Sudoku Pencil Marks: How to Use Notes Like a Pro

Pencil marks are the point where Sudoku turns from a scanning game into a reasoning game. Used well, they make hard puzzles feel calm and orderly. Used badly, they turn the board into a cluttered mess that hides the very move you are looking for. This guide shows you how to write them, when to bother, and how to read them, with real positions from our solver.

If you are brand new to the game, read How to Play Sudoku first. It covers the rules and the first moves, which you will need before notes are useful.

What are pencil marks?

Every empty cell has a set of candidates: the digits from 1 to 9 that are not already used in its row, its column or its 3×3 box. Pencil marks are simply those candidates, written small, so you don’t have to work them out again each time you look at the cell.

The name comes from paper puzzles, where players pencilled in tiny digits they could erase later. In apps the same idea is usually called notes. Whatever you call them, they are a memory aid. They never change the puzzle; they just store what you have already figured out.

When to start writing notes

A common beginner habit is to fill every cell with notes before making a single move. Don’t. At the start of a puzzle most cells have five or six candidates, so the notes are long, slow to write and not very informative. Worse, every number you place afterwards makes several of them out of date.

A better rhythm looks like this:

1. Scan first. Go digit by digit and box by box looking for hidden singles. Easy puzzles can often be finished this way with no notes at all.
2. Note the tight spots. When a box or row needs a digit that fits in only two or three cells, jot it down. These small notes are cheap and very useful.
3. Go full candidates when scanning dries up. Once you have looked at every digit and found nothing, it is time to write out every candidate. By then the board is fuller, so the notes are shorter.

Corner vs centre notes (and Snyder notation)

Some apps and many experienced solvers use two different kinds of note in the same cell:

• Centre notes list the possible digits for this cell. A cell with a centre note of 3 7 can only be 3 or 7.
• Corner notes mark where a digit could go within a box. If the 5 in a box can only go in two cells, you put a small 5 in the corner of both.

A popular way of using corner marks is Snyder notation, a method associated with Thomas Snyder, a three-time World Sudoku Champion. The idea is to write a digit in a box only when it can go in exactly two cells of that box. You skip everything else. The board stays clean, the marks are quick to write, and two marks for the same digit in a box instantly tell you that one of those two cells holds it.

Snyder-style marks are excellent early in a puzzle, because they only record strong information. Their weakness is that they are incomplete: on harder puzzles you will eventually need to know every candidate in a cell, and that is when full centre notes take over.

Full candidates or partial notes?

There are two broad approaches, and most good solvers switch between them.

On Sudoku.my, Easy puzzles only need singles, so partial notes or none at all are fine. Medium adds locked candidates, which partial notes can catch. Hard puzzles need pairs and triples, and those almost always require full candidates in the area you are working on.

When you do write full candidates, be systematic. Work one box at a time, and for each empty cell go 1 to 9 checking the row, column and box. Or go digit by digit: mark every cell in the grid where the 1 can go, then the 2, and so on. The digit-by-digit method is slower but makes it much harder to miss a candidate.

Keeping notes tidy

Notes are only useful if they are true. Every time you place a number, that digit stops being possible in every other cell of the same row, column and box (the cell’s 20 “peers”). Those notes must go.

On paper, that means erasing carefully after every move. In Sudoku.my, the Auto-remove notes setting does it for you: when you place a number, the app clears that digit from the notes of every peer. It is on by default, and you can switch it in Settings if you prefer to do it by hand.

You will see exactly this in the next diagram. Placing the 7 in row 1, column 8 removes the 7 from six notes: row 1, columns 2 and 7; row 3, columns 7 and 8; and column 8 in rows 6 and 9.

Spotting naked singles in your notes

A naked single is a cell with only one candidate left. Without notes they are surprisingly hard to see, because you have to count all 20 peers in your head. With full notes they jump out: they are the cells with a single small digit.

Look around this grid and you will also see how tight the board is getting. Many cells are down to two or three candidates, such as row 2, column 9 with just 3 and 9. After a few more placements, some of those will become naked singles too.

Spotting locked candidates

Locked candidates are the first pattern that really needs notes. If, inside one box, every candidate for a digit lies on the same row or column, that digit must be in that line within the box. So you can remove it from the rest of the line outside the box.

Notice how the notes do the work. The top-left box has four empty cells, and only two of them, row 2 and row 3 of column 3, have a 9 in their notes. Without notes you would have to rebuild that fact from scratch. With them, it is a matter of reading. This is also where the Snyder idea pays off: two 9s marked in the same box, lined up in one column, are a locked candidate waiting to be used.

Spotting pairs

A naked pair is two cells in the same row, column or box whose notes are the same two digits and nothing else. Those two digits must go in those two cells, so you can remove them from every other cell in the unit. Pairs are almost impossible to see without notes, and easy to see with them.

Here the pair clears four other cells. Row 9, column 6 drops from 4 9 to just 9: the pair has created a naked single. That chain reaction is typical, and it only happens if your notes are complete. For the full story, including hidden pairs and triples, read Naked and Hidden Pairs.

Common pencil-mark mistakes

1. Missing a candidate. The most dangerous mistake. If a cell really can be 4 but you forgot to note it, you may “find” a naked single that is wrong. When a deduction feels too good, recheck that cell’s row, column and box.
2. Stale notes. Forgetting to erase a digit after placing it in a peer. Stale notes hide singles and can make pairs look like triples. Auto-remove solves this in the app; on paper, erase right after every placement.
3. Noting too early. Writing full candidates on a nearly empty board wastes time and creates more erasing later.
4. Mixing styles without a rule. If some cells hold full candidates and others only Snyder marks, a cell with one note may not really be a single. Decide which cells are “complete” and treat the rest with care.
5. Only reading notes, never scanning. Notes are a tool, not a replacement for looking. A quick digit-by-digit scan still finds hidden singles faster than reading 50 cells of small print.

How to use notes in Sudoku.my

Notes are built into every game, on every level and in the daily challenge.

• Turn notes on: tap the Notes button under the board. It shows On or Off, and the number pad changes style so you always know which mode you are in.
• Add or remove a note: select a cell and tap a digit. Tap the same digit again to remove it.
• On a keyboard: press N to switch notes on or off, type 1–9 to toggle notes, use the arrow keys to move, Backspace to erase a cell and Z to undo.
• Auto-remove: leave Auto-remove notes on in Settings and placed numbers clean up their peers for you.
• Stuck? Each puzzle has 3 hints, and a hint explains the move it finds, such as a locked candidate or a pair, so you learn to spot it in your own notes next time.

Miko the cat has one more tip: practise notes on Medium puzzles first. They are built to need locked candidates, so you get the payoff of good notes without the full clutter of a Hard grid. When that feels easy, the full set of techniques is waiting in our Sudoku strategies guide.

#Pencil marks#Notes#Candidates