Stuck on a Sudoku? What to Try Next, Step by Step

When you are stuck on a sudoku, work down a fixed checklist from the cheapest check to the rarest pattern, and go back to the top every time you place a digit. Start with a slow rescan for hidden singles, then fill in full pencil marks, then look for pointing and claiming, then pairs, then an XY-Wing. Most stalls end in the first three steps: about 9 in 10 of the puzzles we serve need nothing harder than pointing and claiming. You never need to guess: every step below is pure logic, and each one comes with a real position from our puzzle library where it is the move that breaks the jam.

The order is based on data, not taste. We graded the 457,000 puzzles that Sudoku Royale serves with a solver that always takes the simplest available step. On Hard puzzles, the hardest thing you ever need is a hidden single 76% of the time. On Expert, an X-Wing is required in fewer than 1 in 100 puzzles, while a pointing move or a naked pair shows up constantly. So if you are hunting for an X-Wing before you have rescanned for singles, you are looking in the wrong place.

The stuck ladder

Try each rung in order. The moment one of them gives you something, place it, update your pencil marks, and start again from rung 1. That restart is the habit that separates smooth solvers from stuck ones: a single new digit often unlocks two or three easy moves you would otherwise skip past on your way to the hard patterns.

1. 1

   Rescan every digit for hidden singles

   Take the digits 1 to 9 one at a time and check every box, row, and column for a place where that digit has only one home.

2. 2

   Fill in full pencil marks and look for naked singles

   Write every candidate in every empty cell. Any cell left with one candidate is solved.

3. 3

   Pointing and claiming

   Where a box and a line overlap, a digit stuck in the overlap can be cleared from the rest of the box or line.

4. 4

   Naked and hidden pairs

   Two cells in a group that share the same two candidates, or two digits that only fit two cells.

5. 5

   XY-Wing

   Three cells with two candidates each, linked so that one of two cells must hold a digit.

6. 6

   X-Wing, Swordfish, and simple colouring

   Follow one digit across the whole grid. Rare, but they are what the hardest levels ask for.

7. 7

   Check for a mistake

   If nothing works and the puzzle is not rated extreme, the likeliest cause is a wrong digit or a pencil mark you removed by accident.

Step 1: rescan for hidden singles

A hidden single is a digit that has only one possible cell in a row, column, or box. The cell itself may still look open, which is why it hides. Hidden singles do most of the work in every puzzle up to Hard, and they are the move people miss most, because the usual way of scanning (looking at a cell and asking what fits) cannot see them. You have to turn it around and ask, for one digit, where it can go.

In the grid below, row 7 has three empty cells and needs a 3, a 5, and a 6. Ask where the 3 can go. R7C4 is out because column 4 already has a 3 in R5C4. R7C9 is out because column 9 has a 3 in R4C9. That leaves R7C8. (R7C8 means row 7, column 8. The labels are on the grid edges.)

• 5 clue
• 5 already solved
• 5 new digit
• 5 pattern candidate
• 5 candidate to remove

A good rescan routine is boring on purpose. Go digit by digit, 1 to 9, and for each digit sweep the nine boxes, then the rows, then the columns. It takes a minute or two on paper, and it finds the move more often than anything else on this page. If you want to train the eye for it, the Dojo in Sudoku Royale has Hidden Single drills that serve one board after another where a hidden single is the next move.

Step 2: complete your pencil marks

If a full rescan finds nothing, stop solving by eye and write in every candidate for every empty cell. Partial pencil marks are the most common reason people think they are stuck when they are not: the pattern is there, but half its candidates were never written down, or a candidate was not erased after a placement. Our guide to sudoku pencil marks covers the notation.

With the marks in place, look for any cell with a single candidate (a naked single). Then keep the marks honest: every time you place a digit, erase it from the other cells in its row, column, and box right away. All the techniques below read your pencil marks, so one stale mark can hide every one of them.

Step 3: pointing and claiming

These are the first moves that remove candidates instead of placing digits, and they are what separates Hard puzzles from Medium ones. In our library, 1 in 5 Hard puzzles needs a pointing or claiming step, and on Expert our solver uses a pointing step in 7 out of 10 puzzles.

