Sudoku Notation Systems: How to Read and Write Puzzle Solutions

Every serious Sudoku solver eventually encounters notation—the standardized systems for describing cells, candidates, techniques, and entire puzzles. Whether you’re reading a strategy guide, sharing a puzzle with a friend, or entering a competition, understanding Sudoku notation is essential. This guide covers every major notation system you’ll encounter, from the ubiquitous R1C5 cell references to 81-character strings for digital puzzle sharing.

Why Notation Matters

Notation serves three critical purposes in Sudoku:

1. Communication. When strategy guides describe a technique like “R3C7=4 because of a hidden single in Box 3,” you need to know what R3C7 means to follow along.
2. Solving aid. Pencil mark notation in your own grid is the most important practical tool for solving medium and harder puzzles.
3. Sharing and archiving. Standard formats let you share puzzles across platforms, import them into solvers, and archive them efficiently.

Whether you’re a casual solver or an aspiring competitor, fluency in notation makes you a more effective and knowledgeable player.

Standard Cell Reference Notation (RxCy)

The most widely used system for identifying individual cells is RxCy notation, where R stands for Row and C stands for Column, both numbered 1–9 from top to bottom and left to right.

To indicate a placement, append the digit with an equals sign: R1C5=3 means “the digit 3 is placed in Row 1, Column 5.”

Regions are referenced as:

• R1 through R9: Rows 1–9
• C1 through C9: Columns 1–9
• B1 through B9: Boxes 1–9, numbered left to right, top to bottom

Box numbering follows this layout:

This notation is used in virtually all English-language Sudoku resources, strategy guides, solver outputs, and forums. Master it and you can follow any written Sudoku discussion.

Pencil Mark Notation

Pencil marks (also called candidates or notes) are the notation you use while solving. They represent the possible digits for each empty cell based on current constraints.

How to Write Pencil Marks

In each empty cell, write small numbers representing every digit that could legally occupy that cell based on current row, column, and box constraints. The standard approach uses a positional system within the cell:

1 2 3
4 5 6
7 8 9

Each candidate goes in its corresponding position. If a cell could contain 1, 3, or 7, you’d write small numbers in the top-left, top-right, and bottom-left positions of the cell. If a cell could contain only 4 and 8, only those two positions are filled.

This positional system lets you scan for patterns without reading individual digits. You can spot a naked pair by seeing two cells with marks in the same two positions, or identify an X-Wing by seeing a digit’s candidacy forming a rectangle across the board.

Corner vs. Center Marks

Some digital Sudoku apps distinguish between two types of pencil marks:

• Corner marks (candidates): Small digits placed in the corners or standard positions, representing all possible values for the cell.
• Center marks (shorthand): Larger digits placed in the cell’s center, typically used when you’ve narrowed a cell to 2–3 candidates and want a more visible reminder.

The distinction is a digital convenience—on paper, most solvers use only one type of mark in the positional system described above.

Full vs. Partial Notation

• Full notation: Writing candidates in every empty cell at the start, then updating as you make eliminations. This is the recommended approach for medium and harder puzzles. It takes a few minutes upfront but saves far more time by making all patterns visible.
• Partial notation: Writing candidates only in cells or regions where you’re actively working. Faster to set up but risks missing eliminations in areas you haven’t notated.

For a detailed discussion of how notation affects solving speed, see how to get faster at Sudoku.

Hodoku Notation

Hodoku is a popular open-source Sudoku analysis program, and its notation format is widely used in online forums and discussion groups. Hodoku notation extends the standard RxCy system with specific conventions for describing techniques.

Hodoku Technique Descriptions

Hodoku describes solving steps in a structured format:

• Placements: R3C7=4 (Hidden Single in Row 3)
• Eliminations: R3C7<>4 (eliminated by Naked Pair in Row 3)
• Techniques: Naked Pair: 3,7 in R2C4,R2C8 => R2C1<>3, R2C1<>7

The arrow => separates the pattern from its consequences. The <> symbol means “cannot be” (an elimination).

This format is precise enough to describe any solving step unambiguously and is commonly used when discussing puzzles in forums, requesting help with stuck puzzles, or documenting solution paths.

Online Solver Notation

Various online Sudoku solvers use their own notation conventions, but most are variations on the same core system:

Despite the minor formatting differences, the underlying system is the same: identify the cell and specify either a placement or an elimination.

Competition Notation

In official Sudoku competitions (including the World Sudoku Championship), notation rules are standardized:

Answer Entry

Competitors receive printed puzzle grids and fill in their answers directly. There’s no need for move-by-move notation during competition—only the final answer matters.

