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When a hard Sudoku stops yielding obvious numbers, do not guess or jump straight to an advanced trick. Check the grid for recording errors, rescan rows, columns and boxes, and restart that scan after every placement. If singles no longer help, make complete candidate notes and look for pairs and box-line interactions. Only then move on to patterns such as X-Wing, swordfish, coloring or chains. A useful next move may be a candidate elimination rather than a filled cell.
What should you do first when Sudoku progress stops?
Pause before making another move. A puzzle can feel stuck because a simple placement was missed, a candidate was recorded incorrectly, or the next deduction removes a possibility without filling a cell. Work through those possibilities in order instead of scanning randomly or guessing.
- Check the grid. Compare filled digits with the original givens and verify that no row, column or 3×3 box contains a repeated digit. Re-read any cell you filled recently. This is a practical safeguard against a transcription or note-taking error, not a claim that every stall comes from a mistake.
- Rescan the whole puzzle. Inspect rows, columns and boxes for missing digits and possible locations. Do not look only at the area where you made your last move.
- Look for singles. Find an empty cell with one remaining candidate, then check whether any missing digit has only one possible location in a row, column or box.
- Make complete candidate notes if scanning produces nothing. Use the notes to examine pairs and interactions between a box and its crossing rows or columns.
- Escalate to wider patterns only after those checks. Look for X-Wing or swordfish, then consider coloring or chains if the candidate pattern calls for them.
This order follows the progression in xSudoku.org’s guide to Sudoku solving techniques. Its central practical habit is to re-scan after a placement: a newly filled digit can create an opportunity anywhere in the grid, including in a region you thought you had finished.
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How to rescan without overlooking an easy placement
Sweep by digit
Choose a digit and inspect each 3×3 box where it is still missing. Existing instances of that digit in rows and columns rule out cells in the box. If only one location remains, the digit belongs there. Repeat with the other missing digits.
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A digit-by-digit sweep gives the scan a clear question: “Where can this digit still go?” It can expose a placement that is less visible when you focus on one empty cell at a time. You can also scan by unit—checking each row, column and box for missing digits—but keep track of what you have already examined so that the same regions do not consume all your attention.
Check for both kinds of single
A naked single is an empty cell with only one candidate left. A hidden single is a digit that can go in only one cell in a particular row, column or box, even if that cell has other candidates. The first is easiest to find by asking what can fit in a cell; the second by asking where one digit can fit in a unit.
After placing a single, update the affected row, column and box, then resume a whole-grid scan. Do not assume that the next useful deduction is nearby. A placement can make a digit unique in a distant unit, which is why returning only to the last cell or box can leave easy progress undiscovered.
When should you write candidate notes?
If a careful scan finds no single, write down every digit that could legally go in each empty cell. These possibilities are called candidates. A complete, current set of notes turns an apparently crowded grid into a map of where each digit can still appear.
Notes are only useful if they are accurate. When a digit is placed or eliminated, remove it from every affected candidate list in that cell’s row, column and box. If you notice that a note conflicts with a filled digit or a unit’s remaining possibilities, correct the notes before relying on a pattern. One stale candidate can make a valid pattern look absent—or make an invalid pattern appear real.
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Candidate work does not have to produce a filled number immediately. Eliminating a possibility can make a later single possible, reveal a pair, or expose a larger pattern. Treat a valid elimination as progress, then scan again for what it enables.
Which candidate patterns should you try before advanced techniques?
Naked and hidden pairs
A naked pair occurs when two cells in a unit contain the same two candidates and no others. Those two digits must occupy those two cells in some order, so they can be removed from other cells in that unit. For example, if two cells in a row are both {2, 7}, no other cell in that row can contain 2 or 7.
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A hidden pair is the complementary situation: two digits can appear only in the same two cells of a unit, but those cells may also have other candidates written in them. The pair reserves those cells for the two digits, allowing the other notes there to be removed. In either case, check that the pattern is confined to one unit and that the candidate notes are complete before eliminating anything.
Pairs are useful because they reduce candidate lists without requiring an immediate placement. Once you remove candidates, inspect the affected unit again for a single or another pattern. A pair is not a reason to fill either cell unless the remaining candidates make a placement certain.
Pointing pairs and box-line reduction
A box and one of its crossing rows or columns can constrain each other. If all remaining candidates for a digit inside a 3×3 box lie in a single row, that digit must occupy one of those cells in the box; it can therefore be eliminated from the rest of that row outside the box. The same logic applies when the candidates line up in a column. This is commonly called a pointing pair when two candidates form the line, though the logic can apply whenever the candidates are confined to that line.
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The reverse interaction is often called box-line reduction. If all candidates for a digit in a row or column lie within one 3×3 box, that digit can be removed from other cells in that box outside the row or column. In both directions, the key is the restriction: every possible position in one unit must lie in the intersection with the other unit. A loose alignment is not enough.
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How does an X-Wing work?
