Stuck usually means one of three things, and only one of them is the puzzle's fault. There is a placement already sitting on the board that you walked past. Your pencil marks have gone stale and no longer describe the grid. Or you wrote a wrong digit some time ago and have spent twenty minutes solving a puzzle that stopped having an answer.
Work those three in that order, cheapest first, then work up the ladder of techniques. The checklist below is eight steps. On the grid used here it starts at a genuine dead stop, with 27 cells blank and nothing left to place, and finishes the puzzle.
One thing holds the whole method together. A properly made Sudoku has exactly one solution, which means every remaining digit is reachable by logic alone. So if you feel forced to guess, either the grid in front of you is broken or the move exists and you have not found it. There is no third case.
Stuck on a printed grid? Sudoku Master reads a newspaper puzzle through the phone camera and hands back the finished grid, or nothing at all. Nothing means the digits on the page no longer fit together. Free, offline, and the photo stays on the device.
The checklist, in order
| # | Step | What it costs | What it finds |
|---|---|---|---|
| 1 | Prove the grid is still legal | 30 seconds | A mistake, before it wastes another hour |
| 2 | Sweep all nine digits again | 2 minutes | Hidden singles your last placements opened up |
| 3 | Start where the blanks are fewest | 30 seconds | The unit most likely to give something up |
| 4 | Rewrite the marks, one unit at a time | 3 minutes | Everything below, which needs them |
| 5 | Find the pair | 1 minute | Eliminations across a row, column or box |
| 6 | Read the box against the line | 2 minutes | Eliminations one unit cannot see on its own |
| 7 | Ask what nobody wrote down | 2 minutes | Hidden pairs buried in long candidate lists |
| 8 | Only now, the fish | As long as it takes | X-Wing and up, on the grids that need it |
Do not skip down the list. A technique four rungs up is not a stronger move, it is a slower one, and most stuck grids come unstuck at step 2 or step 5. The ordering is the same ladder used in every Sudoku technique from easiest to hardest, read as a rescue plan rather than a syllabus.
The grid this page uses
Here is the puzzle. It has 31 givens, which is a normal medium.
5 2 6 3 . . 9 8 .
. . . . 6 2 7 . .
9 3 . . 4 . . . 2
1 5 . . 3 . . 4 .
7 . . . . . . . .
. . 3 7 . . . . 1
3 . . . . 8 2 . .
. 9 5 1 . . 8 7 .
. . . . 9 . 4 . .
Plain scanning and singles place 23 digits into it and then stop dead. That is the grid the checklist has to work on:
5 2 6 3 . . 9 8 4
. . . 9 6 2 7 . .
9 3 7 8 4 5 1 6 2
1 5 8 2 3 9 6 4 7
7 . 9 . . . 3 2 8
2 . 3 7 8 . 5 9 1
3 . . . . 8 2 . 9
. 9 5 1 2 . 8 7 .
. . 2 . 9 . 4 . .
Twenty-seven blanks. Rows 3 and 4 are finished, column 7 is finished and box 6
is finished, which makes the thing look nearly done and feel completely stuck.
Rows run 1 to 9 from the top and columns 1 to 9 from the left, so r7c4 is row
7, column 4. Boxes are numbered 1 to 9 reading left to right and then top to
bottom.
1. Prove the grid is still legal
Do this first, always, because every step after it is wasted if the grid is already wrong. Three tests, and they take half a minute between them.
Look for a repeated digit. Read each of the nine rows, then the nine columns, then the nine boxes, and check no digit appears twice. This catches the obvious kind of error, the one where you placed a 7 that was already two cells away.
Look for a cell with nothing left. Take the blanks that already look tight and count what their 20 peers have used. A blank cell with all nine digits banned is proof of an error somewhere earlier.
Look for a digit with nowhere to go. Pick a unit, pick a digit missing from it, and check whether any blank in that unit can still take it. If a box is missing a 3 and none of its blanks can hold a 3, the grid is dead.
Now the uncomfortable part. A wrong digit almost never announces itself where
you put it. Write a 4 into r7c4 on the grid above. It is a legal thing to
write: that cell genuinely holds 4, 5 or 6. Take the forced digits from there in
reading order and fourteen of them go in without a murmur, before r9c1 is left
with nothing at all. Where a wrong digit finally breaks the grid depends on the
order you happen to work in. That it breaks late does not.
