Pencil marks and notes

What it is

Pencil marks are small notes you write in a cell to show which digits could still go there. These possible digits are called candidates. On paper, people write them small in the corner of the cell. On sudoku.ie you switch on notes mode, then tap a cell and the digits you want to note.

Notes turn the puzzle from something you hold in your head into something you can see. Every technique beyond the basics, from pointing to swordfish, is described in terms of candidates. Learning to keep good notes is the single biggest step from Easy to Medium.

How to work out a cell’s candidates

For any empty cell, start with all nine digits, 1 to 9. Then cross out:

1. every digit already in the cell’s row,
2. every digit already in the cell’s column,
3. every digit already in the cell’s box.

Whatever is left are the candidates. If only one is left, you have found a naked single and can fill it in.

A worked example

Take the cell at row 5, column 5, right in the centre of the grid. It sits in box 5.

• Row 5 already contains 1, 3 and 8.
• Column 5 already contains 2 and 6.
• Box 5 already contains 3 and 9.

Put those together and the digits ruled out are 1, 2, 3, 6, 8 and 9. That leaves 4, 5 and 7. So you note 4, 5 and 7 in that cell.

A little later you place a 5 at row 5, column 2. That 5 is in the same row, so 5 can no longer go at row 5, column 5. You remove it from your notes, leaving 4 and 7. Later still, a 4 lands in column 5. Now only 7 remains, and the cell is solved.

Full notes or light notes

There are two common styles.

Full notes means writing every candidate in every empty cell. It takes a few minutes at the start, but it gives you a complete picture. It is the style you need for the harder techniques, because patterns like pairs and X-wings only show up when the notes are complete.

Light notes means only marking a digit when it can go in just two cells of a box. You note it in both cells and leave the rest alone. This keeps the grid clean and is often enough for Easy and Medium puzzles.

A good approach is to start with scanning, use light notes as you go, and switch to full notes when you get stuck.

Keeping notes accurate

Notes are only useful if they are correct. Every time you place a digit, remove that digit from the notes of every cell in the same row, column and box. Make this a habit straight away, before you do anything else.

A common mistake

The biggest mistake is stale notes: forgetting to clear a candidate after placing a digit nearby. A stale candidate can make you think a cell has two options when it really has one, so you miss an easy move. Worse, it can make a pattern look real when it is not, which leads to wrong eliminations.

The second mistake is starting full notes too early. If scanning is still finding placements, use it. Notes are for when the easy moves run out.

When you will need it

On Easy days, notes are optional. Many people solve Monday’s puzzle without any. From Medium onwards (Tuesday, Wednesday and Sunday), notes become very helpful, and on Hard and Expert days they are essential. Every technique guide from here on assumes you are keeping candidates.