How to Use Pencil Marks in Sudoku - SudokuPuzzles.net

Pencil marks are one of the most essential tools for solving Sudoku puzzles, especially as they become more challenging. This technique involves writing small numbers in empty cells to track which numbers could potentially fit there. Mastering pencil marks will dramatically improve your solving efficiency.

What Are Pencil Marks?

Pencil marks (also called candidates or notes) are small numbers written in the corners or edges of empty cells to indicate which numbers could potentially fit in that cell. They help you visualize all possibilities and identify patterns that would otherwise be invisible.

When to Use Pencil Marks

You should start using pencil marks when:

• You can't find any obvious single candidates
• The puzzle becomes complex enough that you can't keep track mentally
• You're working on puzzles rated "Medium" or harder
• You want to identify advanced techniques like hidden pairs or X-Wing

How to Add Pencil Marks

To add pencil marks to a cell:

1. Look at the row, column, and 3x3 box containing the cell
2. Write down all numbers 1-9 that are NOT already present in those units
3. Use small, neat numbers that don't interfere with the main puzzle
4. Update pencil marks whenever you place a number

Pencil Mark Notation Systems

There are several ways to write pencil marks:

• Corner notation: Write numbers in the corners of cells
• Center notation: Write numbers in the center of cells
• Digital notation: Use online tools that automatically track candidates

Using Pencil Marks to Find Patterns

Once you have pencil marks, you can identify:

• Naked singles: Cells with only one candidate
• Hidden singles: Numbers that can only go in one place
• Naked pairs/triples: Groups of cells with the same candidates
• Hidden pairs/triples: Numbers that can only go in specific cells

Maintaining Pencil Marks

Keep your pencil marks accurate by:

• Removing candidates when you place a number
• Updating related cells when you eliminate possibilities
• Using different colors or symbols for different types of marks
• Regularly cleaning up outdated marks

Advanced Pencil Mark Techniques

For very difficult puzzles, consider:

• Coloring: Use different colors to track chains
• Symbols: Use special symbols for certain patterns
• Grouping: Mark cells that belong to the same pattern

Practice Tips

To improve your pencil mark skills:

• Start with easier puzzles to build confidence
• Practice regularly to develop speed and accuracy
• Use consistent notation that works for you
• Don't be afraid to erase and start over if marks become messy