Sudoku Candidates

A candidate is a digit that has not yet been ruled out for an unsolved Sudoku cell.

To calculate candidates, start with digits 1–9 and eliminate every digit already forbidden by the cell's row, column, or box. The digits that remain are the cell's current legal possibilities.

Candidates become essential as Sudoku gets harder because progress is not always an immediate placement. Many intermediate and advanced techniques work by proving that one or more candidates are impossible, which changes the grid until a forced placement or another pattern appears.

What is a candidate in Sudoku?

Suppose an unsolved cell can legally contain 2, 5, or 8. Its candidate set is:

{2, 5, 8}

That notation means:

• 2 has not yet been ruled out;
• 5 has not yet been ruled out;
• 8 has not yet been ruled out;
• every other digit is already impossible because of the current grid.

A candidate is therefore not a prediction about what the solution probably is. It is a statement about what is still possible.

The final value of the cell is one member of that set, but you should not choose it until logic proves which candidate survives.

How do you find the candidates for a cell?

For any empty cell, check the three houses that contain it:

1. its row;
2. its column;
3. its 3×3 box.

Start with:

{1, 2, 3, 4, 5, 6, 7, 8, 9}

Suppose the digits already present across those three houses rule out:

1, 2, 3, 5, 6, 8, 9

The remaining set is:

{4, 7}

So 4 and 7 are the legal candidates for that cell at this moment.

You do not choose between them. You keep both until another placement or deduction eliminates one, or until some house-level logic proves that one of them must be used there.

Candidates are possibilities, not guesses

This distinction is fundamental.

A candidate survives because the current Sudoku constraints do not forbid it.

A guess places one surviving candidate without proving that it must be correct.

For a cell with candidates {4, 7}, both values are currently legal. Entering 4 simply because it looks promising is a guess. Removing 4 because a valid deduction proves it impossible is logic. Once that happens, {7} remains and the cell becomes solved.

Candidate-based solving is therefore a way to postpone commitment until the grid supplies enough information.

Cell candidates vs digit positions in a house

Candidates can be read in two complementary ways.

Cell-first view

Ask:

Which digits can still go in this cell?

A cell such as {2, 5, 8} contains three candidate values. This view is especially useful for Naked Singles, Naked Pairs, Wings, and other techniques built around the contents of particular cells.

Digit-first view

Ask:

Where can this digit still go in this row, column, or box?

A row might contain candidate 6 in only two unsolved cells even though both cells have several other candidates. That positional information is the basis of Hidden Singles, Locked Candidates, strong links, Fish, and many chain techniques.

Learning to switch between those two views is one of the most important steps from beginner to intermediate Sudoku.

Legal candidates vs written pencil marks

A legal candidate is part of the logical state of the puzzle.

A pencil mark or note is a way to display some or all of that state.

If a cell's complete legal set is {2, 5, 8} but you have written only 2 and 8 as selective notes, the underlying candidate 5 has not stopped being possible. Your notation is simply incomplete.

That distinction matters whenever a deduction assumes full candidate information. A pattern cannot be validated safely from incomplete notes if the missing candidates could change the logic.

The dedicated Sudoku Pencil Marks Guide explains full notation, selective notation, Snyder notation, and digital note systems in more detail.

Why candidates change during a solve

Candidate sets describe the current grid, not the puzzle forever.

Whenever a digit is placed, that digit becomes impossible in every unsolved peer of the solved cell. A candidate elimination can also change the structures available elsewhere.

A common sequence looks like this:

1. digit 5 is solved in one cell;
2. 5 is removed from its unsolved peers;
3. another cell changes from {5, 7} to {7};
4. that cell becomes a Naked Single;
5. solving 7 removes more candidates from its peers;
6. another placement or candidate pattern becomes available.

This feedback loop explains why candidate maintenance is part of solving rather than mere bookkeeping.

How candidate eliminations create progress

A Sudoku move does not have to fill a cell immediately.

Suppose a cell contains {3, 8}. A valid technique proves that 3 cannot be there. The new set is:

{8}

The elimination has created a forced placement.

In harder puzzles, an elimination may not produce a Single immediately. It may instead simplify a pair, create a strong link, break a Fish pattern, or expose a chain. The progress is still real because the solution space has become smaller.

That is why advanced Sudoku Guides often describe an outcome as:

eliminate candidate 6 from r4c7

rather than:

place a digit now.

Naked Singles from candidates

If an unsolved cell has exactly one legal candidate, that candidate must be the cell's value.

Example:

{8}

The cell must contain 8 because every other digit has been eliminated.

This is a Naked Single: the solution is visible directly from the cell's candidate set.

Hidden Singles from candidate positions

A Hidden Single uses the digit-first view.

