✏️ Pencil Marks Guide

Sudoku Pencil Marks — The Complete Guide

Pencil marks (also called notes or candidates) are the small numbers you write in an empty sudoku cell to remember which digits could still go there. They are the single most powerful habit in sudoku — once you can use them well, every medium and hard puzzle becomes solvable with pure logic, no guessing.

This is the friendliest, most complete guide to sudoku pencil marks on the web. We cover every notation style real players use — corner marks, center marks, the Snyder method, full notation and the hybrid method — and we show you exactly how each one helps you find naked singles, hidden singles, pairs, pointing pairs and even an X-Wing.

It's written so a 7-year-old can follow along, with tiny worked examples for every technique. Bookmark this page, share it with a sudoku buddy, and come back any time you forget a trick.

What are pencil marks?

Before we dive into techniques, here's the quick definition. Pencil marks have lots of names, and three big ideas behind them.

  • Notes / candidates

    Pencil marks are tiny digits you write inside an empty cell to list every number that could still legally fit there. Other names: notes, candidates, markups, small numbers.

  • Light and erasable

    On paper, write them lightly so you can rub them out. In a sudoku app, tap the Notes button (sometimes a pencil icon) before tapping a digit.

  • A memory aid

    Pencil marks don't solve the puzzle for you — they remember your thinking so you can spot patterns like pairs, triples and hidden singles without redoing the work.

What's in this guide

Notation styles — pick your pencil mark system

There isn't one 'right' way to write pencil marks. These are the four notation systems real sudoku players use. Try each and pick the one that feels best — most kids end up with the hybrid method.

Corner marks

Level: Beginner

When to use it: When you're starting out, or when a digit only has one or two possible homes inside a row, column or box.

How it works: Pick a digit and a unit (row, column or box). Find every empty cell where that digit could legally fit. In each of those cells, write the digit small in a corner — top-left for 1, top-middle for 2, and so on. The position of the mark is the same in every cell, so two cells with a 5 in the same corner instantly look like a pair.

★ Example: In the top-right box, the digit 4 could only fit in two cells, A and B. Pencil a tiny 4 in the same corner of both A and B. Now you've recorded 'a 4 lives somewhere in this pair' without committing to either cell.

💡 Pro tip: Many sudoku apps (including ours) split notes into corners and centres automatically — corner marks are the ones that come from "this digit fits here in this unit".

Center marks

Level: Beginner

When to use it: When a single empty cell only has a few digits left that could fit it.

How it works: Look at one empty cell. List every digit that is NOT already in its row, column or box. Write those leftover digits in the middle of the cell. If only one digit ends up in the middle, you've just found a naked single — you can fill it in.

★ Example: An empty cell sees 2, 4, 7 and 8 in its row, 1, 3 and 6 in its column, and 5 in its box. The only digits not blocked are 9. Write a tiny '9' in the centre — that's a naked single.

💡 Pro tip: Center marks describe the cell ('what fits here?'). Corner marks describe the unit ('where does this digit fit?'). The two together cover every pattern.

Snyder notation

Level: Beginner+

When to use it: On medium and hard puzzles where full notation feels overwhelming, but plain scanning is no longer enough.

How it works: Snyder notation is a famous shortcut by speed-solver Tom Snyder. The rule is simple: for each digit, only write a candidate if that digit can fit in exactly one or two cells of a row, column or box. Skip everything with three or more options. Your grid stays clean and pairs jump out.

★ Example: Going digit by digit through a box, you find that 6 could fit in three cells — skip it. The 7 could fit in only two cells — pencil tiny 7s in those two corners. You've just recorded a future hidden pair candidate without cluttering the grid.

💡 Pro tip: Snyder is brilliant for finding hidden singles and pairs early. Most experts start every puzzle with one Snyder pass.

Full notation

Level: Beginner+

When to use it: On hard, expert and "diabolical" puzzles where you need every candidate visible to spot triples, quads, X-Wings and chains.

How it works: In every empty cell, list every digit that is not already in its row, column or box. The result looks busy, but every advanced technique — naked triples, hidden quads, X-Wings, swordfish — depends on a complete map of candidates.

★ Example: An empty cell sees 1, 3, 4, 8 already nearby. Write {2, 5, 6, 7, 9} in the middle. Repeat for every empty cell. Tedious — but now every pencil-mark trick is on the table.

💡 Pro tip: Use a sudoku app's "auto notes" button for full notation. Filling 50+ cells by hand is exhausting and error-prone.

Hybrid (corner + center)

Level: Beginner+

When to use it: Almost always — this is what most players settle on after a while.