That is why the check comes first. It is also the argument for writing only digits you can justify out loud. If the sentence "it goes here because" does not finish, it is not a placement. It is a guess with good posture.
2. Sweep all nine digits again
The most common reason a grid feels stuck is that it is not. Take each digit 1 to 9, take each box that does not hold it yet, and strike the rows and columns that already carry a copy. One survivor is a placement. The full method is in cross-hatching; here it is a re-check, not a first pass.
Do the sweep even if you did one ten minutes ago. Every digit you have written since is a fresh line to strike, so the answers change under you.
Take the 6 on the stuck grid. Five boxes still need one:
| Box | Where a 6 can still go |
|---|---|
| 4 | r5c2, r6c2 |
| 5 | r5c4, r5c6, r6c6 |
| 7 | r7c2, r8c1, r9c1, r9c2 |
| 8 | r7c4, r8c6, r9c4, r9c6 |
| 9 | r8c9, r9c9 |
No box is down to one cell, so the sweep places nothing. It is still the single most valuable two minutes on this page, for a reason that is easy to miss: look at box 4. Two survivors, and both of them sit in column 2. Hold that thought, because it is the move that finishes the puzzle, and it turned up in a scan that "failed".
A near miss is not a failure. Two survivors in the same row or the same column is an elimination you can spend elsewhere, and noticing which line they share costs nothing.
3. Start where the blanks are fewest
Before writing a single pencil mark, count. Which unit has the fewest empty cells? That is where the grid is tightest and where a mark-up pays back fastest.
Six units on this grid are down to two blanks each:
| Unit | The two blanks |
|---|---|
| Row 1 | r1c5, r1c6 |
| Row 6 | r6c2, r6c6 |
| Column 3 | r2c3, r7c3 |
| Box 2 | r1c5, r1c6 |
| Box 3 | r2c8, r2c9 |
| Box 4 | r5c2, r6c2 |
Not one of them resolves, and that is worth understanding rather than resenting. A unit with two blanks is missing exactly two digits. Unless something outside the unit rules one of those digits out of one of those cells, both cells hold the same two candidates and neither can be settled. Two blanks is a pair, not a placement.
So the fullest units are not free digits. They are the cheapest pairs on the board, and pairs are what steps 5 and 6 run on. Box 4 is on that list.
4. Rewrite the marks, one unit at a time
If you already have pencil marks down, the honest question is whether they are still true. Marks written twelve placements ago describe a grid that no longer exists, and a stale mark is more dangerous than no mark, because you will trust it. Solvers lose whole evenings to a candidate they crossed off mentally and never crossed off on paper.
Rub out and rewrite, and only where you need them. A full mark-up of this grid is 66 small digits across 27 cells. That is a lot of ink to maintain by hand, and every placement you make kills several of them.
Mark the tight units first, which step 3 just handed you. Column 2 is a good place to start here:
| Cell | Candidates |
|---|---|
r2c2 | {1,4,8} |
r5c2 | {4,6} |
r6c2 | {4,6} |
r7c2 | {1,4,6,7} |
r9c2 | {1,6,7,8} |
Five cells, fifteen marks, and the shape of the column is already visible. The discipline for keeping marks usable, including which of the four notations to use, is in how to use pencil marks.
5. Find the pair
Two cells in one unit holding the same two candidates own those two digits between them. You do not know which cell takes which. You do know that no other cell in that unit can have either.
Column 2 has one, and it is right there in the table above. r5c2 and r6c2
both read {4,6}. Between them they use up the 4 and the 6 for the whole
column, so:
r2c2loses its 4 and becomes{1,8}.r7c2loses its 4 and its 6 and becomes{1,7}.r9c2loses its 6 and becomes{1,7,8}.
Three cells lighter, and no digit placed yet. This is the moment people give up on the technique, because it produced no answer. Give it one more move. Naked pairs, triples and quads are worked through properly in naked pairs and triples.
6. Read the box against the line
Step 5 works inside one unit. Step 6 works where two units cross, and it is the step that most self-taught solvers never learn, which is why so many grids stall exactly here.
