How to Use Pencil Marks in Sudoku: A Complete Guide to Notes and Candidates

If you've been solving easy Sudoku puzzles by scanning for obvious numbers, you've probably noticed that medium and harder puzzles feel like hitting a wall. The cells stop being obvious. You stare at the grid and nothing jumps out. The solution? Pencil marks — small notations that track which numbers could go in each empty cell.

Pencil marks (also called notes, candidates, or candidate notation) are the single most important tool for progressing beyond beginner-level Sudoku. They aren't a crutch or a sign of weakness — championship solvers use them, speed solvers use them, and you should too. This guide explains exactly what pencil marks are, when to use them, how to maintain them, and the powerful techniques they unlock.

What Are Pencil Marks in Sudoku?

A pencil mark is a small number written in an empty cell to indicate that the digit is still a possible candidate for that cell. If a cell could contain 2, 5, or 7 — and you've eliminated every other option — you'd write small 2, 5, and 7 in the cell as pencil marks.

On paper, people write these as tiny numbers in the corners or center of a cell. On digital platforms like ours, there's a dedicated notes mode — tap it, then tap a number, and it appears as a small candidate in the cell. You can toggle candidates on and off with a single tap.

The purpose is simple: pencil marks externalize your working memory. Instead of trying to remember which numbers are possible in multiple cells simultaneously, you write them down and free your mind to focus on spotting patterns and making deductions.

Why Pencil Marks Are Essential for Solving Harder Puzzles

On easy Sudoku puzzles, most cells can be solved by a single scan — you look at one row, one column, and one box, and the answer is clear. These puzzles are designed so that you almost always have a cell where only one digit is possible.

Medium and hard puzzles deliberately remove that luxury. You'll reach points where no cell has an immediately obvious answer. Instead, you have cells with two or three candidates, and you need to compare candidates across multiple cells to find your next move. Without pencil marks, you'd need to hold all of that information in your head — which is error-prone and mentally exhausting.

Pencil marks make advanced techniques visible. Patterns like Naked Pairs, Hidden Singles, and X-Wings — the techniques that unlock harder puzzles — are impossible to spot reliably without candidates written down. They transform Sudoku from a memory test into a visual pattern-recognition exercise, which is both more enjoyable and more effective.

When Should You Start Using Pencil Marks?

There are two common approaches, and the best choice depends on your experience level and the puzzle's difficulty.

Approach 1: Fill Pencil Marks After Your First Scan

Start by scanning the grid and filling in any cells where you can immediately identify the answer. Then, for every remaining empty cell, work out which digits are still possible and write them as pencil marks. This gives you a complete picture of the puzzle's state and is the most reliable approach for medium and hard puzzles.

Approach 2: Add Pencil Marks Only When You Get Stuck

Some solvers prefer to scan as far as they can without notes, then add pencil marks only in the area where they're stuck. This is faster on puzzles that are mostly easy with a few tricky spots, but it can leave you without the full context needed for advanced techniques.

For beginners, Approach 1 is strongly recommended. Filling in all candidates may feel slow at first, but it teaches you to think systematically and makes patterns far easier to spot. As you gain experience, you'll naturally develop a feel for when full notation is necessary and when partial notation is enough.

How to Fill In Pencil Marks Correctly

The process is methodical. For each empty cell, you need to determine which digits from 1 to 9 are NOT already present in the cell's row, column, or 3x3 box. Whatever remains becomes your pencil marks. Here's a step-by-step method:

Step 1: Pick an empty cell. Look at the row it's in and note which numbers are already placed. Then look at the column and note those numbers. Finally, check the 3x3 box.

Step 2: Any digit from 1–9 that does NOT appear in the row, column, or box is a valid candidate. Write those digits as small pencil marks in the cell.

Step 3: If only one candidate remains, that's your answer — fill it in as a solved cell immediately.

Step 4: Move to the next empty cell and repeat. Work through the entire grid systematically — row by row or box by box, whichever feels more natural.

The Critical Step Most People Skip: Keeping Pencil Marks Updated

This is where many beginners go wrong. Writing pencil marks once and then forgetting about them defeats the entire purpose. Every time you place a solved number in a cell, you must remove that number from the pencil marks of every other cell in the same row, column, and 3x3 box.

For example, if you solve a cell as 4, go through every unsolved cell in that row and erase 4 from its candidates. Then do the same for the column and the box. This is called elimination, and it's the engine that drives Sudoku solving forward.

After elimination, check whether any cell now has only one candidate remaining. If so, that's your next solved cell — and you repeat the elimination process. This cascade effect is deeply satisfying: one placement often triggers a chain of eliminations that solves several more cells. For more on avoiding this and other common pitfalls, see our article on 9 common Sudoku mistakes beginners make.

Powerful Techniques That Pencil Marks Unlock

Pencil marks aren't just bookkeeping — they're the foundation for every intermediate and advanced Sudoku technique. Here are the most important ones.