How it works: Use corner marks for the "where can this digit go in this unit?" view, and center marks for "what fits in this cell?". Each kind of mark catches a pattern the other misses, and together they make pairs, triples and hidden singles obvious.

★ Example: A box has corner-marked 7s in two cells (a hidden pair signal). One of those cells also has a center-marked {3, 7}. The corner pair tells you 7 lives in those two cells, and the center marks tell you the other cell must be 3.

💡 Pro tip: If your app supports both, learn to use them — it really is faster than full notation for most puzzles.

Techniques pencil marks unlock

Pencil marks aren't just tidy — they reveal patterns you cannot see without them. These are the eight most useful techniques, in roughly the order you'll meet them.

Naked single from notes

Level: Beginner

When to use it: After you center-mark a cell and only one digit ends up in the middle.

How it works: Naked singles are the most common payoff of pencil marks. If a cell's center marks shrink to a single digit, that digit is the answer. Place it, then erase that digit from the pencil marks of every cell it can see.

★ Example: A cell starts with center marks {3, 7}. You place a 7 in its column elsewhere. Erase the 7 from the cell — now it's just {3}, a naked single.

💡 Pro tip: Whenever you place a number, sweep its row, column and box and remove that digit from any pencil marks. Half of all naked singles appear this way.

Hidden single from notes

Level: Beginner

When to use it: After you corner-mark a digit and only one cell in a unit carries the mark.

How it works: Hidden singles are easy to miss without notes. If a digit only has one corner mark inside a row, column or box, that cell is where the digit goes — even if the cell still has other center marks.

★ Example: In a row, the digit 8 has been corner-marked in only one cell. That cell still shows center marks {2, 6, 8} too. The corner mark wins: place 8 in that cell.

💡 Pro tip: Always do a Snyder pass at the start. Hidden singles uncovered early speed up the whole puzzle.

Naked pair

Level: Beginner+

When to use it: When two cells in the same row, column or box have exactly the same two center marks.

How it works: If cell A has center marks {3, 7} and cell B has {3, 7}, then 3 and 7 must live in A and B (we just don't know which is which). Erase 3 and 7 from the center marks of every other cell in that unit.

★ Example: In a column, A is {3, 7}, B is {3, 7}, C is {3, 5, 7}. After spotting the pair, erase 3 and 7 from C, leaving {5} — a brand-new naked single!

💡 Pro tip: Naked pairs cascade. One pair often creates a single, which creates another pair, which clears another cell.

Hidden pair

Level: Beginner+

When to use it: When two digits' corner marks land in the same two cells of a unit.

How it works: If digits 4 and 8 each only have corner marks in cells A and B inside a box, then 4 and 8 belong in A and B. Erase every OTHER mark from those two cells — they're now a confirmed pair.

★ Example: Box: corner marks for 4 are in A and B only. Corner marks for 8 are in A and B only. A's center marks are {2, 4, 8}, B's are {4, 6, 8}. Strip the extras: A is {4, 8}, B is {4, 8}.

💡 Pro tip: Hidden pairs become naked pairs once you erase the extras. Same end state, different route in.

Pointing pair / pointing triple

Level: Beginner+

When to use it: When all the corner marks for a digit inside a 3×3 box sit on the same row or column.

How it works: If the 5 in a box can only go in cells lined up across row 4, then the 5 in that box must be in row 4. That means the 5 cannot be anywhere else in row 4 — erase its corner marks from cells in row 4 in other boxes.

★ Example: Top-left box: corner marks for 2 are only in row 1. Erase corner marks for 2 from every other cell in row 1.

💡 Pro tip: Pointing pairs are the bridge from beginner to intermediate. They explain why notes outside a box suddenly disappear.

Box-line reduction

Level: Beginner+

When to use it: When all the corner marks for a digit inside a row or column sit inside one 3×3 box.

How it works: It's the mirror of a pointing pair. If the 5 in row 4 can only go in cells inside the centre box, the 5 must be in the centre box (in row 4) — so the 5 can't be in the rest of the centre box.

★ Example: Row 4: corner marks for 5 only land inside the centre box. Erase corner marks for 5 from the centre box's other rows (rows 5 and 6).

💡 Pro tip: Pointing pairs erase OUTSIDE the box. Box-line reductions erase INSIDE it. Same idea, opposite direction.

Naked triple

Level: Intermediate

When to use it: When three cells in one unit share only three candidates between them.

How it works: If three cells in a row have center marks like {1, 4}, {1, 4, 6} and {4, 6}, together they cover only {1, 4, 6}. Those three digits live in those three cells. Erase 1, 4 and 6 from every other cell in the row.

