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:
- Look at the row, column, and 3x3 box containing the cell
- Write down all numbers 1-9 that are NOT already present in those units
- Use small, neat numbers that don't interfere with the main puzzle
- 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- Regularly cleaning up outdated marks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