Sudoku Notation Guide
Notation is the language of Sudoku solving. Whether you are reading a technique guide, tracking candidates on a tough puzzle, or discussing strategy with other solvers, understanding the different notation systems helps you communicate clearly and solve more effectively. This guide covers the four most important notation systems every Sudoku player should know.
Why Use Notation?
Good notation transforms Sudoku from a memory challenge into a visual logic puzzle. Here is why it matters.
Reduce Mental Load
Writing down candidates means you do not have to hold them all in your head. This frees your mind to focus on pattern recognition and logical deductions instead of memorization.
Enable Advanced Techniques
Techniques like naked pairs, X-Wings, and coloring are impossible without written candidate information. Notation is the foundation of every intermediate and advanced solving method.
Catch Mistakes Early
When all candidates are visible, errors become obvious. A missing candidate or an impossible placement stands out immediately, letting you correct course before the mistake propagates through the grid.
Communicate with Other Solvers
Standard notation like RnCn lets you discuss cells, techniques, and solutions with other players unambiguously. It is the shared language of the Sudoku community.
1. Row-Column (RnCn) Notation
Row-column notation is a standardized way to reference any cell on the Sudoku grid. Each cell is identified by its row number and column number, written as RnCn. Rows are numbered 1 through 9 from top to bottom, and columns are numbered 1 through 9 from left to right. For example, R1C5 refers to the cell in the first row and fifth column, which is the center cell of the top row.
When to Use
Use RnCn notation when discussing specific cells in written guides, forum posts, or solver output. It is essential for communicating puzzle logic clearly with other solvers because it removes all ambiguity about which cell you mean. You will encounter it frequently in technique tutorials, puzzle walkthroughs, and competition discussions.
How It Works
Count the row from the top of the grid. The topmost row is row 1 and the bottommost row is row 9.
Count the column from the left of the grid. The leftmost column is column 1 and the rightmost column is column 9.
Combine them as RnCn. For instance, the cell in row 4, column 2 is written as R4C2.
To reference a box, use B followed by the box number (1 through 9). Boxes are numbered left to right, top to bottom. The top-left box is B1, the top-center box is B2, and so on.
You can combine references for clarity. For example, 'R4C2 in B4' tells the reader exactly where to look and confirms the box context.
Pros
- +Universally understood across the Sudoku community
- +Completely unambiguous: every cell has a unique reference
- +Essential for written communication and solver logs
- +Works for any grid size, not just standard 9x9
Cons
- -Not used during actual solving on paper or in apps
- -Can feel verbose when describing many cells at once
- -Requires counting rows and columns, which takes practice to do quickly
2. Pencil Mark / Full Candidate Notation
Full candidate notation involves writing every possible value as a small number inside each empty cell. When you first set up the grid, you analyze each empty cell and list every digit from 1 to 9 that is not already present in the same row, column, or box. As you apply solving techniques, you eliminate candidates until cells are reduced to a single value, at which point you can fill in the answer.
When to Use
Use full candidate notation for any puzzle rated hard or above. It is the foundation of all advanced solving techniques because methods like naked pairs, X-Wings, and coloring require you to see every candidate in every cell. Even on medium puzzles, pencil marks help you avoid mistakes and spot patterns faster.
How It Works
Start with any empty cell. Check its row, column, and 3x3 box to see which digits (1 through 9) are already placed.
Write the remaining digits as small numbers inside the cell. Many solvers write them in a 3x3 grid pattern within the cell: 1-2-3 on top, 4-5-6 in the middle, 7-8-9 on the bottom.
Repeat for every empty cell in the puzzle. This initial setup takes a few minutes but pays off immediately.
Whenever you place a solved digit, remove that digit from all pencil marks in the same row, column, and box.
After every elimination, check if any cell has been reduced to a single candidate (a naked single). If so, place that digit and continue eliminating.
Periodically scan for hidden singles: a candidate that appears only once in a row, column, or box, even if the cell has multiple pencil marks.
Pros
- +Provides complete information for every cell at a glance
- +Required for intermediate and advanced solving techniques
- +Eliminates guesswork by making all possibilities visible
- +Helps you catch errors early because missing or extra candidates stand out
Cons
- -Time-consuming to set up for the entire grid
- -Can make the grid look cluttered, especially early on
- -On paper, erasing and rewriting can get messy
- -Overkill for easy puzzles where scanning alone is sufficient
3. Snyder Notation
Snyder notation, named after competitive puzzle solver Thomas Snyder, is a minimalist marking system. Instead of writing all candidates in every cell, you only mark a candidate when it is restricted to exactly two cells within a 3x3 box. These marks are placed in the corners of the cell to distinguish them from solved values. The result is a much cleaner grid that still captures the most useful information for solving.
When to Use
Use Snyder notation for easy and medium puzzles where you want to keep the grid clean while still tracking key restrictions. It is especially popular in speed-solving because you can mark far fewer cells while still spotting pairs, pointing pairs, and box-line reductions. Many solvers start with Snyder notation and transition to full candidates only when they get stuck.
How It Works
For each 3x3 box, consider each missing digit one at a time.
Check if that digit can go in only two cells within the box (the row and column constraints eliminate all other positions).
