Beginner course · Lesson 3
Pencil marks that actually help
Candidate notes are a working map of what can still fit. Used carefully, they reveal singles and pairs. Used too early or left out of date, they become noise. The aim is not to write more—it is to make every note trustworthy.
What a pencil mark means
A note says that a digit is not present in the cell’s row, column or 3×3 box. It does not claim that the digit belongs there. If a cell contains notes 2 and 7, either value is still legal until another deduction removes one.
When to start making notes
Begin with direct scanning. Nearly complete rows, columns and boxes often yield several placements without notation. Add notes when repeated scans stop producing naked or hidden singles. On an easy puzzle, you may need notes in only one crowded area; on a harder puzzle, complete candidates are more useful.
- Choose a useful area. Start in a box or row with many givens.
- Check all three constraints. Remove digits already used in the row, column and box.
- Record every remaining candidate. Do not omit a legal digit because it feels unlikely.
- Update nearby notes immediately. After a placement, remove that digit from every peer.
- Rescan for consequences. Look for cells reduced to one candidate and digits reduced to one position.
Worked example: notes becoming a single
The highlighted centre cell has only candidate 5 after its row, column and box are checked. A candidate list of one is not merely a note—it is a naked single, so place the 5 and clear the marks.
Full notation or selective notation?
Selective notes
Record candidates only in promising cells—usually those with two or three possibilities. This keeps the grid calm and is often enough for easy and medium puzzles. Its weakness is that you cannot safely count candidates across a whole unit unless that unit is fully noted.
Full notes
Record every legal candidate in every empty cell. This takes longer, but makes hidden singles, pairs and advanced patterns easier to verify. Use it when a puzzle has stopped moving or when you want to practise technique spotting.
Patterns clean notes reveal
- Naked single: one cell has one candidate.
- Hidden single: one digit appears in the notes of only one cell in a unit.
- Naked pair: two cells in a unit contain the same two candidates, so those digits can be removed from the unit’s other cells.
- Locked candidate: all candidates for one digit inside a box lie on the same row or column.
Three habits that prevent mistakes
Write small, read slowly. A misplaced candidate can poison several later deductions. Erase as you go. Stale notes are no longer legal candidates. Do not promote a hunch. Two candidates mean “not decided,” even if one seems more likely.
Try a clean-note pass
Open an Easy practice puzzle and scan first. When you stall, fully note one 3×3 box. Make one logical placement, then update only its row, column and box before continuing.
Open practice mode