Pointing works like this: if, inside one box, a digit can only go in cells that sit on one row (or one column), then that digit must be in that row inside this box. So it cannot be anywhere else on that row.

Claiming (also called box-line reduction) is the mirror image: if a digit on one row can only go in cells inside one box, remove it from the rest of that box. Both are explained with more examples in the guide to pointing pairs and box-line reduction.

Step 4: pairs

A naked pair is two cells in the same row, column, or box that both have exactly the same two candidates. Those two digits must fill those two cells, in some order, so no other cell in that group can hold either digit.

The hidden pair is the version that is harder to see: two digits that, within a group, fit only the same two cells. Those cells then lose all their other candidates. When you are stuck with a board full of cells that each hold two options, read how to solve sudoku when there are two options.

Step 5: XY-Wing

On the hardest puzzles most players meet, the XY-Wing is the move. In our library, the XY-Wing is the hardest technique needed in 72% of Master puzzles. You find it by looking only at cells with exactly two candidates, which makes the search smaller than it sounds.

You need a pivot cell with candidates X and Y, and two cells it can see (the pincers): one with X and Z, one with Y and Z. Whatever the pivot turns out to be, one of the pincers must be Z. So any cell that sees both pincers cannot be Z.

The Dojo's XY-Wing drill is the quickest way to get fast at spotting this, because every board in the drill has one waiting.

Step 6: X-Wing, Swordfish, and simple colouring

These patterns follow a single digit across several rows and columns. The X-Wing is the famous one, but it is much rarer than its reputation: our solver needs it in 0.7% of Expert puzzles and 0.3% of Master puzzles, and the Swordfish is rarer still. Simple colouring is the exception. It is the hardest technique needed in 95% of the puzzles we rate Extreme. The advanced strategies guide walks through colouring and the other rare patterns.

The practical rule: look for these only after steps 1 to 5 have come up empty on a fresh pass, and pick one digit at a time. Scanning for "any fish" across nine digits at once is how people lose ten minutes.

Step 7: check for a mistake

If you have been through every rung and nothing moves, and the puzzle is not from the hardest tier of a serious puzzle book, suspect your own board before the puzzle. Look for a cell with no candidates left, or a digit that has no legal place in some row, column, or box. Either one proves a wrong digit or a wrongly erased candidate somewhere upstream. Our guide to finding a mistake in sudoku shows how to track it down without starting over.

How the ladder lines up with difficulty levels

Knowing the level of a puzzle tells you how far down the ladder you will need to go. This table shows, for each of Sudoku Royale's six Classic levels, the hardest technique a puzzle at that level requires, measured across the full library of rated puzzles.

The full ranking, with every technique in order and an example of each, is in sudoku techniques in order of difficulty. If you are new to the solving loop itself, start with how to solve sudoku step by step.

If the ladder runs out

Some puzzles, mostly in newspaper "fiendish" tiers and puzzle books, need techniques beyond this list: unique rectangles, BUG+1, chains. About 9% of the puzzles our generator produced needed something past the 13 techniques our solver knows (everything on this page, plus triples and Jellyfish), and we keep those out of the app for that reason. If you meet one elsewhere and every cell is down to two candidates, what to do when you are stuck with only pairs covers the patterns that finish those boards. And if you are tempted to just try a number and see, read whether you can solve sudoku without guessing first.

Getting unstuck in Sudoku Royale

In Classic mode, a lightbulb sits beside the grid. It starts to glow after 90 seconds without a correct placement, and tapping it names one technique that works on your board right now, with a one-line explanation and a Learn button that opens the lesson for it. It never tells you the digit, so you still find the move yourself, which is the part that makes you better. For singles it also highlights the cell. Hints are unlimited and there are no ads between puzzles. More on this in how sudoku hints work.

If the same technique keeps stopping you, the Dojo has drills for every rung of the ladder from hidden singles to simple colouring, and Sensei Royale looks at where you lose the most time and gives you one technique to work on next.