Naked singles

What a naked single looks like

Pick any empty cell. Look along its row, down its column and inside its 3×3 box. Each of those three groups already holds some digits, and the cell cannot repeat any of them. If the digits you can see between the three groups cover eight of the nine possibilities, the ninth is forced. Nothing about the rest of the grid matters; the cell settles itself.

The diagram above comes from a real puzzle in this site's Easy pool and was produced by the same engine that powers the in-game hints. It shows the cell r3c2 (row 3, column 2), and the caption states the conclusion: only 1 is left, because every other digit is already present in a row, column or box that the cell shares. Notation throughout this series is row first, then column, counted from the top left, and boxes are numbered 1 to 9 in reading order.

How to spot them without pencil marks

You do not need candidate notes to find naked singles. Two scanning habits are enough.

• Crowded cells. Look for empty cells whose row, column and box are all well filled. A cell that touches a nearly complete row and a nearly complete column is the best place to start.
• Digit-by-digit elimination. For one empty cell, run through 1 to 9 and cross out each digit you can see in its row, column or box. If one digit is left standing, you have your single.

The first habit finds singles quickly in the opening minutes. The second is slower but certain, and it is what the engine does internally for every empty cell on every pass.

With pencil marks, they announce themselves

Once you write candidates into the cells, a naked single is simply a cell with exactly one mark. That is why notes are worth the effort even on easy grids: they turn a visual search into a lookup. The in-game auto-notes button fills every candidate for you, and with the "auto-eliminate" setting on, placing a digit clears it from the peers' notes at once, so new single-candidate cells appear immediately after each move. The guide on how to use pencil marks covers when to write notes by hand and when to let the game do it.

Why the deduction is airtight

Sudoku's only rule is that each row, column and box contains every digit once. A digit that is already in a group cannot appear a second time in it. A naked single is nothing more than that rule applied to one cell from three directions at the same time. There is no guess, no "probably", and no assumption about the rest of the puzzle, which is why naked singles are the foundation that every other technique builds on. Larger techniques such as naked pairs are really just this idea spread over several cells at once.

Common mistakes

• Forgetting the box. Row and column are easy to scan; the box is the group most often overlooked. If a cell looks like it has two candidates, check whether its box already contains one of them.
• Trusting a single that rests on a wrong digit. A naked single is only as good as the digits it was derived from. If an earlier entry was a guess, the single inherits the error. Turn on mistake feedback, or check the board after a streak of entries, to catch this early.
• Stopping when the singles run out. When no cell has one candidate, that does not mean the puzzle is stuck. It means a different view is needed, and the natural next one is the hidden single, which looks at where a digit can go rather than what a cell can hold.
• Chasing singles in a random order. Work by the most constrained area first. Filling one cell often creates the next single immediately, so a chain of placements through a single band or stack is common.

Where the site's grading needs it

The site grades puzzles by the techniques a human needs, not by the number of clues. Easy is defined as naked singles and hidden singles only. In the committed frequency data, produced by scripts/technique-frequency.ts over 1,000 stored classic puzzles per tier, naked singles were used in 1,000 of 1,000 puzzles at every tier from Easy to Evil. Method matters here: each puzzle is solved cheapest technique first, and a technique counts if the solve used it at least once. So the figure says that every puzzle, however hard, still ends in naked singles once the harder deductions have opened it up. The page on how Sudoku difficulty is graded explains the tiers and their limits, and the technique frequency guide shows the full table.

A short routine you can reuse

1. Scan the most filled rows, columns and boxes for cells with only one possible digit.
2. Place every single you find, then re-scan the cells that share a row, column or box with the new digit, because they are the ones that just changed.
3. When a full pass finds nothing, switch to hidden singles.
4. If both kinds of single are exhausted, add notes and look at naked pairs.

How the engine and the hints find them

The technique engine behind the in-game hints keeps, for every cell, a bitmask of the digits still possible. Placing a digit clears its bit from every cell that shares a row, column or box with it. A naked single is then a cell whose mask has exactly one bit set, which the engine can detect with a single check per cell. Because naked singles are the cheapest technique, the engine always looks for them first; a harder technique is only reported when no cell anywhere has a single candidate. That ordering is also why a hint at level two will never name an advanced pattern while a plain single is available.

In the variants

The idea is identical in every variant, but the number of groups that eliminate candidates changes. On the diagonal board, a cell on a main diagonal also loses every digit already placed on that diagonal, so cells on the diagonals reach a single sooner. On the anti-knight board, a cell also loses the digits a chess knight's move away, which can be as many as eight extra cells. On the killer board, cage totals feed the same machinery. More eliminating groups means more naked singles, which is one reason these boards feel different even when the grid is the familiar 9×9.

Check your understanding

• A cell sees the digits 1, 2, 3, 4, 5, 6, 7 and 9 across its row, column and box. What goes in the cell, and what is the name of the technique?
• A cell has two candidates, 3 and 8, but its box already contains an 8 elsewhere. How many candidates does it really have?
• You placed a 5 in r4c4. Which other cells need their notes updated?

The answers are 8, one (the 3, because the cell was never really able to hold the 8), and every empty cell in row 4, column 4 and box 5.

Practice

Play an Easy puzzle on the classic Sudoku board and watch for cells that fill without any hint. If you get stuck, the first hint level tells you where to look, the second names the technique, and the third shows the move before you choose to apply it, so you can use it as a coach without giving up the whole answer. The 4×4 board is a gentle place to see the idea on a grid small enough to hold in your head.

Next in the series: hidden singles. Back to the full technique list.