If you have ever stared at a Sudoku grid for several minutes without being able to place a single number, you already understand why pencil marks exist. Pencil marks — also called candidate notes, possibility lists, or simply candidates — are the small numbers you write inside a cell to record every digit that could legally go there. Far from being a sign of weakness or confusion, using pencil marks is the single most powerful habit that separates casual players from confident solvers. In this guide, we will explain exactly what pencil marks are, when to start using them, how to write them efficiently, and how to use them to unlock solving techniques that are simply impossible without them.
What Are Pencil Marks and Why Do They Matter?
A pencil mark is a small digit written inside a Sudoku cell to indicate that the number is still a possible candidate for that cell. For example, if a cell could contain either a 3, a 7, or a 9, you would write those three digits lightly in the corner or centre of the cell. As you gather more information from the rest of the grid, you eliminate candidates one by one until only one number remains — and that is the number that belongs in the cell.
The reason pencil marks matter so much is that human working memory is limited. A standard 9×9 Sudoku grid has 81 cells, up to 50 or more of which may be empty at the start of a hard puzzle. Trying to track every possibility for every empty cell purely in your head is exhausting and error-prone. Pencil marks move that cognitive load off your brain and onto the paper (or screen), freeing you to concentrate on spotting patterns.
In digital Sudoku apps, pencil marks are usually called “notes” and can be toggled on with a dedicated button. On paper, you simply write small digits with — as the name suggests — a pencil, so you can erase them cleanly as you make progress. Either way, the concept is identical: record what is possible, then systematically narrow it down.
When Should You Start Using Pencil Marks?
Many beginners assume pencil marks are only for experts tackling fiendish puzzles. In reality, the right time to add candidate notes depends on the difficulty of the puzzle you are solving and how far you have already progressed using straightforward elimination.
A sensible approach for most solvers is a two-pass system:
- First pass — naked singles and hidden singles: Before adding any pencil marks, scan the grid for cells where only one number can logically go (naked singles) or rows, columns, and boxes where a particular digit has only one possible home (hidden singles). These placements require no notes. Fill in everything you can find this way.
- Second pass — full candidate notation: Once you are stuck and cannot make any further placements by straightforward scanning, that is your signal to add pencil marks. Go through every remaining empty cell and write all valid candidates inside it. From this point forward, every time you place a number, return to your notes and remove that digit from all cells in the same row, column, and 3×3 box.
On easy puzzles, you may finish entirely during the first pass. On medium puzzles, you might place ten or fifteen numbers before needing notes. On hard, expert, or extreme puzzles, you may need to switch to full candidate notation surprisingly early. The key is not to fight the process — as soon as scanning stops working, add your notes without hesitation.
How to Write Candidate Notes Efficiently
There is more than one way to lay out pencil marks inside a cell, and the system you choose can make a significant difference to your solving speed and accuracy.
The fixed-position system is the most popular method among serious paper solvers. You mentally divide each cell into a 3×3 mini-grid of nine positions, and each digit always occupies the same position: 1 in the top-left, 2 in the top-centre, 3 in the top-right, 4 in the middle-left, 5 in the centre, 6 in the middle-right, 7 in the bottom-left, 8 in the bottom-centre, and 9 in the bottom-right. When a digit is still a candidate, you write it; when it is eliminated, you erase it. Because every digit always sits in the same spot, you can scan for patterns across multiple cells at a glance without having to read each number individually.
The list system simply involves writing the candidates as a small sequence of digits across the top or bottom of the cell — for example, “1 4 7” — in ascending order. This is quicker to write initially but becomes harder to scan when you are looking for patterns across many cells.
For digital play, most apps handle the layout for you automatically, which removes this concern entirely. However, understanding the fixed-position system is still valuable because it mirrors what the app does behind the scenes and trains your eye to read candidate patterns quickly.
A Worked Example: Using Pencil Marks to Find a Naked Pair
Let us walk through a concrete example to show how candidate notes unlock solving techniques you cannot use without them.