Two shapes, and they are mirror images.
Pointing. If every place a digit can go inside a box lies on one row or one column, the digit is on that line somewhere. So it is nowhere else on that line, including the parts outside the box.
Box-line reduction. If every place a digit can go inside a row or column lies inside one box, the digit is in that box somewhere. So it is nowhere else in that box.
Now use the near miss from step 2. Box 4 can only take its 6 at r5c2 or
r6c2, and both are in column 2. Whichever one gets it, column 2's 6 belongs to
box 4. Every other cell in column 2 loses its 6, which strikes r7c2 and
r9c2.
That is the same elimination step 5 found, arrived at from the other side. This
grid gives it a third time: column 1's blanks are r2c1 {4,8}, r8c1 {4,6}
and r9c1 {6,8}, so column 1's 6 has to be at r8c1 or r9c1, both in box
7. Box 7's 6 is therefore in column 1, and r7c2 and r9c2 lose their 6 again.
Three routes, one deduction. That is normal and it is a good sign. When a grid offers the same elimination by three different names, it is telling you that the elimination is the hinge. The pair of shapes is worked through in pointing pairs and box-line reduction.
What that one elimination does
r7c2 no longer has a 6. Look at row 7 with that change in place:
| Cell | Candidates |
|---|---|
r7c2 | {1,7} |
r7c3 | {1,4} |
r7c4 | {4,5,6} |
r7c5 | {5,7} |
r7c8 | {1,5} |
Row 7 still needs a 6, and exactly one cell can take it. Place a 6 at r7c4.
The rest is a landslide. r9c4 becomes 5, r5c4 becomes 4, r5c2 becomes 6,
and from there the last 26 cells fall to singles, naked and hidden, and nothing
harder. One elimination, found by looking twice at a scan that appeared to fail,
and the puzzle is over.
That is why the checklist is ordered the way it is. The cheap steps are not a warm-up for the expensive ones. They are where the hinge usually sits, and steps 7 and 8 are there for the grids where it does not.
7. Ask what nobody wrote down
Hidden pairs are the step people skip because they are the only one that asks you to read your marks backwards. Instead of looking for two cells with two candidates, you look for two digits that appear in only two cells of a unit, even when those cells are carrying four or five candidates each.
Say a box's 3 and its 8 can each only go in r4c5 and r6c6. Those two cells
take the 3 and the 8 between them, so every other candidate in both cells can be
rubbed out, however long the list looked. Nothing about the cells announces
this. The two digits do.
There is no hidden pair on the grid on this page, and saying so is more useful than pretending there is. The test still takes two minutes: for each unit, count how many cells could hold each missing digit, and look for two digits sharing the same two cells. The worked cases are in hidden pairs and triples.
8. Only now, the fish
If steps 1 to 7 are genuinely exhausted, the grid is above newspaper hard and the next rung is the X-Wing: one digit confined to the same two columns in two different rows, which lets you strike it from the rest of those columns.
One warning before you go hunting. Patterns up here are common. Useful
eliminations up here are not. This grid carries three X-Wings and two of them
are worthless. The 1 sits in exactly r1c5 and r1c6 in row 1 and in exactly
r5c5 and r5c6 in row 5, columns 5 and 6 in both. The 8 does the same in rows
2 and 9 across columns 1 and 2. Textbook shapes, and neither removes a single
candidate, because no other cell in those columns held the digit anyway.
The third one is real. The 6 in column 1 is confined to rows 8 and 9, and so is
the 6 in column 9, so the 6 leaves r9c2, r9c4, r8c6 and r9c6. That
leaves box 8 one home for its 6, at r7c4. It is the placement step 6 already
made, reached the expensive way.
So a pattern that removes no candidate is not a move, and a pattern that duplicates a cheaper one is not a shortcut. Work out what an X-Wing would actually strike before you spend ten minutes confirming it, and see the X-Wing explained with real grids for the shape and a quick way to test it.
When the honest answer is to stop
Two situations are not solved by trying harder.
The grid is broken. You did step 1 and it passed, and forty moves later something still contradicts. Then the error is older than the check, or the puzzle itself was misprinted. Both happen. A puzzle with two solutions is broken rather than hard, and no amount of logic will choose between them.
