Chain Sudoku – Hard

Chain Sudoku

Chain Sudoku uses a 9x9 grid with numbers 1 to 9. Unlike classic Sudoku, the focus here is not on the 3x3 blocks but on the drawn chains. The cells are connected by lines to form chains. Each chain forms its own region.

The basic idea remains similar to Sudoku: each row, each column, and each chain contains the numbers 1 to 9 exactly once. The chains thus take on the role of the regions. Therefore, the actual course of the line in the puzzle is more important than a square block.

Basic Rules

• The playing field consists of 9 rows and 9 columns.
• Each row contains the numbers 1 to 9 exactly once.
• Each column contains the numbers 1 to 9 exactly once.
• The connected cells of a chain form an additional region.
• Each chain contains the numbers 1 to 9 exactly once.
• The chains are not just auxiliary lines but real regions of the puzzle.
• The chains can run straight, bend, or cross multiple rows.
• The given numbers cannot be changed.

Strategies for Solving

1. Treat a chain like a region

If eight numbers are known in a chain, the last cell is unambiguous.

The chain already contains the numbers 1, 2, 3, 5, 6, 7, 8, and 9. The only missing number in this chain is 4. Therefore, the empty chain cell in row 1, column 4 must be a 4.

This step is clear because the chain must contain the numbers 1 to 9 exactly once as a region. No guesswork is involved.

2. Combine chains and columns

A cell always belongs to three areas: its row, its column, and its chain. This means a number can be missing in the chain but still be excluded from a potential cell because it already appears in the row or column.

The chain is the same as in the previous example. Considering only the chain, the missing 4 would be the target. Additionally, column 4 already shows a 4 outside of the chain. This confirms that the 4 should not be placed in any other cell in this column. In Chain Sudoku, this combination of chain rule and column rule is particularly important.

3. Carefully track the course of the chain

The biggest difficulty in Chain Sudoku is often not the rule but the overview. A chain can run around a corner and continue in another row. Therefore, a chain should always be fully tracked before drawing a conclusion.

Typical solving process

1. Start by checking rows and columns with many numbers.
2. Then look for chains where many numbers are already present.
3. Note the missing numbers in each important chain.
4. Compare potential chain cells with their rows and columns.
5. Enter only numbers that fit uniquely in the row, column, and chain.

Common mistakes

<li Partially tracking a chain and thus assuming an incorrect region.
• Confusing chains with normal 3x3 blocks.
• Entering a number that fits the row but already appears in the chain.
• Not updating candidates after each new entry.
• Guessing too early instead of using the chain rule as a reliable elimination.

Tips for Beginners

• Start with chains where many numbers are already given.
• Follow the course of the chain completely before determining missing numbers.
• Always check the row, column, and chain together for each cell.
• If stuck, look not only for almost complete rows but also specifically for almost complete chains.

Chain Sudoku feels familiar but requires a different mindset about regions. Those who track the chains carefully can make many safe deductions directly from the connected cells.