Sudoku Tips & Strategy

Scanning and Cross-Hatching: Your First Move Every Time

Scanning is the habit of picking one digit and sweeping it across the whole grid before touching anything else. Cross-hatching is the targeted version: you focus on a single 3x3 box and ask where one specific digit can go inside it. Take the digit 5. Look at the box you're solving. Now trace every row and every column that already contains a 5 and mentally cross out all the cells those lines pass through. Since a 5 can't repeat in any row, column, or box, those cells are eliminated. If only one empty cell in the box survives, that cell must be a 5. For example, if a box has a 5 sitting in the row above its top cells and another 5 in the column on its left, those two lines may eliminate every candidate cell except one, instantly placing your digit. Always start here, because it requires no notes and solves most easy puzzles entirely on its own.

Pencil Marks: The Foundation for Everything Harder

Pencil marks (also called notes or candidates) are the small digits you write in a cell to record which numbers could still legally go there. Once cross-hatching stops producing easy placements, you switch to pencil marks so you can reason about possibilities instead of holding them in your head. Fill a cell's notes by checking its row, column, and box and writing down every digit that doesn't already appear in those three groups. For instance, a cell whose row contains 1, 4, 9, whose column contains 2, 7, and whose box contains 4, 6 would get the notes 3, 5, 8. The discipline that matters most: every time you place a final digit, immediately erase that digit from the notes of every other cell in its row, column, and box. Clean, up-to-date notes are what make every advanced technique below possible. Sloppy notes cause wrong placements that are painful to unwind.

Naked Singles: When a Cell Has Only One Option

A naked single is a cell whose pencil marks have been whittled down to a single candidate. Because that's the only digit that can legally fit, you place it with certainty. These appear constantly once your notes are accurate, and they often cascade: placing one naked single lets you erase a candidate elsewhere, which exposes the next naked single, and so on. For example, if a cell shows the notes 3 and 7, then you place a 7 in another cell in the same row, you erase the 7 here and the cell becomes a lone 3 a naked single you place immediately. After every placement, glance at the affected row, column, and box to catch the chain reaction these create.

Hidden Singles: The One Spot a Digit Can Live

A hidden single is the mirror image of a naked single. Instead of a cell with one candidate, it's a digit that has only one possible home within a particular row, column, or box even though that cell still shows several candidates. The digit is 'hidden' among other notes. To spot it, pick a unit (say, a row) and a digit (say, 6). Scan the cells in that row and count how many still list 6 as a candidate. If exactly one does, that cell is a 6, regardless of whatever other notes it carries. For example, a row might have three empty cells and only the middle one includes 6 in its notes; that cell is a 6, and you can erase its other candidates. Hidden singles are the single most common 'I'm stuck' breakthrough, so when scanning fails, hunt for them deliberately, one digit at a time.

Naked Pairs: Locking Two Cells Together

A naked pair is two cells in the same unit (row, column, or box) that both contain exactly the same two candidates and nothing else for example, two cells each showing only 4 and 8. You can't yet know which holds the 4 and which holds the 8, but you do know those two cells will consume both digits between them. That means no other cell in that shared unit can be a 4 or an 8, so you erase 4 and 8 from every other cell's notes in that row, column, or box. This rarely places a digit by itself, but the eliminations frequently reduce a neighboring cell to a naked single or expose a hidden single. Naked pairs are your first real 'elimination' technique the kind that progresses a puzzle without directly filling a square.

Pointing Pairs: When a Box Aims at a Line

A pointing pair (or pointing triple) happens when, inside a single 3x3 box, all the candidate cells for one digit fall on the same row or the same column. Suppose every cell in a box that could be a 2 sits in that box's top row, and there are two or three such cells. The 2 for that box must end up in that row, even though you don't know which cell yet. Therefore a 2 cannot appear in that same row anywhere outside the box, so you erase 2 from the notes of the row's cells in the two neighboring boxes. The arrow 'points' out of the box along the shared line. This is a powerful intersection technique because it lets one box trim candidates in distant cells, often setting up a hidden single two boxes away.

