Pencil marks

Sooner or later, scanning stops finding numbers: you go through the nine digits in the nine boxes and none has a single place. In Easy puzzles this hardly ever happens; in the others it always does. It is time to write notes.

Notes are the candidates of each empty cell, written small inside it: the numbers that can still go there. Instead of keeping them in your head, you leave them in view. That makes it possible to see things you can't see by looking only at the given numbers.

How to write them

For each empty cell, look at its row, its column and its box. Write down the numbers that appear in none of the three.

In this grid, scanning no longer finds anything. We start with the seven empty cells of box 5, the middle one, writing the notes for each of them.
One of them is special: the one in row 4, column 6. Row 4 already has the 2, 3, 4, 7 and 8; column 6 adds the 1, 5 and 6. Only the 9 is left, and it is this cell's number.
After placing the 9, remove the 9 from the notes of the cells that see it: two in row 4 and four in box 5. Forgetting this step is the most common mistake with notes, on paper. In the game it is automatic: the «Clear notes on placing» option, in the ⋮ menu, is on from the start and does it for you. But the reverse only happens with auto notes on: without them, if you later erase or change the 9, the notes it removed do not come back.

A cell left with a single candidate is a naked single. Notice that scanning would not find it: the 9 appears only once in this grid. Neither row 4, nor column 6, nor box 5 leaves it with a single place.

One number at a time

Writing notes cell by cell means looking at three units at once, which makes it easy to forget a number. It is usually faster to do as in scanning: choose a number and go through the nine boxes, writing it in every cell where it can still go. After nine passes the grid has all its notes, each one checked the same way.

Counting candidates

Once the notes are written, it is worth counting them. A cell with one candidate is solved; a cell with two is where patterns like the naked pair tend to appear; a cell with five or six rarely gets you anywhere.

The same grid with all the notes. Of the 40 empty cells, only one has a single candidate; eleven have two.

Notes you can trust

All or nothing. A missing note makes a cell look as if it has fewer options than it does, and leads to the wrong number. In a unit, either you write the notes for every empty cell, or you draw no conclusions from them.
Up to date. Every number placed is removed from the notes of the 20 cells it sees. In the game this is automatic; if you turn the option off, or play on paper, you have to do it by hand.
Watch out for changed numbers. When a number is erased or changed, the notes it removed from neighbouring cells are not restored, unless auto notes are on. If the number was wrong, it may have taken another cell's correct candidate with it. A missing note is worse than none.
When in doubt, count again. If a conclusion looks odd, redoing that cell's notes from its row, column and box takes a few seconds. If the problem is bigger, «Clear notes only», in the ⋮ menu, clears them all and keeps the numbers; redoing the notes from scratch is often faster than hunting for the wrong one.

When you suspect a number already placed, the same menu has «Erase wrong numbers». It removes only the numbers that are wrong and keeps the others, but it counts as help, just like «Show mistakes». And without auto notes, the notes those numbers removed from their neighbours do not come back either: after using it, check the notes around the cells left empty, or clear them and redo them.

Three ways to write them

In the game, notes are written with the Notes button, next to the keypad. The first tap switches from Number mode to notes, in the style you used last time; each tap after that changes the style. The three dots on the right show which one you are in. To write numbers again, tap Number.

The style only changes how the notes are shown: they are always the same notes. When you change style, the ones already written appear in the new form, and any of them can be changed or erased in any style.

The same notes in the three styles, in the order the button goes through them.

Candidates: each number in its fixed place inside the cell, the 1 in the top left corner, the 9 in the bottom right corner. It is the easiest to read, because finding a number means always looking at the same spot in each cell.
Corner: the numbers around the cell, next to the corners and the edges.
Centre: the numbers in a row, in the middle of the cell. It takes up less space and reads like a list.

Some experienced players use Snyder notation: in a box, a number is only noted when it has two or three possible places, and those notes go in the corner, while the centre holds the full list for cells that already have few candidates. For that, each style's notes have to be independent. In the ⋮ menu, «Separate notes by style (Snyder)» does exactly that: what you write in the corner can only be changed in the corner, and the same for the centre and the candidates. When you turn the option off, the notes of the three styles merge back into one.

On a computer keyboard, Shift with a number writes it as a note, in the chosen style, without leaving Number mode.

Auto notes

The button with the dotted square and an «A», in the top row, turns on auto notes: the game writes the candidates of every empty cell. While they are on, the button is filled and notes are shown and written in the Candidates style, the only one where up to nine numbers per cell are easy to read; you can still remove them by hand. Erasing or changing a number puts it back in the notes of the neighbouring cells where it becomes possible again. A second tap turns them off, clears the notes, even the ones written by hand, and brings back the style you were using before. With notes separated by style, only the Candidates notes are cleared.

The same button, off and on.

They save work, but they count as help from the moment you turn them on, even if you turn them off straight away: the solve still goes into your statistics, flagged, but it is left out of the comparisons with other players.

With the notes written, what is left is learning to read what they say. The first thing to look for is the simplest: a cell with a single candidate, the naked single.