You have been staring for twenty minutes. By then you are reading the board from memory instead of looking at it. Put it down, come back cold, and start again at step 2. That is on the checklist because it works, not because it is kind. What your eye is actually doing in those twenty minutes is in why some puzzles feel impossible.
I built Sudoku Master, and the setting that earns its keep on a stuck grid is the dullest one in it. Notes are cleared automatically when you place a digit, which ends the step 4 problem before it starts: nothing on the board is older than your last placement. What the app will not do is talk you through a technique. Its solver checks the grid and hands back the answer or nothing at all, so it can tell you that you have gone wrong without telling you where. Worth knowing before the moment you need it. Which size of hint to spend, and when, is a separate question, worked through in how to use a hint.
Common mistakes
Hunting a hard technique first. An X-Wing is not a better move than a hidden single, it is a slower one. Most stuck grids are stuck at step 2.
Trusting old pencil marks. Every digit you place kills candidates elsewhere. Marks you have not touched since are a picture of a grid you have already left, and they are convincing while they lie.
Throwing away a near miss. Two survivors in one line is the raw material for steps 5 and 6. On this grid it was the entire solution.
Skipping the legality check because you are careful. Everyone is careful. The wrong digit above still bought fourteen happy placements before anything broke.
Marking the whole grid. Sixty-six candidates to maintain, when the tightest unit needed fifteen. Mark where the grid is tight.
Questions people ask
Is it ever OK to guess in Sudoku?
Not on a properly made puzzle. It has exactly one solution, so every digit is reachable by logic. If you guess and you are wrong, the grid stays legal for a long time and then collapses somewhere unrelated, which is far worse than being stuck. Guessing is only defensible on a puzzle you already suspect is broken.
How do I find a mistake without starting the puzzle over?
Run the three tests in step 1: a repeated digit in a row, column or box; a blank cell with no candidate left; a missing digit with nowhere to go in some unit. The third is the one that catches the subtle errors. If all three pass and the grid still will not move, the error is not detectable yet and you may have to rebuild from the givens.
Can a Sudoku actually be unsolvable?
A published puzzle can be misprinted, and a puzzle with two or more solutions is faulty rather than hard. Both are rare and both exist. What is not rare is a correct puzzle that needs a technique you have not learned, and it feels identical from the inside.
Should I take a hint when I am stuck?
A hint that places a digit ends the deduction you were about to make. A hint that tells you which unit to look at leaves the puzzle intact. If you take one, take it after step 2, so you know you are not paying for something you could have scanned.
Do I have to pencil-mark the whole grid to get unstuck?
No, and a full mark-up usually costs more than it returns. The grid on this page takes 66 candidates across 27 cells, every one of which you then have to maintain. Column 2 alone took fifteen marks and held the pair that finished the puzzle. Mark the tightest units, work them, and leave the rest of the grid alone.
How long should I sit with a stuck grid before I put it down?
Until you have finished step 2 twice with nothing to show for it. After that a cold ten minutes away beats another hour at the table, and nothing on the page changes while you are gone.
Why do I get stuck at the same point in every hard puzzle?
Because there is one rung of the ladder you have not learned, and puzzles graded at that level are built to require it. For most solvers it is step 6, the box against the line. Learn that one shape and a whole grade of puzzles opens up.
Is restarting the puzzle ever the right call?
Sometimes, and it costs less than it sounds. The case for it is when step 1 says the grid is illegal and the hunt for the bad digit comes up empty. Copying the givens out again takes a couple of minutes on a puzzle you now know well, and it beats another hour spent on a grid that has no answer in it.
Keep reading
- Cross-hatching: how to read a Sudoku grid quickly, which is step 2 done properly and the place most stuck grids come unstuck
- Sudoku: rules, techniques and solving, if you would rather see the whole ladder at once
- Pointing pairs and box-line reduction, the step that finished the grid on this page and the one most solvers are missing
- Every Sudoku technique, ordered from easiest to hardest, for what sits above step 8
- How to use a Sudoku hint without ruining the puzzle, for when the checklist runs out
- Why some Sudoku puzzles feel impossible, when the grid is not actually the problem
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