Sudoku DG – Easy

Sudoku DG

Sudoku DG is a variation of classic Sudoku. DG typically stands for "Disjoint Groups." Besides rows, columns, and 3x3 blocks, there is an additional rule: cells with the same relative position within the nine 3x3 blocks also form a group. Each of these groups must contain the numbers 1 through 9 exactly once.

In many representations, these groups are color-coded. All cells with the same color belong to a Disjoint Group. This additional rule acts like nine more hidden regions and is often the most important entry point.

Basic Rules

• Each row must contain the numbers 1 through 9 exactly once.
• Each column must contain the numbers 1 through 9 exactly once.
• Each 3x3 block must contain the numbers 1 through 9 exactly once.
• Additionally, all cells with the same position within their 3x3 blocks form a Disjoint Group.
• Each Disjoint Group must also contain the numbers 1 through 9 exactly once.
• A cell belongs to four areas: row, column, 3x3 block, and Disjoint Group.

Strategies for Solving

The most important difference from traditional Sudoku is the fourth check group. A candidate can be eliminated even if it is still allowed in its row, column, and block, but already exists in the matching Disjoint Group.

1. Using a Nearly Complete Disjoint Group

In the following example, we consider the middle cells of all nine 3x3 blocks. These nine cells form a Disjoint Group.

In the considered cells, numbers 1, 2, 3, 4, 5, 6, 7, and 9 already appear. The only missing number is 8.

This conclusion would not be visible in normal Sudoku. It arises exclusively from the DG rule.

2. DG Rule as a Candidate Elimination

A cell can be restricted by its Disjoint Group even if the number still appears possible in the row, column, and block.

Looking again at the middle position of the 3x3 blocks, the number 1 is already present in this group. Another cell with the same relative position therefore cannot be a 1. The DG rule thus removes candidates before a cell is necessarily solved.

Sudoku DG becomes particularly powerful when a cell is simultaneously restricted by the block and the Disjoint Group.

Typical Solving Process

1. First check rows, columns, and 3x3 blocks as in classic Sudoku.
2. Next, consider the nine Disjoint Groups.
3. Look for Disjoint Groups that already contain many numbers.
4. Eliminate candidates that already appear in the associated Disjoint Group.
5. Combine DG eliminations with block and column logic.
6. Check all four areas for each entry.

Common Mistakes

• Treat Disjoint Groups like additional 3x3 blocks. They are not made of neighboring cells but of cells with the same position in different blocks.
• Only check rows, columns, and blocks, and forget color or position cues.
• Assign the same number twice in the same Disjoint Group.
• Incorrectly determine the relative position, confusing top-left with top-middle, for example.

Tips for Beginners

• Choose a position, for example all middle cells of the blocks, and check that group thoroughly.
• Work with colors or markings if the puzzle offers them.
• For each cell, additionally ask: Which number already appears at the same block position in other blocks?
• DG conclusions are often subtle but very strong.

Sudoku DG extends classic Sudoku with an additional layer of order. The colors or matching block positions provide new eliminations and make the puzzle significantly more interesting.