Sudoku Solving Techniques: From Naked Singles to X-Wings

The Sudoku techniques that solve Hard and Expert grids: naked and hidden singles, pairs, pointing pairs, box-line reduction and the X-Wing, explained in order.

Updated 7 min read By CodingEagles
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Sudoku techniques are a ladder. You reach for the simplest one that makes progress, place a digit, and the board changes, so you drop back to the bottom of the ladder and start again. Hard and Expert grids just need rungs that easy grids never reach. Here they are in order, each one ready to try on the Sudoku board.

Start with singles

Two patterns place a digit outright, and you should exhaust both before anything fancier.

A naked single is a cell whose candidates have all been eliminated except one. The remaining digit is forced. Keep your notes current and naked singles appear on their own as you fill the grid.

A hidden single is a digit that fits in only one cell of a row, column or box, even when that cell still shows several candidates. Scan each unit for a candidate that lives in just one place. Hidden singles are the single most common way Hard puzzles open up, and beginners miss them because the cell looks crowded.

Pairs and triples remove candidates

When no single is available, look for groups that share candidates.

A naked pair is two cells in the same unit that hold the same two candidates and nothing else, such as two cells both showing only {4, 7}. Those two digits must occupy those two cells in some order, so you can erase 4 and 7 from every other cell in that unit. A naked triple is the same idea across three cells and three digits.

A hidden pair is two digits that, between them, can only go in two cells of a unit. Once you spot it, you can strip every other candidate out of those two cells.

These do not place a digit by themselves. They clear candidates, which then exposes a single somewhere else.

Interactions between a box and a line

Two techniques use the overlap between a 3x3 box and a row or column.

A pointing pair (or triple) happens when a candidate inside one box is confined to a single row or column of that box. Since it has to live on that line within the box, you can remove it from the rest of the line outside the box.

Box-line reduction is the mirror image. If a candidate in a row or column only appears within one box, you can remove it from the other cells of that box.

Both are quiet but powerful, and they unlock most Expert grids without anything more exotic.

The X-Wing

The X-Wing is the first technique that reasons across the whole board rather than one unit. Find a candidate that appears in exactly two cells of one row, then a second row where the same candidate also appears in exactly two cells, in the same two columns. Those four cells form a rectangle. The candidate must sit on one diagonal of that rectangle, which means it cannot appear anywhere else in those two columns. Erase it from the rest of both columns.

It takes practice to spot, but once you can, it cracks the puzzles that seem to have no moves left.

How to climb the ladder

The discipline matters more than any single trick:

  • Always use the simplest technique that works. Reach for an X-Wing only when singles, pairs and box-line moves have all dried up.
  • After every placement, reset to the top of the ladder. One new digit often makes a naked single appear elsewhere.
  • Keep notes honest. Most “impossible” grids are really a missed elimination two moves back.

If the named patterns are new, read how to play Sudoku first for the scanning basics, then open the Sudoku board on Hard and work the ladder one rung at a time.

Frequently asked questions

What is the difference between a naked single and a hidden single?
A naked single is a cell that has only one candidate left after you eliminate digits its row, column and box already contain. A hidden single is a digit that can legally go in only one cell of a unit, even though that cell still shows other candidates. Both are forced placements.
Do you ever have to guess in Sudoku?
A properly made puzzle never requires guessing, because it has exactly one solution reachable by logic. If you feel forced to guess, you have usually missed an elimination. The harder techniques exist precisely so you can keep deducing instead of guessing.
What is a pointing pair in Sudoku?
A pointing pair is when a candidate digit in a 3x3 box is confined to a single row or column within that box. Because it must sit in that line inside the box, you can erase that candidate from the rest of the same row or column outside the box.

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