Sudoku Pencil Marks

Pencil marks are the small notes used inside unsolved Sudoku cells to record candidate information.

The distinction between the logic and the notation is important:

• a candidate is a digit that remains logically possible;
• a pencil mark or note is how that possibility is displayed or recorded.

On paper, the name comes literally from writing small digits in pencil. In digital Sudoku, the same feature is usually called Notes, Candidates, or Pencil Marks. The purpose is the same: make enough of the candidate structure visible to support reliable deductions without confusing a possibility with a solved value.

What do pencil marks mean?

If an unsolved cell contains small notes such as:

2 5 8

those marks normally mean that 2, 5, and 8 are being tracked as possible values for that cell.

With full candidate notation, every displayed note should be a currently legal candidate and every legal candidate should be represented. With selective notation, only some useful possibilities are written down.

Either way, the marks do not mean that one digit is more likely than another. They record unresolved possibilities, not guesses.

Pencil marks, notes, and candidates: what is the difference?

Sudoku apps often use these words interchangeably, but a precise vocabulary helps:

• candidate — a digit that has not been logically ruled out;
• pencil mark / note — a visible record of candidate information;
• candidate set — the complete set of legal candidates for one cell;
• notation system — the method a solver uses to decide which candidate information to display.

For example, if a cell's legal candidate set is {3, 7}, writing small 3 and 7 notes records that complete state.

If the legal set is {3, 5, 7} but you have written only 3 and 7 as selective notes, 5 has not become impossible. It is simply absent from your notation.

If candidates themselves are new to you, read Sudoku Candidates before relying on notes for intermediate techniques.

When should you start using pencil marks?

You do not need to fill every empty cell with notes as soon as a puzzle opens.

A useful progression is:

1. scan for direct placements;
2. solve obvious Singles;
3. when progress slows, begin recording candidate information;
4. increase the completeness of the notation when the techniques you need require it.

On an Easy Sudoku, you may finish with little or no notation. On a Hard or Expert puzzle, a reliable candidate grid often becomes necessary because the solve progresses through candidate eliminations rather than immediate placements.

The best moment to add notes is therefore not a fixed move number. It is when the information you can hold mentally is no longer enough to see the next deduction reliably.

Do you need pencil marks to solve Sudoku?

No. Pencil marks are a solving tool, not a Sudoku rule.

Simple puzzles can often be solved through scanning, last-missing-digit logic, and Singles. Experienced speed solvers may also delay full notation deliberately to keep the board visually clean.

As difficulty rises, however, candidate relationships become more important. Locked Candidates, subsets, Fish, Wings, Coloring, and Chains are much easier to analyze when the relevant candidate state is visible and trustworthy.

The goal is not to maximize the number of tiny digits on the board. The goal is to make the right information visible for the next layer of logic.

Sudoku pencil-mark notation systems

There is no single mandatory way to write Sudoku notes. Different methods trade completeness for speed and visual clarity.

Full candidate notation

With full notation, every unsolved cell displays every digit that is currently legal there.

If a cell can contain only 2, 5, or 8, you record:

{2, 5, 8}

Full notation has several advantages:

• the candidate state is explicit;
• Naked Singles are immediately visible;
• subsets can be checked systematically;
• advanced patterns can rely on candidate absence as meaningful information;
• teaching examples are easier to validate.

The drawback is visual density. Early in a puzzle, many cells can contain several candidates, producing a crowded grid before that information is actually useful.

Selective notation

With selective notes, you record only candidate information that seems useful.

You might track one digit across a box, mark a constrained pair, or add notes only in the part of the grid where progress has stopped.

Selective notation can be faster and visually cleaner, especially on Easy and Medium puzzles. But it comes with an important limitation: an unmarked digit may still be logically possible.

That means you cannot safely treat incomplete notes as a full candidate grid when applying a technique whose proof depends on knowing every remaining candidate.

Snyder notation

Snyder notation is a well-known selective marking system associated with competitive Sudoku solver Thomas Snyder.

The standard idea is box-focused: for a particular digit, if that digit has exactly two possible cells within a 3×3 box, mark the digit in those two cells. If it has only one position, you have a Hidden Single and can solve it. If it has three or more possible positions, you normally leave it unmarked for the moment.

This produces a sparse grid that emphasizes high-value positional information without writing every candidate everywhere.

Snyder notation can help reveal patterns such as:

• Hidden Singles as a digit narrows from two positions to one;
• Hidden Pairs when two digits are restricted to the same two cells;
• pointing relationships when two positions align on one row or column.

It is best understood as a notation discipline, not a separate solving rule. The deductions you make from Snyder marks are still standard Sudoku logic.

Its main limitation is deliberate incompleteness. When a puzzle requires candidate-heavy techniques outside the information Snyder notation records, you may need to expand to full candidate notation.

Hybrid notation

A hybrid approach changes notation as the puzzle changes.

For example:

1. begin with scanning and no notes;
2. use selective or Snyder-style marks during the early candidate phase;
3. switch to full candidates when the puzzle stalls or advanced techniques become necessary.

This avoids treating one notation system as universally superior. Different solving states need different amounts of visible information.

How to add correct pencil marks

For one empty cell using full candidate notation:

1. Start with digits 1–9.
2. Remove every digit already present in the same row.
3. Remove every digit already present in the same column.
4. Remove every digit already present in the same box.
5. Record the remaining digits as the cell's candidate set.

Where should pencil marks go inside a cell?

Paper and digital interfaces use several layouts.

One common system places each candidate in a consistent mini-grid position — 1 near the top-left, 5 near the center, 9 near the bottom-right. This makes a candidate digit visually consistent across cells.

Other interfaces simply arrange notes compactly, or distinguish corner marks and center marks for different kinds of information.

