A pencil mark is a small digit written in a cell to record that the value is still possible there. It sounds trivial and it changes everything: techniques that are invisible without candidates become obvious with them.
When to start marking
Not immediately. On easy and medium puzzles, scanning places plenty of digits with no notes at all, and writing a full candidate grid first wastes time and clutters the board. The right moment is when a complete scan of all nine digits produces no placements.
At that point, fill candidates for the whole grid at once. Partial marking — noting a few cells here and there — is where most errors come from, because you forget which cells you have done.
Full notation versus targeted notation
Full notation means every empty cell carries its complete candidate list. It is thorough, it makes pairs and triples visible, and it is what the fill-candidates button produces. The cost is visual noise.
Targeted notation means marking only one digit across the grid, or only one box in detail. It is cleaner and it works well when you are hunting a specific pattern, but it relies on you remembering what you have and have not covered.
The practical recommendation: full notation once scanning dies, then work from it. Targeted notation is for experienced solvers who know exactly what they are looking for.
The stale candidate
The commonest sudoku error is not a wrong digit — it is a candidate you forgot to remove after placing a number elsewhere. One stale mark can lead to a chain of false deductions. The board here removes candidates automatically when you place a digit, which eliminates the problem entirely.
Keeping candidates accurate
Whenever a digit is placed, it must vanish from the candidates of every cell in that row, column and box. Doing this by hand is where errors creep in, especially near the end of a long puzzle when attention drops.
On this board the update is automatic, so the candidate lists always reflect the real state of the grid. If you are solving on paper, get into the habit of doing the three-region sweep immediately after every placement, before doing anything else.
Reading the marks
Once candidates exist, several techniques become straightforward:
- Naked single — a cell with exactly one candidate. Place it.
- Hidden single — a digit that appears as a candidate in only one cell of a row, column or box. Place it, even if that cell has several candidates.
- Naked pair — two cells in the same region with the same two candidates. Those two digits belong to those two cells, so remove them from every other cell in the region.
- Locked candidate — a digit whose candidates within a box all sit in one row or column. It must go somewhere on that line inside the box, so remove it from the rest of that row or column.
None of these are visible without candidates, which is why marking is the gateway to hard puzzles rather than a crutch.
Reducing the clutter
A full candidate grid is dense. Two habits help. First, resolve every naked and hidden single before looking for anything more complex; each placement removes candidates elsewhere and thins the grid. Second, work one region at a time rather than letting your eye roam — a single box, then the next.
A worked sequence
- Scan all nine digits. Place whatever appears.
- Repeat until a full sweep gives nothing.
- Fill candidates for the whole grid.
- Sweep for naked singles, then hidden singles. Place them; candidates update.
- Sweep for naked pairs and locked candidates. Each one removes marks, often producing new singles.
- Return to step 4 and repeat until the grid is done.
That loop solves virtually every puzzle up to expert level. Anything harder requires techniques built on the same foundation, so the notation habit is worth getting right early.