Sudoku Pencil Marks and Notes Explained

Pencil marks are the small numbers you write in an empty sudoku cell to track which digits could still go there. "Notes", "pencil marks" and "candidates" all mean the same thing: on paper you pencil them into the corner of a cell, and in an app you switch on a notes mode and tap them in. Once the easy placements run out, notes are how you find naked pairs, pointing pairs and X-Wings. This guide covers when to start taking notes, the two main ways to write them, and how notes work on a phone.

Notes, pencil marks and candidates: one idea, three names

A candidate is a digit that is still possible for a cell. A pencil mark is a candidate you have written down. "Notes" is what most apps call the feature that lets you write them. If a cell in row 4 has a 2 and a 7 as its only options, you note 2 and 7 in that cell. When one of them gets ruled out, you remove it, and when only one is left, that digit is the answer.

When to start using notes

You do not need notes for every puzzle. A practical rule: if you have scanned the grid twice and cannot find another single, start writing candidates.

• Easy puzzles: usually solvable with naked singles and hidden singles alone. Solving these without notes is good scanning practice.
• Medium puzzles: you will usually stall once the singles dry up. Add notes at that point.
• Hard and Expert puzzles: most placements depend on candidate analysis, so writing notes early saves time.

Real players follow the same curve. In Sudoku Royale's Practice mode, notes get used on about 46% of puzzles overall, from 18% on Easy up to 84% on Expert.

Snyder notation: the minimal method

Snyder notation is named after puzzle author Thomas Snyder, and the rule is short: only note a digit when it has exactly two possible cells inside a 3x3 box. Go box by box. For each missing digit, count where it can go. Two spots means you mark both. Three or more means you leave it. One spot means you place it, because that is a hidden single.

The grid stays clean, and the useful patterns jump out. Two cells in a box with the same two marks form a naked pair. A digit whose two marks sit in the same row or column is a pointing pair. The weakness is that Snyder marks leave out digits with three or more spots, so on harder puzzles some patterns stay hidden until you add more.

Full notation: every candidate in every cell

Full notation means writing every possible digit in every empty cell. For each cell, check its row, column and box, and note any digit from 1 to 9 that is not already there. You get complete information and a busy grid.

Keep each digit in a fixed spot inside the cell, laid out like a phone keypad:

  1 2 3
  4 5 6
  7 8 9

With fixed positions you can scan a whole row for "is there a 7 here?" by looking at the bottom-left corner of each cell, without reading every mark. Full notation is what you need for X-Wing, Swordfish and the other advanced strategies like XY-Wing and coloring.

To keep it readable, place every single you can before you start, and remove a candidate from the row, column and box the moment you place that digit. You also do not always need the whole grid: hunting an X-Wing on 7s only needs to know where the 7s can go.

The hybrid approach most solvers end up with

1. Start with no notes and solve by scanning.
2. When scanning stalls, add Snyder marks.
3. If that is not enough, switch to full notation in the area you are working on.

You write as little as possible and still have the information when you need it.

How notes work in a sudoku app

Every good sudoku app has a notes mode, and the basics are the same almost everywhere:

• A notes toggle. Switch it on and the digits you enter become small candidates. Switch it off and they become answers.
• Adding and removing. Entering a digit that is already noted in a cell removes it, so the same action toggles a candidate on and off.
• Automatic cleanup. Many apps remove a candidate from the row, column and box when you place that digit. This fixes the most common paper mistake: forgetting to update your marks.
• Auto-fill candidates. Some apps can fill in every candidate for you. It saves time on hard puzzles, but you skip the part where you work out the candidates yourself, which is where a lot of scanning skill comes from.

Phones add one real problem: cells are small, and nine tiny digits in one cell are hard to read and hard to hit. Apps with larger touch targets for notes are easier on the eyes and the thumb.

How notes work in Sudoku Royale

Sudoku Royale is a classic, ad-free sudoku app for iPhone. Here is exactly how its notes work:

• The Notes toggle sits under the number bar at the bottom of the screen. With Notes on, picking a digit for a cell adds it as a note, or removes it if it is already there.
• Painting a note across cells. With Notes on, select a digit on the number bar, then drag across empty cells to write that note into each of them in one stroke. Handy for Snyder marks, where the same digit goes into two cells of a box.
• Two-finger notes. Hold a cell with one finger and tap or swipe digits with the other to add several candidates to that cell without lifting.
• Automatic cleanup. When you place a digit, its notes disappear from the same row, column and box.
• No auto-fill. Sudoku Royale does not fill in candidates for you. You write your own notes, which is the part that trains your eye.

One more detail changes how you use notes. In Sudoku Royale a wrong digit is rejected and never lands on the board. That means your notes are never built on top of a mistaken placement, which is the classic way a paper grid falls apart three steps later. For the full set of controls, see how to play sudoku on iPhone, and for the two ways to enter digits, see number-first vs cell-first entry.

Common pencil mark mistakes

Marking too much, too early

Full notation on an easy puzzle wastes time you could spend placing digits. Start without notes and add them when you stall.

Forgetting to update

On paper, the most dangerous error is placing a 5 and leaving 5 as a candidate elsewhere in its row, column or box. Every deduction after that is built on a wrong list. Apps that clean up automatically remove this risk.

Trusting marks over the grid

Notes are a record of your analysis, and the analysis can be wrong. Before acting on a naked pair or an X-Wing, check the elimination against the actual digits in the grid.

Notes by difficulty level

Different difficulty levels call for different amounts of notation:

• Easy: no notes needed.
• Medium: Snyder marks once scanning stalls. Enough for pairs and pointing pairs.
• Hard: full notation in the areas you are working on.
• Expert and above: full notation across the grid for advanced strategies.

New to sudoku? Start with how to play sudoku, then come back here when your first medium puzzle stalls.