An X-Wing is a pattern for one candidate digit across two rows and two columns. In each of two rows, that digit must be possible in exactly the same two columns. The four candidate positions form the corners of a rectangle. Because each row must contain the digit in one of its two candidate cells, the two rows together occupy both shared columns. As a result, the digit can be removed from other candidate cells in those columns outside the two pattern rows.
How to check one
- Choose one digit. Look at its candidate positions across the grid, not at all candidates in a cell at once.
- Compare rows. Find two rows in which the digit appears as a candidate in exactly two cells per row.
- Confirm the columns match. The two candidate cells in each row must lie in the same pair of columns. If one row has a candidate in another column, the proposed rectangle does not meet the pattern’s constraints.
- Eliminate only outside the rectangle. Remove that digit from other candidate cells in the two shared columns, but not from the four corners.
- Update and rescan. Check whether an elimination creates a single or reveals another candidate pattern.
For instance, suppose digit 6 has candidates in columns 2 and 8 in row 3, and also only in columns 2 and 8 in row 7. Those four positions form an X-Wing. A 6 cannot also be placed elsewhere in column 2 or column 8, so remove 6 from candidate lists in those columns outside rows 3 and 7. This example illustrates the logic; it does not describe a particular published puzzle.
The reasoning works with rows and columns reversed: two columns can each contain the candidate in the same two rows, allowing eliminations from those rows elsewhere. Do not call any four-corner arrangement an X-Wing. The candidate positions for the selected digit must satisfy the two-by-two restriction, and the notes must be correct before you eliminate candidates.
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When should you move on to swordfish, coloring or chains?
If singles, pairs and box-line interactions do not help, inspect candidate positions across the grid for more advanced structures. A swordfish extends the same broad idea as an X-Wing across three rows and three columns. Coloring and chains follow linked candidate implications to find a contradiction or force an elimination. These methods require more tracking, and the guide places them after simpler techniques because they take longer to apply and can be misused when an easier deduction remains.
Do not search for an advanced pattern merely because the puzzle is labelled “hard.” Difficulty labels are not a universal technique standard: one publisher’s or app’s rating does not establish which method a particular grid requires. A hard puzzle may still have a missed single, and a more advanced puzzle may require a different chain of deductions. Let the candidates in the current grid determine which method is relevant.
Keep the scope of each advanced check narrow. Select one digit, map its candidate positions, and test whether they meet a recognized pattern’s constraints. If they do not, do not force a pattern onto them. Return to the notes, confirm their accuracy, and try another digit or technique. This reduces the risk of making an attractive but unsupported elimination.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.What if no pattern produces a number?
Separate two kinds of progress. A placement fills a cell; an elimination removes one candidate from a cell. If a sound technique produces only an elimination, record it and continue. A later scan may reveal a single, and a different unit may become easier to read after the candidate map changes.
If the grid still appears unchanged, check your process rather than escalating automatically:
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- Were all candidates entered for every empty cell, and are they consistent with the row, column and box?
- Did you remove a candidate only where the pattern logically rules it out?
- For a proposed pair or line interaction, are the candidates truly confined to the cells you are using?
- For an X-Wing, does the selected digit occur in exactly the same two candidate columns in both selected rows, or the same two rows in both selected columns?
- After each valid elimination, did you update the affected notes and rescan the grid?
If you use a hint, ask for the next logical elimination or placement and its reason rather than only requesting a completed solution. A reason lets you verify the move against your candidate notes and learn what to look for next. A hint that gives only a finished grid may get you past this puzzle without explaining the deduction that caused the stall.
How can you practise hard-Sudoku techniques?
Choose puzzles a little beyond your current comfort level so they are likely to call for a method you want to learn. That is practical guidance, not a measured promise that a particular practice schedule will improve solving speed or performance. If you are learning candidate patterns, write full pencil marks and use a puzzle where you can pause to check the logic at each elimination.
When a technique is unfamiliar, do not try to memorize a shape without its reason. For an X-Wing, the reason is that the two rows must use the same two columns, so those columns cannot contain the digit elsewhere. For a pair, the reason is that two cells have reserved the two digits within their unit. Understanding what must be true makes it easier to distinguish a genuine pattern from a similar-looking arrangement.
After solving, review the first point at which your scan stopped producing placements. Ask whether the missed move was a single, a candidate elimination, or a pattern you had not yet learned. That review gives you a specific technique to practise on the next puzzle instead of treating “hard” as a single level of skill.
Quick Recap
Quick decision path when you are stuck
- Verify the givens, filled digits and notes; correct any conflict before continuing.
- Sweep missing digits through boxes, rows and columns, using the intersecting units to rule out cells.
- Check both naked singles in cells and hidden singles in units.
- After any placement, restart a whole-grid scan.
- If no placement appears, complete candidate notes and inspect naked or hidden pairs, then pointing pairs and box-line reductions.
- If those do not help, test candidate patterns such as X-Wing or swordfish, and consider coloring or chains only when their logic fits the grid.
- Record sound eliminations, update notes and scan again; use a reasoned hint if you need help identifying the next deduction.
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