★ Example: Row 7: A={1,4}, B={1,4,6}, C={4,6}. Cell D in the same row has center marks {2, 4, 6, 8}. Strip 4 and 6 from D — it becomes {2, 8}.

💡 Pro tip: Triples are a step up. Get rock-solid with pairs first; triples will come naturally.

X-Wing (advanced)

Level: Advanced

When to use it: On hard puzzles where the easier techniques have stopped paying off.

How it works: Find a digit whose corner marks form a perfect rectangle: in two rows, the digit's marks land in the same two columns. Those four cells form an X-Wing. The digit must take a diagonal pair of these cells, so you can erase that digit's corner marks from the other cells of those two columns.

★ Example: Digit 6: in row 2, corner marks for 6 are only in columns 3 and 8. In row 6, corner marks for 6 are also only in columns 3 and 8. That's an X-Wing on 6. Erase corner marks for 6 from the rest of column 3 and column 8.

💡 Pro tip: X-Wing only works because pencil marks are perfectly accurate. One missed mark and the trick fails — keep your notation tidy.

Pencil marks on paper vs in an app

Whether you're solving on a printable sheet or in a sudoku game, the marks themselves are the same — but the practical tips differ a bit.

  • Use a real pencil

    On paper, always use a pencil with a clean eraser — never a pen. Press lightly so you can rub marks out without smudging.

  • Tiny, neat handwriting

    Your marks should be small enough that nine of them fit in one cell without touching the answer. Practise writing tiny — it's the #1 paper skill.

  • Erase as you place

    The instant you write a final answer, sweep the same row, column and box and rub out that digit from every pencil mark. Tidy notes find pairs much faster.

  • Tap Notes mode in apps

    In our games, tap the pencil/Notes button so digit taps add candidates instead of placing. Tap Notes off when you're sure of an answer.

  • Use Auto Notes

    Apps usually have an Auto Notes button that fills full notation everywhere instantly. It's the fastest way into hard puzzles, but learn manual notation first so you understand what the auto-marks mean.

  • Highlight, don't guess

    If your app lets you colour pencil marks (some do), use a colour to track a hypothesis like an X-Wing. Don't 'try' a digit and see what happens — that's guessing.

Common pencil mark mistakes (and how to fix them)

Almost every kid makes these mistakes when starting with notes. Spotting them in advance is the fastest way to skip past them.

  • Adding notes too early

    On easy puzzles, plain scanning solves the grid before notes are needed. Try scanning first — only switch to pencil marks when easy moves dry up.

  • Forgetting to erase after a placement

    When you place a digit, every pencil mark of the same digit in its row, column and box becomes wrong. Sweep them all immediately, or your next move will be a guess.

  • Mixing notation styles

    Don't switch between Snyder and full notation halfway through. Pick one (hybrid is fine) and stick to it for the whole puzzle so you trust your own marks.

  • Filling notes randomly

    Pencil marks are not decoration. Each digit should be placed because the rules allow it, not because the cell looks empty. Always check row, column AND box.

  • Treating "maybe" as a mark

    If you're not sure whether a digit fits, it does or it doesn't — there's no such thing as a maybe-mark. Re-check the rules and decide.

  • Not re-scanning after notes

    Each new digit you place creates new singles and new pairs. After every placement, re-scan the surrounding cells — the next move is usually right next door.

A 2-week pencil marks practice plan

Want pencil marks to feel automatic? Try this fortnight of short daily sessions — about 15 minutes a day. By day 14, notes will feel like a reflex.

  1. Day 1–2: Easy 9×9 with corner marks

    Solve one easy puzzle a day. Add corner marks the moment scanning slows down. Goal: corner marks become a habit, not an effort.

  2. Day 3–4: Add center marks

    Same easy puzzles, but now also center-mark any cell with three or fewer candidates. Watch naked singles appear.

  3. Day 5–6: Snyder method

    Try a medium puzzle and start with one Snyder pass — corner marks for digits with one or two homes per unit. Hidden singles will jump out.

  4. Day 7–9: Pairs & pointing pairs

    On medium puzzles, focus only on spotting naked pairs, hidden pairs and pointing pairs. Erase, place, repeat.

  5. Day 10–12: Full notation on hard puzzles

    Switch to hard puzzles and use a sudoku app's Auto Notes button. Practise reading the grid — triples and box-line reductions are the new targets.

  6. Day 13–14: Try an X-Wing

    Look for an X-Wing on an expert puzzle. You probably won't find one every game — but knowing the shape changes how you read every grid.

Frequently asked questions about pencil marks

What are pencil marks in sudoku?