The exact physical position is not part of Sudoku logic. Consistency matters more than choosing one universal layout. A note should be easy to identify and clearly different from a solved digit.

How pencil marks change after a move

Pencil marks are not permanent.

Suppose a cell contains candidates {4, 7}. If a 4 is later solved in the same row, 4 is no longer legal in that cell. Its complete candidate set becomes:

{7}

That creates a Naked Single.

One placement can remove the same candidate from several peers, and those removals can expose new Singles, subsets, links, or other patterns.

Candidate maintenance is therefore a repeating cycle:

place or eliminate → update notes → re-scan → find the next deduction.

How to read pencil marks for useful patterns

Notes become valuable when you read relationships rather than individual tiny numbers.

Singles

A cell with one candidate is a Naked Single. A digit with one candidate position left in a house is a Hidden Single.

Pairs and subsets

Two cells restricted to the same two candidates can form a Naked Pair. Two digits restricted to the same two positions can form a Hidden Pair.

Locked Candidates

If every candidate for one digit inside a box lies on the same row or column, the digit is locked to that line inside the box and can produce eliminations outside it.

Advanced patterns

Fish, Wings, Coloring, and Chains depend on increasingly structured candidate relationships. At that level, full or otherwise verified candidate information is usually more useful than sparse beginner notes.

The purpose of notation is not merely to remember possibilities. It is to make these structures visible enough to reason about them.

Manual notes vs automatic candidates

Digital Sudoku can manage notation in different ways.

Manual notes

You add and remove every note yourself.

This resembles pencil-and-paper solving and makes candidate maintenance part of the challenge. It also means your displayed notes may be incomplete or contain mistakes unless you update them carefully.

Automatic candidates

The game calculates every currently legal candidate for you.

This removes bookkeeping and makes pattern recognition easier. It also makes some deductions — especially Naked Singles — visually more obvious because the candidate grid is always complete.

Automatic candidates do not perform advanced deductions by themselves. They normally remove only candidates made illegal by solved digits; techniques such as Locked Candidates or X-Wing still require logical reasoning to eliminate additional candidates.

Hybrid notes

A digital interface may know the complete legal candidate state while allowing the player to choose which notes are displayed.

That is an important distinction for teaching: the logical state and the visible notation do not have to be identical.

Pencil marks on paper vs digital Sudoku

The underlying logic is the same, but the workflow differs.

On paper:

• you calculate and erase notes manually;
• notation speed and visual cleanliness matter more;
• selective systems such as Snyder notation can reduce writing.

In digital Sudoku:

• notes can be toggled quickly;
• peers may update automatically after a placement;
• full candidates can be generated instantly;
• filters can temporarily show one digit across the whole grid.

Neither environment is inherently more legitimate. They simply move different amounts of bookkeeping between the player and the interface.

Common pencil-mark mistakes

Treating a note as a guess

A note means “still possible,” not “probably correct.” Never place a candidate merely because it is one of two notes in a cell.

Leaving impossible candidates behind

If a digit is solved in a row, column, or box, that digit is no longer legal in its unsolved peers. Stale notes can hide Singles and create false advanced patterns.

Using incomplete notes as if they were complete

Selective notation is useful, but its absences are not automatically logical eliminations. Before applying a technique that requires complete candidate sets, make sure your notation actually represents them.

Adding notes without checking all three houses

A digit can be absent from the row but already present in the column or box. Full candidate legality always depends on all three constraints.

Filling every note before checking for easy moves

Notes are a tool, not a ritual. Direct placements may still be available and can simplify the candidate state before you spend time building full notation.

Never changing notation style

Sparse notes can be efficient early and insufficient later. If your current notation no longer exposes the information needed for the next technique, expand it rather than forcing the puzzle to fit the notation method.

A practical pencil-mark workflow

A flexible human-solving workflow is:

1. Scan for obvious placements first.
2. Add selective notes when useful information becomes hard to hold mentally.
3. Use Snyder-style box marks if that suits your solving style.
4. Keep looking for Singles and Locked Candidates as the grid changes.
5. Expand to full candidate notation when intermediate or advanced patterns require complete information.
6. After every placement or elimination, update the relevant notes and re-scan for simpler moves.

This keeps notation proportional to the puzzle rather than turning note entry into a goal by itself.

FAQ

Are pencil marks allowed in Sudoku?

Yes. Pencil marks are notes used by the solver. They do not alter the puzzle or add new rules.

Should I write every possible number in every empty cell?

Not necessarily. Full candidate notation is safest for systematic advanced solving, while selective notation can keep easier puzzles cleaner. The important part is knowing whether the deduction you are using assumes complete candidate information.

What is Snyder notation in Sudoku?

Snyder notation is a selective system in which a digit is typically marked when it has exactly two possible cells within a 3×3 box. It keeps early candidate information sparse and can expose Singles, pairs, and pointing relationships. Harder puzzles may eventually require full notation.

Is Snyder notation a Sudoku technique?

It is better described as a notation method. Snyder marks help you see standard deductions; they do not create a new logical rule.

Why did one of my notes disappear?

If a digit is solved in the same row, column, or box — or a valid technique eliminates it — that digit is no longer a candidate and its note should be removed.

Are automatic candidates cheating?

They automate candidate bookkeeping, not the logical deduction itself. Whether you use them is a play preference. They can be especially useful when learning advanced techniques because the candidate state stays complete and visible.

What is the difference between notes mode and normal number entry?

Normal entry claims a solved value for a cell. Notes mode records unresolved possibilities without claiming that any one of them is the final answer.

What to learn next

Once you can maintain and interpret candidates confidently, study Naked Singles and Hidden Singles. Then move into Locked Candidates, Naked Pairs, and Hidden Pairs, where candidate notation begins to create systematic eliminations across a house.