Stuck on a Sudoku? A checklist to find the next number
If you are stuck on a Sudoku, first check that nothing on the board is wrong, then look again for a square with only one possible number and for a number with only one possible square. If you find neither, write notes in the square with the fewest options and look for a pair, which is the next technique up.
That is the order our Sudoku solver works through when you press Next step. Below it is written out as a seven-step checklist, followed by the numbers that show why it works.
Why check in this order?
A Sudoku stalls for one of three reasons:
- Something on the board is wrong. A wrong number or a wrong note makes every later step fail.
- There is a simple move you have not seen yet. On Easy and Medium this is nearly always the reason, as the numbers further down show.
- The puzzle needs a harder technique. Pairs, pointing pairs and the X-Wing only come in when the simple moves run out.
The checklist starts with the quickest checks and ends with the slowest. A mistake is quick to rule out and wastes the most time if you miss it, so it goes first. Hunting for pairs takes the longest, so it goes last.
What is the checklist?
1. Look for a number that appears twice
This is the first thing the solver does. If a number repeats in a row, column or box, it says “Some numbers repeat in a row, column or box” and shows them in red.
In our game you get this check for free. A wrong number turns red as soon as you place it, and the Mistakes counter goes up. On paper, run your eye along each row, column and box before anything else.
2. Make sure the puzzle can still be finished
Next the solver checks that an answer still exists. A number can be wrong without repeating anything, and then the solver says “This puzzle has no answer. One of the numbers is in the wrong place.”
In our game the numbers are checked for you, but your notes are not. If you removed a note that should have stayed, you can end up with a square that seems to have no options left. Look over the notes around the last few numbers you placed. If you typed in a puzzle from a newspaper or an app, check every starting number against the original.
3. Look for a square with only one option
Now the solver looks for a naked single: an empty square where eight of the nine numbers already appear in its row, column or box. It starts at the top left and works along each row.
You will find these fastest in busy parts of the board, where a square sits in a full row and a full column. In our game, tap an empty square and its row, column and box are shaded, so you can check all three at once.
4. Look for a number with one home in each row
Then the solver turns the question around. For each row, it takes each missing number and counts the empty squares where that number could go. If there is only one, that is the answer, even if the square could hold other numbers too. This is called a hidden single.
5. Do the same for each column
The solver goes through all nine columns the same way. Columns are easy to skip by eye, so it is worth doing them on purpose.
6. Do the same for each box
Last of the simple moves, the solver checks the nine boxes. Boxes are often the quickest to scan by eye, because their squares sit close together. In our game, tap any number on the board and every copy of it lights up, which shows you at once which squares in a box are ruled out. Our post on hidden singles works through this with real grids.
7. Find the square with the fewest options
If none of the above turns anything up, the solver says “There is no single to find here. The next step needs a harder technique, such as a pair or an X-Wing.” To keep you moving, it fills in the empty square with the fewest possible numbers.
That square is where you should look too. Write notes in it and in the other empty squares of its row, column and box. Then look for two squares in the same row, column or box that share the same two notes. That is a naked pair, and it lets you clear those two numbers from the rest of that row, column or box. Our strategy guide covers pairs, pointing pairs and the X-Wing, in the order you will need them.
How often is a missed single the problem?
Most of the time, on the first four levels. We made 1,000 puzzles at each level with the same generator our game uses. Then we had a computer solve each one using only the moves in this checklist, plus pairs, pointing pairs, triples and X-Wings. The table shows how many puzzles finished with singles alone, how many also needed one of those techniques, and how many needed something harder still.
| Level | Singles only | Pairs to X-Wings | Harder |
|---|---|---|---|
| Easy | 1,000 | 0 | 0 |
| Medium | 988 | 1 | 11 |
| Hard | 893 | 37 | 70 |
| Expert | 677 | 102 | 221 |
So on Easy and Medium, if nothing is wrong on the board, a single is almost always waiting for you. Steps 3 to 6 will find it. On Hard, about one puzzle in ten needs something more. On Expert it is about one in three.
On the Hard puzzles that needed more than singles, the singles ran out with about 34 of the 81 squares still empty, on average. So hitting a wall with plenty of the board left to fill is normal on Hard, and step 7 is where to go next.
What if the checklist still finds nothing?
Take a break first. Press Pause, look away for a minute, then go through steps 3 to 6 once more. It is easy to miss a single when you have been staring at the same squares for a while.
If you are still stuck, you have two ways forward:
- Use Hint in our game. If you have not selected an empty square, Hint fills the square with the fewest options, the same square the solver picks in step 7. It costs 15 points from your Score.
- Use Next step in the solver. Type the puzzle into the Sudoku solver and press Next step. It fills one square and tells you which move found it, so you can spot the same pattern next time.
What else do people ask about getting stuck?
Is it cheating to use a hint or the solver?
It is your game, so you decide. A hint in our game costs 15 points from your Score, and the solver's Next step tells you which move found the number, so you learn it instead of just copying the answer.
Will I ever have to guess?
No. Every puzzle here has exactly one answer, so there is always a reason for the next number. The hardest puzzles can need techniques beyond this checklist, though. In our test, 221 of 1,000 Expert puzzles did.
Why do I get stuck more on Hard than on Medium?
Hard starts with fewer numbers, so the simple moves run out more often. In our test, 988 of 1,000 Medium puzzles could be finished with singles alone, against 893 on Hard and 677 on Expert.
What is the checklist again?
- Look for a number that appears twice.
- Make sure the puzzle can still be finished, and check your notes.
- Look for a square with only one option.
- Look for a number with one home in each row.
- Do the same for each column.
- Do the same for each box.
- Find the square with the fewest options and look for a pair.
Open the Sudoku solver and press Next step on the puzzle you are stuck on, or play Sudoku now and try the checklist on a fresh puzzle.
More from the blog
Hidden singles: the first Sudoku technique to learn
Hidden singles in Sudoku, explained with worked grids from our Easy level. Learn to find the one square a number can go, using the game's own controls.
Killer Sudoku combinations chart: 2 and 3 square cages
Every way to fill a two or three square Killer Sudoku cage, total by total, worked out in full. Keep it open while you play and spot the easy cages.
Why every puzzle here has exactly one answer
How the puzzles on this site are made, why a proper Sudoku can only be finished one way, and what the difficulty levels really change.