Pencil marks are small numbers you write inside an empty sudoku cell to record which digits could still legally fit there. They are also called notes, candidates, markups or small numbers. Pencil marks let you spot patterns like naked singles, hidden singles, naked pairs and pointing pairs that are almost impossible to see without notes.

What's the difference between corner marks and center marks?

Corner marks answer the question 'where in this row, column or box could this digit go?'. You write the digit in the same corner of every cell where it could fit. Center marks answer 'which digits could fit in this one cell?' — you list those digits in the middle of the cell. Most strong players use both at once (the hybrid method).

What is the Snyder method (Snyder notation)?

The Snyder method is a famous notation shortcut by speed-solver Tom Snyder. The rule: for each digit and each unit (row, column, box), only pencil-mark the digit if it can fit in exactly one or two cells of that unit. You skip everything with three or more options. The result is a clean grid where hidden singles and hidden pairs jump out — perfect for medium puzzles.

Should I use full notation or Snyder notation?

It depends on the puzzle. For medium puzzles, Snyder notation is faster — your grid stays clean and you find hidden singles quickly. For hard, expert and 'diabolical' puzzles, you need full notation (every candidate in every cell) so that advanced patterns like naked triples and X-Wings are visible. Most players start with Snyder and switch to full notation when they get stuck.

When should kids start using pencil marks?

Kids should start using pencil marks the first time scanning stops finding new digits — usually on a medium 9×9 puzzle. On 4×4 and easy 9×9 puzzles, scanning and naked singles in your head are usually enough. The moment you say 'I'm stuck', it's pencil marks time.

Are pencil marks cheating?

No, not at all. Pencil marks are how every serious sudoku solver works. They don't change the puzzle or tell you the answer — they just help you keep track of your own logic. Speed-solving competitions allow pencil marks, and most printed sudoku books leave space in each cell exactly so you can write notes.

How do you use pencil marks digitally?

In a sudoku app, look for a Notes button (often a pencil icon). Tap it to switch to Notes mode, then tap a digit to add or remove that candidate from the selected cell. Tap the Notes button again to switch back to placement mode. Many apps also have an Auto Notes button that fills full notation in every empty cell at once.

What is the Auto Notes feature?

Auto Notes (sometimes 'Pencil Mark All' or 'Fill Candidates') is a one-tap button that fills every empty cell with full notation — every digit that could legally fit. It saves several minutes on hard puzzles. The trade-off: you lose the practice of building notes yourself, so use it only after you understand the manual method.

How do pencil marks help you find naked singles?

A naked single is a cell with only one possible digit. Center marks make naked singles obvious — when a cell's list of candidates shrinks to one digit, you write it in. Every time you place a number on the board, you should erase that digit from the candidates of every cell in the same row, column and box. About half of all naked singles appear this way.

Can you solve sudoku without pencil marks?

Easy 9×9 sudoku puzzles can be solved without pencil marks using only scanning and singles. Medium and harder puzzles almost always need notes — the techniques required (naked pairs, pointing pairs, X-Wings) all depend on accurate candidates. If you want to grow past easy puzzles, pencil marks are the next step.

How do you erase pencil marks correctly?

On paper, use a soft eraser and rub gently — pencil marks should be light to begin with. In an app, tap Notes mode and then tap the digit you want to remove from the selected cell. Always erase a candidate the moment its digit appears anywhere in the same row, column or box — letting old notes linger is the most common cause of wrong answers.

What pencil should I use for sudoku on paper?

A standard HB or 2B pencil works well — soft enough to write tiny marks easily, hard enough that the lines stay sharp. A mechanical pencil with a 0.5 mm or 0.7 mm lead is fantastic because it never needs sharpening, and the line stays the same width for every mark. Avoid pens of any kind — you cannot solve sudoku in pen and erase your way out of mistakes.

Do speed solvers use pencil marks?

Yes — every world-class sudoku solver uses pencil marks on hard and expert puzzles. They use Snyder notation for the early scan, then switch to full notation when stuck. The fastest solvers in the world have all written about which notation system they use; there is no top player who solves expert puzzles in their head.

What's a "highlight" or "colour" in a sudoku app?

Some sudoku apps let you highlight a specific digit (showing every cell where that digit appears or could appear) and some let you colour pencil marks. Highlighting is fantastic for spotting hidden singles and X-Wings. Colours are useful for tracking a hypothesis without committing to it — but they are still pencil marks, not guesses.

You're ready — pick up that pencil!

Pencil marks turn sudoku from a guessing game into pure logic. Start with corner marks, add center marks, learn Snyder, and within a couple of weeks you'll be solving puzzles you couldn't touch before. Save this page, share it with a sudoku-loving friend, and most of all — have fun.

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