Sudoku strategies and techniques

Stuck on a medium or hard grid? These are the techniques that get you moving again, easiest first: the same order our solver tries them in and our levels introduce them. Every example is a real step from a puzzle you can play here, with the pencil marks exactly as they stand at that moment.

Play Hard SudokuTry Evil

Start with the basics

Every technique here sits on top of two moves: the only square left for a digit in a row, column or box, and the last digit standing in a square. If those are new, read how to play Sudoku first.

Everything below also works on pencil marks, the small candidate digits in each empty square. Fill them in for the part of the grid you’re working on before you go hunting, and keep them clean: when you place a digit, clear it from its row, column and box. In the diagrams, yellow marks the candidates that make the pattern and red marks the ones it removes.

Locked candidates

Locked candidates come in two directions. Pointing: a digit’s candidates inside a box all sit in one row or column, so the rest of that line loses the digit. The beginner’s guide walks through one. Claimingis the mirror image: a row or column’s candidates for a digit all sit inside one box, so the rest of that box loses it.

Here, the only squares of column 7 that can still take a 1 are rows 4 and 5, and both are in the middle-right box. Column 7 must get its 1 from that box, so the box’s 1 is in column 7, and no other square of the box can hold one: cross the 1 off row 4, column 9 and row 5, column 8.

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Yellow: the only places for the 1 in column 7, all in the shaded box. Red: the 1s this clears from the rest of the box.

Naked pairs and triples

If two squares in the same row, column or box have exactly the same two candidates and nothing else, those two digits are spoken for. One square gets one, the other gets the other. No other square in that unit can hold either.

In the middle-left box below, row 6, column 1 and row 6, column 2 can each only be 3 and 7. That clears 3 and 7 from the rest of the box:

  • row 4, column 1: remove 7
  • row 5, column 2: remove 3 and 7
  • row 5, column 3: remove 7
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The yellow pair holds only 3 and 7, so the red candidates in the rest of the shaded box can go. Faint digits are the other pencil marks.

A naked triple is the same idea with three squares sharing three candidates between them. Not every square needs all three: {1,2}, {2,3} and {1,3} is a triple too. They are rare: just one of our 546 puzzles needs one.

Hidden pairs

Flip the naked pair around. If two digits can only go in the same two squares of a unit, those squares must hold those two digits, whatever else is pencilled in them. So every other candidate in those two squares can go.

In row 5, the 6 and 7 can only go in row 5, column 1 and row 5, column 7. Those squares are therefore 6 and 7 in some order, so their other candidates go:

  • row 5, column 1: remove 5 and 8
  • row 5, column 7: remove 1 and 8
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The yellow 6 and 7 appear nowhere else in the shaded row, so the red extras in those two squares can go.

Hidden pairs are harder to see than naked ones because the extra candidates disguise them. A good habit: for each row, column and box, count where each digit can go. Any two digits with the same two squares are a hidden pair.

The X-Wing

Now we look at one digit across the whole grid. In rows 3 and 4, the 1 can only go in columns 1 and 5. Those four squares form a rectangle.

Each of the two rows needs its 1, and the only way to give both of them one is along a diagonal of the rectangle: top-left with bottom-right, or top-right with bottom-left. Either way, columns 1 and 5 each get their 1 from inside the rectangle. So no other square in those columns can be a 1: cross it off row 1 of column 1, and rows 1, 5 and 9 of column 5.

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Every 1 candidate on the board. The yellow four form the rectangle in the shaded rows; the red 1s share its columns and can go.

To find one, pick a digit, pencil only that digit, and look for two rows (or two columns) where it has exactly two spots each, lined up with each other.

The XY-Wing

An XY-Wing uses three squares that each have exactly two candidates. The middle one, the pivot, sees the other two, the pincers.

  • The pivot, row 5, column 3, is 2 or 3.
  • One pincer, row 6, column 1, is 2 or 4. The other, row 1, column 3, is 3 or 4.
  • If the pivot is 2, the first pincer must be 4. If the pivot is 3, the second pincer must be 4. Either way, one of the pincers is a 4.

So any square that sees both pincers can’t be a 4. Here that is row 1, column 1, which loses its 4.

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The shaded pivot and pincers with their two candidates each. The red 4 sees both pincers, so it can go.

Swordfish and beyond

A Swordfish is an X-Wing stretched over three rows and three columns, and the XYZ-Wing is an XY-Wing whose pivot has three candidates. Puzzles built to be extreme go further still, into chains and larger fish. They are real techniques, but you can stop here with a clear conscience: none of our 546puzzles needs them, and neither does most of what you’ll find in a newspaper.

When you’re stuck

  1. Rescan for singles. After any elimination, a single is the most likely thing to appear.
  2. Check your pencil marks against the placed digits. A stale mark hides moves and invents fake ones.
  3. Look for locked candidates in every box, then every row and column.
  4. Find squares with only two candidates: they make pairs and XY-Wings.
  5. For each digit, look for rows or columns where it has exactly two spots: that’s where X-Wings live.
  6. Still nothing? In our Sudoku, Hint names the technique that proves the next move. Three per grid, and on practice levels nothing is lost by using them.

Which level needs what

Strategy questions

What order should I try Sudoku techniques in?

Easiest first, and go back to the start after every placed digit: singles, then locked candidates, then pairs, then X-Wings and XY-Wings. Most grids that feel stuck are waiting on a single you haven't spotted, so the cheap checks pay off.

What is an X-Wing in Sudoku?

When a digit can go in only two squares in each of two rows, and those squares line up in the same two columns, they form a rectangle. The digit must sit on one diagonal of it, so it can be removed from every other square in those two columns. The same works with rows and columns swapped.

Do I need to learn every technique to solve hard Sudoku?

No. Singles and locked candidates solve everything up to our Hard level. Pairs unlock Expert, and the X-Wing and XY-Wing unlock Evil. Beyond those, only one of our 546 puzzles needs a naked triple, and none needs guessing.

What is the hardest Sudoku technique?

Chains and fish larger than a Swordfish, used on puzzles built to be extreme. Everyday hard puzzles, including all of ours, stop at the X-Wing and XY-Wing. Learning those two covers almost anything you'll meet in a newspaper or an app.

Put pairs to work on Expert