Sudoku Tips: Strategies That Actually Help

What are the main sudoku tricks?

Sudoku tips in short: Follow each digit through the rows and columns, look for squares where only one digit fits, and look for digits that have just one spot left in a row, column or box. When that runs dry, pencil in the candidates and look for pairs and for digits that sit in a single row of a box. A well-made sudoku never makes you guess.

How to read the examples: columns are labeled A to I and rows 1 to 9, so C3 is the square in column C, row 3. Candidates are the digits that can still go in an empty square because its row, column and box are all still missing them. If you want a refresher on the basic rule first, start with the sudoku rules.

1. Scanning: follow one digit across the grid

To scan, pick one digit and trace it through the whole grid. Every copy that’s already placed blocks its row and its column for that digit. If only one square in a box is left unblocked, that’s where the digit goes.

In this example, 7s are already placed in F2, I3, B4, H6 and D7. Now look at the center box (D4 to F6). The 7 in B4 blocks row 4 and the 7 in H6 blocks row 6. The 7 in D7 blocks column D and the 7 in F2 blocks column F. That leaves E5 as the only open square in the box, so the 7 goes there, even though row 5 is still completely empty.

On its own, E5 could still hold a 6, 7, 8 or 9. Staring at that square gets you nowhere; following the digit does. Start with digits that already appear often, since they block a lot of lines. Then go through 1 to 9 in order so you don’t skip any.

2. The only digit for a square (naked single)

Now flip it around. Pick a square and collect every digit that already sits in its row, its column and its box. If that leaves just one digit unaccounted for, it belongs in that square.

Take H6. Row 6 has 1, 3 and 8. Column H has 2, 4 and 9. The middle-right box (G4 to I6) has 2, 6 and 7. Put together, that’s 1, 2, 3, 4, 6, 7, 8 and 9, which leaves only the 5 for H6.

Scanning for 5s would have missed this one: row 6, column H and the box each still have other open spots for a 5. That’s why it pays to check individual squares, especially where the row, column and box are already crowded.

3. The only spot in a row, column or box (hidden single)

When you scanned, you looked for a digit’s last spot in a box. You can ask the same question of every row and every column. In a row, the columns and boxes do the blocking; in a column, it’s the rows and boxes.

Row 9 has 3, 2, 8 and 4. It’s missing 1, 5, 6, 7 and 9, and the open squares are A9, D9, E9, G9 and I9. Where can the 6 go? Not A9, because column A already has a 6 in A2. Not D9 either, because of the 6 in D1. G9 and I9 are out because the bottom-right box already has a 6 in G8. That leaves E9.

Again, the square alone doesn’t give it away: E9 could hold a 1, 5, 6 or 9. The answer only shows up when you ask where the 6 can go in this row. That question pays off in rows and columns that are already fairly full.

4. Notes: keeping track of candidates

Sooner or later, scanning and looking stop paying off. That’s when you pencil the possible digits into the empty squares. To keep your notes useful instead of confusing, stick to three habits:

• Write them all. Note every possible digit, not just the ones that catch your eye. Leave one out and a square looks settled when it isn’t.
• Clean up right away. As soon as you place a digit, erase it from the notes in its row, its column and its box.
• Keep a fixed layout. Put each digit in the same spot within the square every time, say 1 in the top left and 9 in the bottom right. Pairs jump out at you that way.

Column D shows how much the cleanup matters. It already holds 8, 6, 1, 4 and 5, with D2, D4, D8 and D9 still open.

At first, only D8 has a single candidate. Row 8 has 8, 2 and 3, the bottom-center box has 5, 6, 7, 3 and 8, and column D adds 1 and 4. That leaves 9 for D8. Erase the 9 from the other notes in the column and D9 is down to 2. After that, D2 is left with 7 and D4 with 3. One certain digit plus careful erasing solves the whole column. You could also spot the 3 in D4 with technique 3: from the start, it has only that one spot in column D.

Don’t start taking notes too early. In easy puzzles you can often get to the end without them. When you do take notes, cover every empty square, or at least a whole row, column or box.

5. Pairs: two squares, two digits (naked pair)

When two squares in the same row, column or box have exactly the same two candidates, those two digits are split between them. You don’t know yet which goes where, but you do know that neither digit can appear anywhere else in that row, column or box.

This example is a sudoku partway through. Techniques 1 to 3 won’t find another digit here. Look at row 3: it has 6, 5, 8 and 1 and is missing 2, 3, 4, 7 and 9.

Row 3, column B and the top-left box rule out everything except 2 and 7 for B3. Row 3, column I and the top-right box do the same for I3. So one of these squares gets the 2 and the other gets the 7. That removes 2 and 7 from the rest of row 3: E3 loses its 2 and G3 loses its 7, leaving G3 with just the 4.