Imagine a row in which candidate 6 appears in only one unsolved cell. That cell might contain {2, 6, 9}, so it is not a Naked Single. But if no other cell in that row can contain 6, then 6 must be placed there.

The 6 is “hidden” among other candidates inside the cell but is unique as a position within the house.

This is why scanning candidate positions across a row, column, or box is just as important as counting candidates inside one cell.

How candidates reveal subsets

Candidate relationships can reserve several digits for several cells.

Suppose two cells in the same house both contain only:

{3, 8}

Those two cells must contain 3 and 8 in some order. Therefore no other cell in that house can contain candidate 3 or 8.

That is a Naked Pair.

Triples and larger subsets extend the same idea. Hidden subsets reverse the perspective by looking for digits restricted to a particular group of cells.

The important lesson is that candidates do more than describe uncertainty. Their distribution creates logical structure.

How candidates support advanced techniques

As difficulty increases, candidates become the raw material for many technique families:

• Locked Candidates compare where one digit can appear across an intersecting box and row or column;
• Fish compare candidate positions for one digit across several rows and columns;
• Wings use small candidate sets in linked cells;
• Coloring follows strong relationships for one candidate digit;
• Chains connect candidate truths and falsehoods through cells and houses.

You do not need to understand those techniques to learn candidates. The point is that accurate candidate state lets all of them exist.

Complete vs partial candidate notation

A solver can work with candidates without displaying every one of them.

Complete candidate notation

Every unsolved cell shows every currently legal candidate.

This is the clearest state for systematic intermediate and advanced solving because you can trust that an absent candidate has genuinely been eliminated.

Partial or selective notation

Only selected candidate information is recorded.

This can keep the board cleaner and is often efficient on easier puzzles, but the notes no longer represent the complete logical state. Before applying a technique that depends on full candidate sets, you may need to complete or verify the notation.

Do you need to write every candidate?

No.

Many Easy puzzles can be solved using direct scanning and Singles without writing full candidates. Some experienced paper solvers deliberately use sparse notation until the puzzle becomes difficult enough to justify a full candidate grid.

The correct question is not:

Have I filled every empty cell with notes?

It is:

Do I have enough reliable candidate information for the deduction I am trying to make?

For learning advanced techniques, full candidates are often the safest teaching state because the relevant relationships are explicit.

How to keep candidate lists accurate

Candidate errors can make valid techniques appear invalid — or worse, make an invalid deduction appear valid.

Use this discipline:

1. Check the row, column, and box before adding a candidate.
2. After every solved digit, remove that digit from all unsolved peers.
3. Apply proven candidate eliminations immediately.
4. Do not keep a candidate simply because it was possible several moves ago.
5. Before using an advanced pattern, confirm that its relevant candidate state is complete and current.
6. If something produces a contradiction unexpectedly, re-check earlier notes before assuming the puzzle is wrong.

Accurate candidates matter more than having many candidates visible.

Candidates in digital Sudoku

Digital Sudoku can expose candidate state in several ways:

• manual notes entered by the player;
• automatic candidates calculated from current legality;
• automatic removal of notes from peers after a placement;
• digit filters showing every possible position for one number;
• teaching overlays that temporarily highlight the candidates involved in a technique.

These interface choices change the amount of bookkeeping required, but not the underlying logic.

One useful product distinction is between:

• legal candidate state — what is actually possible according to the puzzle;
• displayed notes — what the interface or player chooses to show.

Keeping those ideas separate avoids treating a missing visual note as if it were automatically a logical elimination.

FAQ

How many candidates can a Sudoku cell have?

An unsolved cell can initially have several legal candidates. As constraints accumulate, the set shrinks. When only one legal candidate remains, the cell is a Naked Single.

Is a cell solved when it has two candidates?

No. A cell such as {3, 8} means both values remain possible. You need another deduction before one can be eliminated or one value can be proved.

Are notes and candidates the same thing?

Not exactly. Candidates are logical possibilities; notes or pencil marks are the visible notation used to record them. Full notes may mirror the complete candidate state, while selective notes do not.

What is the difference between a Naked Single and a Hidden Single?

A Naked Single has only one candidate inside the cell. A Hidden Single can have several candidates in its cell, but one digit has only one possible position in a row, column, or box.

Should candidates update automatically?

That depends on the solving experience. Automatic candidates reduce bookkeeping. Manual candidates require more maintenance but can be useful for learning the consequences of each placement. The logical definition of a candidate is the same either way.

Can a candidate be legal now and impossible later?

Yes. Candidates reflect the current grid. A later placement or valid elimination can remove a candidate that was previously legal.

What to learn next

Continue to Sudoku Pencil Marks to learn how candidate information can be recorded efficiently. Then study Naked Singles, Hidden Singles, and Locked Candidates to see the first major deductions created by candidate state.