X-Wing: A Gentle Step into Advanced Logic

X-Wing is your first taste of techniques that span the whole grid, and it's worth meeting once the above tools stop being enough. Find a single digit say 7 that appears as a candidate in exactly two cells in one row, and exactly two cells in a second row, with all four cells lining up in the same two columns. They form the corners of a rectangle (the 'X'). Here's the logic: in each of those two rows the 7 must go in one of those two columns, and because of how the corners interlock, the two 7s are forced to sit in opposite corners. Either way, both of those columns will have their 7 used up by these rows. So you can erase 7 from every other cell in those two columns. You don't need to find X-Wings to enjoy Sudoku, but recognizing the rectangle pattern is a satisfying milestone and the gateway to the harder logic beyond it.

Quick tips

• Always exhaust scanning and cross-hatching before writing any pencil marks, you'll solve easy puzzles faster and keep the grid uncluttered.
• Keep your notes honest: the instant you place a digit, erase it from every related cell's candidates, or every technique above will mislead you.
• When you feel stuck, switch from looking at cells to looking at digits, march 1 through 9 and ask 'where can this number go in each box?' to surface hidden singles.
• Work one technique at a time in order of difficulty; jumping to X-Wing when a hidden single is sitting right there just wastes effort.
• Never guess on a true Sudoku. Every well-formed puzzle is solvable by pure logic, so if you're tempted to guess, there's a deduction you've missed.
• Use a pencil (or the app's notes mode) so eliminations are reversible, confident solving comes from being able to trust and update your marks.
• After placing any digit, immediately re-scan its row, column, and box, single placements often trigger a chain of naked and hidden singles.

Frequently Asked Questions

How do I get better at Sudoku?

Improve in stages rather than all at once. Master scanning and cross-hatching until they're automatic, then learn to keep accurate pencil marks. From there, add one technique at a time in order: naked singles, hidden singles, naked pairs, pointing pairs, and eventually X-Wing. The biggest single jump in skill comes from disciplined note-taking, erasing candidates the moment you place a digit, because every advanced deduction depends on clean notes. Solve regularly at a difficulty that makes you think but doesn't make you guess.

What's the best first move in a Sudoku puzzle?

Start by scanning the most common digit on the board. Find the number that already appears most often and cross-hatch it through the boxes where it's missing, since digits with many copies already placed are the easiest to pin down. Also look at the most-filled rows, columns, and 3x3 boxes first; a box with only one or two empty cells frequently resolves immediately. Avoid writing pencil marks until simple scanning stops producing placements.

Is every Sudoku puzzle solvable without guessing?

A properly constructed Sudoku has exactly one solution and can always be reached through pure logic, no guessing required. If you feel forced to guess, it almost always means there's a deduction you haven't spotted, such as a hidden single or a pointing pair. Step back, pick a single digit, and check each unit methodically. Guessing tends to create errors that are hard to trace, so it's better to find the logical step than to gamble.

What should I do when I'm completely stuck?

First, verify your pencil marks are current, an outdated candidate left in a cell is the most common reason a puzzle seems impossible. Then hunt for hidden singles by going digit by digit through each box, row, and column. If that fails, look for naked pairs and pointing pairs to eliminate candidates and open new placements. Working through these in order will almost always break the logjam without resorting to guessing.

What's the difference between a naked single and a hidden single?

A naked single is a cell that has only one candidate left in its notes, so that digit obviously goes there. A hidden single is a digit that can legally go in only one cell within a row, column, or box, even though that cell may still show several other candidates, the right digit is 'hidden' among the others. Naked singles are found by looking at a cell's options; hidden singles are found by looking at where a single digit can live across a whole unit.

Do I have to use pencil marks to solve hard Sudoku?

For easy and many medium puzzles you can often solve by scanning alone. But for hard puzzles, pencil marks are essential, every technique beyond simple scanning (naked pairs, pointing pairs, X-Wing) works by eliminating candidates, and you can't track eliminations reliably in your head. Get in the habit of filling notes once scanning stalls, and keeping them updated after each placement.