Naked Singles

The simplest technique: when a cell has only one pencil mark left, that's the answer. This happens naturally as you eliminate candidates. With well-maintained pencil marks, naked singles become immediately visible — you just look for cells with a single small number.

Hidden Singles

A hidden single occurs when a particular digit appears as a candidate in only one cell within a row, column, or box — even though that cell has other candidates too. For example, if 8 only appears as a pencil mark in one cell of a row, then 8 must go in that cell, regardless of what other candidates are there. Without pencil marks written down, hidden singles are nearly impossible to spot consistently.

Naked Pairs and Triples

When two cells in the same row, column, or box contain exactly the same two candidates — say 3 and 7 — those two numbers must go in those two cells (you just don't know which goes where yet). This means you can eliminate 3 and 7 from every other cell in that group. The same logic extends to triples: three cells sharing the same three candidates lock those numbers in place.

Pointing Pairs

Sometimes a candidate within a 3x3 box is restricted to a single row or column. When that happens, you can eliminate that candidate from the same row or column outside the box. This interaction between boxes and lines is only visible when your pencil marks are complete and up to date.

For a deeper dive into these and more advanced patterns like X-Wing and Swordfish, check out our complete guide to Sudoku tips and tricks.

Common Pencil Mark Mistakes to Avoid

Forgetting to Eliminate After Placing a Number

This is the number one cause of errors for intermediate players. You excitedly fill in a cell but forget to remove that digit from the candidates in connected cells. Later, you end up with incorrect candidates that lead to contradictions. Make elimination a strict habit: every time you place a digit, immediately scan the row, column, and box and remove it from all pencil marks.

Missing a Candidate When First Filling In Notes

If you accidentally leave a valid candidate out of a cell's pencil marks during the initial setup, you'll miss the correct answer for that cell entirely. This often leads to getting stuck with no logical way forward. Take your time during the initial notation phase and double-check your work — especially on harder puzzles where accuracy matters most.

Writing Too Many Notes and Not Cleaning Up

A grid overflowing with pencil marks can feel overwhelming. The key is that pencil marks should always be shrinking, not growing. As you make progress, candidates get eliminated. If your pencil marks aren't getting shorter over time, you may be skipping the elimination step. On digital platforms, toggle off candidates as soon as they're eliminated — it keeps the visual clutter manageable.

Pencil Marks on Paper vs Digital: Which Is Better?

Both work well, but they have different strengths. On paper, pencil marks give you a tactile experience and complete control over placement — some solvers use specific cell positions for specific numbers (1 in the top-left corner, 2 to its right, and so on) to make scanning faster. The downside is that erasing and rewriting on paper gets messy, especially on smaller grids.

Digital platforms handle the mechanics for you. Toggling a candidate on or off is instant and clean. Some platforms even offer auto-candidate features that fill in all valid pencil marks with one tap — though many solvers prefer to do it manually, since the process of working out candidates teaches you about the puzzle's structure. Online Sudoku also makes it impossible to accidentally erase a solved number while erasing a nearby pencil mark, which is a common frustration on paper.

Pro Tips for Efficient Pencil Mark Usage

Work Digit by Digit, Not Cell by Cell

Instead of picking a cell and figuring out all its candidates, try picking a digit (say, 4) and scanning the entire grid to see where 4 can and can't go. This is often faster because you're holding one number in mind rather than juggling nine. Go through all digits from 1 to 9 and you'll build a complete set of pencil marks.

Focus on Cells with Fewer Candidates First

Cells with just two candidates are the most likely to yield a quick solve — either through direct elimination or by forming part of a Naked Pair. After updating your pencil marks, scan for cells with two or three candidates before looking at cells with more. This simple priority system dramatically improves your solving efficiency.

Don't Pencil Mark What's Already Obvious

If during your initial scan you can immediately solve a cell, just place the answer — don't bother writing it as a lone pencil mark first. Reserve notation for cells that genuinely have multiple possibilities. This keeps your grid cleaner and your workflow faster. For more speed-focused strategies, take a look at our guide on how to solve Sudoku faster.

Frequently Asked Questions

Conclusion

Pencil marks are the bridge between casual Sudoku and truly skillful solving. They turn an overwhelming grid into a manageable system, reveal hidden patterns, and make advanced techniques possible. If you've been avoiding them because they seem tedious or like cheating, give them a real chance — most solvers who start using pencil marks consistently never go back.

Start by filling in candidates on your next medium-difficulty puzzle. Focus on keeping them updated after every placement. Within a few puzzles, the process will feel natural, and you'll start noticing patterns — Naked Pairs, Hidden Singles, Pointing Pairs — that were invisible before.

Ready to practice? Play a free Sudoku puzzle now — try a medium puzzle, switch on notes mode, and see the difference pencil marks make.