Pencil marks — the small candidate digits solvers write in the corners of unsolved cells — are the most misused tool in Sudoku. Used well, they make the invisible visible: a Naked Pair that would take a minute of mental bookkeeping to confirm is simply there, two matching pairs of digits staring back at you. Used badly, they bury the puzzle under 200 tiny numbers, half of them stale, and turn solving into data entry. The difference is knowing when to mark, what to mark, and how to keep the marks honest.
What pencil marks actually are
A cell's candidates are the digits that don't yet conflict with its twenty peers (the cells sharing its row, column, and box). Pencil marks are just a written cache of that computation. That framing matters, because it tells you exactly what marks are for: they are for techniques that operate on candidates. Subset techniques (pairs, triples, quads) and fish patterns are pattern-matching over candidate lists — without written candidates you must hold those lists in working memory, which for most humans caps out around a pair.
The first rule: don't mark too early
Every digit you place invalidates marks in up to twenty cells. Mark the whole grid at the start of an easy puzzle and you will spend the entire solve erasing — and easy puzzles never needed candidates in the first place, because singles and Omission are all visible to a trained scan.
The professional habit is: scan first, mark when the scan stalls. Place every digit your eyes can find. Only when a full pass of cross-hatching and box counting yields nothing do you pay the cost of writing candidates — and by then the grid is fuller, so there is far less to write.
Two schools: full candidates vs. Snyder notation
Full-candidate notation
Write every legal candidate in every unsolved cell. This is what most apps mean by “auto-notes,” and it is the right mode for deliberate technique practice: naked subsets appear as literal matching sets, hidden subsets as digits confined to few cells, and fish as a digit's candidate positions across rows. The cost is visual noise and, on paper, real maintenance labor.
Snyder notation
Named for Thomas Snyder — multiple-time World Sudoku Champion and one of the strongest competitive solvers ever — this system marks only digits confined to exactly two cells within a box, written in cell corners. Nothing else gets marked. The insight is economic: bilocation within a box is the highest-value information per pencil stroke. Those two-cell constraints are exactly what produce the next placement (when one of the two cells resolves, the other is forced) and they chain into pointing pairs and X-Wings. Snyder notation keeps the grid nearly clean while capturing most of the deductive power, which is why it dominates competitive solving, where erasing costs seconds.
A sensible hybrid, used by many strong solvers: Snyder corners while the puzzle is flowing, then full candidates — often only in the stuck region — when the puzzle demands subset or fish logic.
The maintenance discipline
Stale marks are worse than no marks: every candidate-based technique silently assumes the candidates are correct. A leftover 5 in a cell whose column just gained a 5 can produce a “Naked Pair” that isn't one, and the resulting eliminations corrupt the puzzle in ways you may not notice for ten minutes. Two habits keep marks trustworthy:
- Erase immediately, in a fixed order. The instant you place a digit, remove it from the marks in the cell's box, then its row, then its column. Always the same order, so it becomes one motion instead of a search.
- Trust broken means rebuild. If you find any inconsistency — a mark that should be gone — assume there are others. Re-derive the candidates in that region rather than patching the one you noticed.
Digital play changes this economy: auto-updating candidates make maintenance free, which is precisely why serious learners should sometimes turn auto-notes off. The maintenance work is where beginners internalize peer relationships. Precision Sudoku's player takes the elimination-first idea to its logical end — you remove candidates rather than write digits, and a cell resolves when one candidate remains — which keeps your attention on the eliminations that constitute actual solving. Notice the design choice shared by this site, Snyder notation, and expert paper habits alike: attention is the scarce resource, and notation exists to spend it well.
Reading patterns from marks
Once candidates are written and clean, specific shapes become searchable:
- Cells with two candidates (bivalue cells) — the raw material of Naked Pairs and nearly every advanced chain technique. Many solvers mark or mentally note them as a matter of course.
- Matching candidate sets in one unit — two cells showing the same two digits, three cells whose candidates union to three digits: naked subsets, eliminating those digits from the rest of the unit.
- A digit appearing only twice in a unit — bilocation, the seed of Hidden Pairs, X-Wings, and coloring techniques.
This is why the walkthrough pages on this site show the full candidate grid before and after each technique: the skill being trained is seeing the pattern in the marks, not verifying it abstractly.
Common pencil-mark mistakes
- Marking everything at the start. Costs minutes, and the marks decay immediately. Scan first.
- Believing unverified marks. If you didn't maintain them, re-check a cell's candidates against its peers before building a deduction on them.
- Writing marks without reading them. Marks are a search structure, not a diary. After writing candidates in a region, immediately scan it for pairs and confined digits — that is the payoff you wrote them for.
- Using marks to avoid learning to scan. If you need full candidates to find Hidden Singles, the fix is cross-hatching practice, not more notation.
The endpoint of good pencil-mark habits is choosing your notation like a tool: bare grid for singles, corners for flow, full candidates for surgery. Drill each mode on puzzles that demand it — pick the technique and the generator supplies the puzzle.