Imagine you are looking at a row in your Sudoku grid. After placing all the obvious numbers, five cells in this row are still empty, and the remaining digits to be placed are 1, 2, 5, 7, and 8. You add pencil marks to each empty cell based on the constraints from the columns and boxes they belong to:
- Cell A: candidates 1, 5, 7
- Cell B: candidates 2, 8
- Cell C: candidates 1, 2, 5, 8
- Cell D: candidates 2, 8
- Cell E: candidates 1, 5, 7
Notice that cells B and D both contain exactly the same two candidates: 2 and 8. This is called a naked pair. Because one of those two cells must contain a 2 and the other must contain an 8, neither 2 nor 8 can appear anywhere else in the row. You can therefore eliminate 2 and 8 from cell C, leaving cell C with only candidates 1 and 5.
Now look at cells A, C, and E. The digit 7 appears only in cells A and E, nowhere else in the row. This means 7 must go in one of those two cells, so you can eliminate 7 from cell A or E depending on column constraints — or you may spot a hidden single that pins 7 directly. Either way, your candidate notes made this entire chain of logic visible. Without them, spotting a naked pair across a row of partially filled cells would be extremely difficult and unreliable.
This same principle extends to naked triples, naked quads, hidden pairs, hidden triples, X-Wings, Swordfish, and many more advanced Sudoku techniques. All of them rely on reading patterns in your candidate notes. The notes do not solve the puzzle for you — they make the puzzle’s hidden structure visible to your eye and mind.
Common Mistakes to Avoid with Pencil Marks
Pencil marks are enormously helpful, but only when maintained accurately. Here are the most common errors solvers make — and how to avoid them:
- Forgetting to update notes after placing a digit. Every time you write a confirmed number in a cell, you must immediately erase that digit from all candidate lists in the same row, column, and 3×3 box. Stale notes lead to false patterns and wrong answers.
- Adding notes too early. If you fill in pencil marks before completing your initial scan for naked and hidden singles, you end up doing unnecessary work, because many of those candidates will be immediately eliminated anyway.
- Writing candidates too large. Oversized pencil marks make it difficult to fit all nine possible candidates and can make the grid look cluttered. Keep your notes small and neat.
- Not erasing eliminated candidates promptly. On paper, resist the temptation to just mentally note that a candidate is gone. Erase it physically. On a screen, remove the note as soon as it is eliminated. Clean notes are reliable notes.
- Guessing instead of reading notes. Some solvers add pencil marks and then ignore them, guessing at answers instead. Candidate notes are meant to support logical deduction, not decorate the grid. Trust the process and let the patterns reveal themselves.
Pencil Marks and Digital Sudoku Apps
If you play Sudoku on a phone or tablet, you will find that most quality apps include an automatic notes feature that fills in all valid candidates at once. This can be a tremendous time saver, especially on hard puzzles where manually entering notes for 50+ cells is tedious. However, there are two things worth knowing about auto-fill notes.
First, using the auto-fill feature means you miss the learning experience of manually scanning rows, columns, and boxes to determine candidates. That manual scanning process itself sharpens your eye for Sudoku patterns. If you are trying to improve as a solver, consider entering notes by hand at least some of the time.
Second, auto-fill notes only show basic candidates based on the Sudoku rules — they do not apply any solving logic. The advanced eliminations (from naked pairs, X-Wings, and so on) are still for you to find and act on. The app sets the table; you still do the solving.
Some apps also offer a “check notes” feature that highlights incorrect candidates. This is helpful for absolute beginners but can become a crutch over time. Challenge yourself to maintain your own accurate candidate lists as your skills grow.
Key Takeaways
- Pencil marks (candidate notes) record every possible digit for each empty cell, reducing mental load and making patterns visible.
- Use a two-pass approach: fill in obvious placements first, then add full candidate notation when you are stuck.
- The fixed-position system — where each digit always occupies the same spot within a cell — makes scanning for patterns across multiple cells much faster.
- Candidate notes are essential for applying techniques like naked pairs, hidden pairs, X-Wings, and Swordfish.
- Always update your notes immediately after placing a confirmed digit — stale candidates cause errors.
- Digital apps often include auto-fill notes, which save time but are best combined with manual practice to develop your solving eye.
Learning to use pencil marks confidently is one of the most rewarding steps you can take as a Sudoku solver. The moment a naked pair jumps out at you from a row of candidate notes, or a hidden single reveals itself because your notes are clean and current, you will understand why experienced players swear by this habit. Start small — try adding notes on your next medium-difficulty puzzle and see how much further you get. With a little practice, candidate notation will feel less like extra work and more like a superpower. Head over to the puzzle pages at playsudoku.org and put your new skills to the test today.