respectively.

## Step 1

For this sample comparison Sudoku, we have eight numbers already revealed. These are the numbers 1 and 9 respectively.

## Step 2

An intial strategy for comparison sudokus is to find other cells that might contain a 1 or 9. These can be recognized by the fact that the cell is either larger or smaller than all neighboring cells. Attention: this does not necessarily mean that a cell marked in this way automatically corresponds to a 1 or 9. For example, the 3 can also be surrounded by cells that are all larger than the 3 - for example, if the cell is located at the edge of the board.

Fortunately, we already have some defaults in this example sudoku, so finding the first 1 and 9 is considerably easier.

Due to the default nines in cells A6, E7, and G8, the 9 for row 9 can only be in cell B9 or C9. Cell C9 has neighbors that are larger than itself. Therefore, only cell B9 remains as the last possibility for the 9th row.

## Step 2

An intial strategy for comparison sudokus is to find other cells that might contain a 1 or 9. These can be recognized by the fact that the cell is either larger or smaller than all neighboring cells. Attention: this does not necessarily mean that a cell marked in this way automatically corresponds to a 1 or 9. For example, the 3 can also be surrounded by cells that are all larger than the 3 - for example, if the cell is located at the edge of the board.

Fortunately, we already have some defaults in this example sudoku, so finding the first 1 and 9 is considerably easier.

Due to the default nines in cells A6, E7, and G8, the 9 for row 9 can only be in cell B9 or C9. Cell C9 has neighbors that are larger than itself. Therefore, only cell B9 remains as the last possibility for the 9th row.

## Step 3

Using the same strategy, we can uncover the 9 in cell C3. For column 3 in the top left box, only this cell has no neighbors that are larger.

## Step 3

Using the same strategy, we can uncover the 9 in cell C3. For column 3 in the top left box, only this cell has no neighbors that are larger.

## Step 4

By searching further, we can already uncover all the nines in this comparison sudoku.

## Step 4

By searching further, we can already uncover all the nines in this comparison sudoku.

## Step 5

The same strategy helps us to find the first hidden one. For column G, the last two possibilities for the 1 are the cells G1 and G3. Since G1 also has neighbors that are smaller, we know that this cell is out of the question for our 1.

Following this pattern we can solve all still hidden ones.

## Step 5

The same strategy helps us to find the first hidden one. For column G, the last two possibilities for the 1 are the cells G1 and G3. Since G1 also has neighbors that are smaller, we know that this cell is out of the question for our 1.

Following this pattern we can solve all still hidden ones.

## Step 6

It's time to uncover the first number that is neither a 1 nor a 9. Again, the comparison symbols help us to do this. Cell D9 is the only cell in the corresponding box at the bottom center that has no neighbors that are larger. Since we have already uncovered all the nines, we know that in the box itself and also in all possible neighboring boxes there cannot be a larger number in the cell.

## Step 6

It's time to uncover the first number that is neither a 1 nor a 9. Again, the comparison symbols help us to do this. Cell D9 is the only cell in the corresponding box at the bottom center that has no neighbors that are larger. Since we have already uncovered all the nines, we know that in the box itself and also in all possible neighboring boxes there cannot be a larger number in the cell.

## Step 7

Following this pattern, we can also reveal the number 8 for cells E7 and B8. These are cells that have no larger neighbors.

## Step 7

Following this pattern, we can also reveal the number 8 for cells E7 and B8. These are cells that have no larger neighbors.

## Step 8

Using the same procedure, we can uncover or at least narrow down all other eights.

For the 2 in cell F4, we could rule out all other possibilities. This includes the cells D6 and E4, because we have already uncovered all one and therefore know that also in the neighboring boxes no number can be smaller than the searched 2.

## Step 8

Using the same procedure, we can uncover or at least narrow down all other eights.

For the 2 in cell F4, we could rule out all other possibilities. This includes the cells D6 and E4, because we have already uncovered all one and therefore know that also in the neighboring boxes no number can be smaller than the searched 2.

## Step 9

By further comparison with the neighboring cells, we can gradually solve a large part of the Sudoku. In between, the solution strategies from the classic Sudoku also help us here and there.

## Step 9

By further comparison with the neighboring cells, we can gradually solve a large part of the Sudoku. In between, the solution strategies from the classic Sudoku also help us here and there.

## Step 10

With the last numbers to be revealed, we can successfully conclude the comparison sudoku.

## Step 10

With the last numbers to be revealed, we can successfully conclude the comparison sudoku. 