If yes, write that digit as a small number in the corner of both cells. Use consistent corner positions: top-left corner for smaller digits, bottom-right for larger ones, though any consistent system works.
If a digit can go in three or more cells within the box, do not mark it yet. Only two-candidate restrictions are marked in Snyder notation.
As you place digits and the grid evolves, some three-candidate situations will become two-candidate situations. Add Snyder marks as this happens.
When you need more detail than Snyder provides, transition to full candidate notation for the remaining unsolved cells.
Pros
- +Keeps the grid clean and readable
- +Much faster to set up than full pencil marks
- +Sufficient for easy and most medium puzzles
- +Pairs and pointing pairs are immediately visible
- +Popular in speed-solving competitions
Cons
- -Incomplete: does not capture all candidate information
- -Insufficient for advanced techniques like X-Wing or Swordfish
- -Requires a transition to full marks on harder puzzles
- -Beginners may struggle to judge which marks to add
4. Center Marks vs Corner Marks
Center marks and corner marks are two different purposes for small numbers written in cells, and understanding the distinction is crucial for effective notation. Center marks list the remaining candidates for a specific cell, answering the question 'what values can this cell hold?' Corner marks indicate that a particular digit is restricted to specific cells within a box, answering the question 'where can this digit go in this box?' Many digital Sudoku apps support both types, and experienced solvers often use them together.
When to Use
Use center marks when you are doing full candidate analysis and need to track every possibility for each cell. Use corner marks when you are applying Snyder notation or want to track box-level restrictions. The most effective approach for hard puzzles is to combine both: corner marks for quick Snyder-style box analysis and center marks for detailed cell-level candidate tracking.
How It Works
Center marks: Write candidates in the center of the cell. In apps, these usually appear as a cluster of small numbers in the middle. They represent every digit that cell could be.
Corner marks: Write candidates in the corners of the cell. In apps, these appear in the top-left, top-right, bottom-left, or bottom-right corners. They represent Snyder-style box restrictions.
When a center-marked cell is reduced to one candidate, that cell is solved. Fill in the digit and update all related cells.
When a corner-marked digit is placed somewhere in the box, remove the corner marks for that digit from all cells in the box.
To combine both: use corner marks first for a clean Snyder pass. When you get stuck, add center marks to the remaining unsolved cells for full candidate analysis.
In digital apps, the two types are usually entered with different buttons or key modifiers. Learn your app's specific controls to use both efficiently.
Pros
- +Using both gives you the most complete picture of the puzzle
- +Corner marks keep Snyder information visually separate from cell candidates
- +Center marks support all advanced solving techniques
- +Digital apps handle the visual layout automatically
Cons
- -On paper, mixing both can make cells hard to read
- -Requires understanding the conceptual difference between the two
- -Different apps implement the distinction differently, which can cause confusion
- -More marks to maintain means more opportunities for bookkeeping errors
Which Notation Should You Use?
The right notation depends on the puzzle difficulty and your solving goals. Use this decision flow to choose the best approach.
Easy puzzles: No notation needed
If the puzzle is rated easy, try solving it with scanning alone. Look for naked singles and hidden singles without writing anything down. This builds your pattern recognition skills.
Medium puzzles: Start with Snyder notation
Snyder notation gives you just enough information to spot pairs and pointing pairs without cluttering the grid. Mark candidates only when a digit is restricted to two cells in a box.
Hard puzzles: Full pencil marks from the start
Hard puzzles require techniques like naked pairs, hidden triples, and box-line reduction. These techniques depend on having complete candidate information, so fill in all pencil marks before you begin solving.
Expert and evil puzzles: Full marks with both center and corner
The hardest puzzles benefit from using corner marks for Snyder-style box analysis alongside center marks for full candidate tracking. This dual system gives you the most information with the clearest visual organization.
Speed solving: Snyder first, then transition
Competitive solvers often start with Snyder notation for speed, then switch to full candidates only if needed. This hybrid approach minimizes setup time while still providing full information when the puzzle demands it.
Frequently Asked Questions
What are pencil marks in Sudoku?
Pencil marks are small numbers written inside empty cells to track which candidates (possible values) remain for that cell. In full candidate notation, you write every possible number that has not been eliminated by the row, column, or box constraints. As you solve, you erase candidates that are no longer valid until only one remains.
What is Snyder notation and when should I use it?
Snyder notation is a streamlined marking system where you only write a candidate in a cell when that number is restricted to exactly two places within a 3x3 box. The marks are placed in the corners of the cell. This keeps the grid much cleaner than full pencil marks and is usually sufficient for easy and medium puzzles.
What is the difference between center marks and corner marks?
Corner marks (used in Snyder notation) indicate that a number must go in one of the marked cells within a box. They answer the question 'where can this number go in this box?' Center marks list the remaining candidates for a specific cell. They answer the question 'what can go in this cell?' Many solvers use both at the same time.
What does R3C7 mean in Sudoku?
R3C7 is row-column notation that refers to the cell at row 3, column 7. Rows are counted from top to bottom (1 through 9) and columns from left to right (1 through 9). This notation is commonly used in written Sudoku guides, solver output, and online discussions to unambiguously identify any cell on the grid.