The same idea works with three squares that share only three candidates between them, called a triple. Not every square has to hold all three digits: 1 2, 2 3 and 1 3 make a triple, too.

6. Box and line: when a digit points out of its box (pointing pair)

Sometimes you can’t tell which square in a box a digit belongs in, but you can tell which row. If every candidate for a digit inside a box lies in the same row, the digit has to be in that row within that box, so you can erase it from the rest of the row. Columns work the same way.

This example is another position partway through, with no digit that follows directly. The bottom-right box (G7 to I9) is missing 2, 4 and 7, and its open squares are G7, H9 and I9. G7 can’t be a 4, because column G already has one in G5. So the 4 goes in H9 or I9, which means it’s definitely in row 9.

That rules out a 4 everywhere else in row 9, including E9. Column E has only two open squares left, E1 and E9, and it’s missing 3 and 4. Since E9 can’t be the 4, it gets the 3, and E1 gets the 4.

It also works the other way around: if every candidate for a digit in a row falls inside a single box, you can erase that digit from the other squares of that box.

Advanced: the X-Wing in brief

An X-Wing links two rows. If a digit has only two possible squares in each of two rows, and those squares line up in the same two columns, then in each of those columns the digit has to sit in one of the two rows. You can erase it from every other square in both columns. Swap rows and columns and it works just the same.

This example is about the 6. Row 6 has four open squares: A6, B6, G6 and I6. A6 and G6 are out because columns A and G already have a 6, in A3 and G1. That leaves B6 and I6. Row 7 has five open squares: B7, D7, E7, G7 and I7. D7 and E7 are out because the bottom-center box already has a 6 in E8, and G7 is out because of the 6 in G1. That leaves B7 and I7.

If the 6 is in B6, row 7 forces it into I7. If it’s in I6, it has to go in B7. Either way, columns B and I each get their 6 in row 6 or row 7, so you can erase the 6 from every other square in those two columns. I4 had 4 and 6 as candidates; now only the 4 is left.

How do you solve sudoku without guessing?

Work in a fixed order. The simple techniques are quick to spot, and you only reach for the more involved ones when nothing else works.

1. Scan the digits 1 to 9 through every box, starting with the ones you see often.
2. Check rows, columns and boxes with only a few open squares: which digit is missing, and where can it go?
3. Look for squares where only one digit still fits.
4. When nothing else turns up, pencil in the candidates, all of them, in every empty square.
5. Search your notes for pairs and for digits that sit in a single row or column of a box.
6. After every new digit, clean up your notes and go back to step 1.
7. Only when all of that comes up empty is it worth hunting for an X-Wing.

Step 6 is the one to hold on to. Every new digit can open up a simple move somewhere else, so after each placement, go back to the easy checks first.

Common mistakes

• Guessing and hoping. A digit that “probably” fits often leads to a contradiction many moves later, and by then it’s hard to find where things went wrong. Only enter what you can justify.
• Looking from one side only. If you only check squares, you’ll miss digits with a single spot left. If you only trace digits, you’ll miss squares with only one option. Switch between the two.
• Patchy notes. One forgotten candidate can make a square look settled when it isn’t. Take notes completely or not at all.
• Forgetting to erase. Every time you place a digit, erase it from the notes in its row, column and box. Otherwise pairs and single candidates stay hidden.
• Misreading pairs. A pair only works inside the row, column or box that both squares share, and the two candidates have to match exactly.
• Solving on top of a mistake. If a digit shows up twice or a square runs out of candidates, go back to your last safe position instead of pushing on.

Help when you’re stuck: sudoku in Sudocrime

In Sudocrime, every chapter comes with a sudoku: a 4×4 puzzle in the practice case and a 6×6 puzzle in “Silence at Lindenrain”. If you get stuck, the hint works in three steps. First it shows you where to look, such as a row where one digit has only one spot left. Then it explains the reasoning, for example which digits a square’s row, column and box already contain. Only at the end does it fill in the number. Those are exactly the techniques from this page: the only digit for a square and the only spot in a row, column or box.

You take notes with the Notes switch. If you’d rather not enter the candidates yourself, choose Fill notes in the help menu. The app then adds the possible digits to every empty square, replacing your notes there. That counts as a hint and can be undone. To see how the sudoku, the statements and the floor plan come together in a case, read How a murder sudoku works. The basic rule is explained in the sudoku rules, and for practice on a smaller grid, try the 6×6 sudoku guide. For the other kinds of sudoku beyond the classic 9×9, from killer to murder sudoku, see sudoku variants.