Solution Verification

For answer keys and verification, competitions typically use a row-sequence format: the digits for selected rows (or sometimes columns or diagonals) are written as a sequence. For example, if the answer key requires rows 2, 5, and 8, a correct answer might be:

Row 2: 5 3 8 1 9 7 6 4 2
Row 5: 7 1 4 6 2 3 8 9 5
Row 8: 2 9 6 4 5 8 3 7 1

This partial-check system allows quick verification without requiring competitors to transcribe the entire grid.

Time Bonuses

Some competitions award time bonuses for early completion. Solvers signal completion by raising their hand, and their solving time is recorded. Notation speed—how quickly you can write digits—becomes a minor competitive factor, which is one reason competitive solvers practice neat, fast handwriting.

81-Character Strings

The 81-character string is the standard format for digitally representing a Sudoku puzzle. It encodes the grid as a single line of text by reading cells left to right, top to bottom.

Format Rules

• Filled cells are represented by their digit (1–9).
• Empty cells are represented by a dot (.) or a zero (0).
• The string is exactly 81 characters long.
• No spaces, line breaks, or separators.

Example

The first row might be ..3.2.6.., the second 9..3.5..1, and so on, concatenated into one unbroken string:

..3.2.6..9..3.5..1..18.64....81.29..7.......8..67.82....26.95..8..2.3..9..5.1.3..

Usage

81-character strings are used for:

• Sharing puzzles in forums, messages, and social media.
• Importing puzzles into solver software and apps.
• Database storage for puzzle collections.
• Clipboard exchange between different Sudoku programs.

Most Sudoku apps and websites accept 81-character strings as input. To try a puzzle someone shared, simply paste the string into a compatible solver.

Variations

Some extended formats include additional metadata:

• Pencil mark strings: 81 groups of candidate digits, separated by dots or spaces.
• Puzzle + solution pairs: Two 81-character strings, one for the puzzle and one for the solution.
• Formatted strings: Insert line breaks every 9 characters for readability, sometimes with additional breaks between bands.

Other Sharing Formats

Sudoku Puzzle Format (SPF)

Some puzzle archives use structured text files with metadata:

# Puzzle: Daily Challenge 2026-03-15
# Difficulty: Hard
# Source: SudokuPulse
..3.2.6..
9..3.5..1
..18.64..
...81.29.
.7.......
8..67.82.
...26.95.
.8..2.3..
9..5.1.3.

This format adds human-readable metadata and arranges the grid in a 9-line layout for visual clarity.

QR Codes for Puzzles

QR codes can encode 81-character strings, allowing puzzles to be shared in print media (magazines, newspapers, puzzle books) with a scannable link to a digital version. A reader scans the QR code, which opens the puzzle in a web-based solver or app. This bridges the gap between paper and digital solving.

Comparing Notation Systems

Practical Tips for Using Notation

1. Learn RxCy first. It’s universal and used in every resource. Once you know it, all other systems are easy to learn.
2. Use positional pencil marks. Always write candidates in the same position (1 top-left, 2 top-center, etc.) for rapid pattern recognition.
3. Practice full notation on hard puzzles. The time invested in writing candidates pays off immediately. See our guide to Sudoku strategies for how notation enables technique application.
4. Keep an 81-character string of interesting puzzles. When you encounter a great puzzle, save it as a string for future reference or sharing.
5. Understand your app’s notation. Different apps handle pencil marks differently. Spend 5 minutes learning your preferred app’s candidate entry system for faster input.

Frequently Asked Questions

What does R1C5 mean in Sudoku?

R1C5 refers to the cell at Row 1, Column 5 on the Sudoku grid. Rows are numbered 1–9 from top to bottom, and columns are numbered 1–9 from left to right. Adding a digit (R1C5=3) means that cell contains the digit 3. This is the standard notation used in strategy guides, solver outputs, and online forums worldwide.

What is an 81-character Sudoku string?

An 81-character string represents an entire Sudoku grid in a single line of text by reading all 81 cells left to right, top to bottom. Digits 1–9 represent filled cells, and dots (.) or zeros (0) represent empty cells. This compact format is the standard way to share, store, and import puzzles across apps and websites.

How do pencil marks work in Sudoku?

Pencil marks are small candidate numbers written in empty cells to indicate which digits are still possible based on row, column, and box constraints. Using a positional system (each digit occupies the same position in every cell), pencil marks make patterns like naked pairs and hidden singles visually apparent. They’re the most important solving aid for medium and harder puzzles.

What notation is used in Sudoku competitions?

Competitions use standardized answer grids where solvers write final answers directly. For verification, selected rows are checked against an answer key. During the solve, competitors use whatever personal notation works for them (usually pencil marks). Communication about puzzles in competition settings uses the standard RxCy format.

How do I share a Sudoku puzzle with someone?

The easiest way is to convert the puzzle to an 81-character string and share it as text. Most Sudoku apps and websites can import puzzles from this format. Simply list the digits left to right, top to bottom, using dots for empty cells. Many solvers also have built-in share features that generate links or QR codes.