Naked Pairs

The Naked Pairs technique is one of the most common and powerful tools for cracking medium and hard Sudoku puzzles. It relies heavily on you filling out pencil marks (candidates) for empty cells.

How it Works

If you find two cells within the same group (a row, a column, or a 3x3 block) that contain exactly the same two candidates—and no other candidates—you have found a Naked Pair.

Because those two specific cells can only be filled by those two specific numbers, it is mathematically impossible for those numbers to appear anywhere else in that group. Therefore, you can safely erase those two numbers from the candidate lists of every other empty cell in that group.

Example

Imagine a 3x3 block where two cells only have the pencil marks "3" and "7". You don't know which cell is the 3 and which is the 7 yet, but you know for a fact that they occupy those two cells. If another cell in that same 3x3 block has the pencil marks "3, 7, 9", you can safely erase the 3 and the 7, leaving "9" as the only possible answer for that cell!

Hidden Pairs

The Hidden Pairs technique is the inverse of Naked Pairs. It can be harder to spot because the pair is "hidden" among other candidate numbers in the cells.

How it Works

You are looking for a situation where two candidate numbers appear in exactly two cells within a specific group (row, column, or block), and nowhere else in that group. Even if those two cells have other pencil marks in them, the fact that our two target numbers can ONLY go in those two cells means they must be the answer.

Therefore, you can safely delete all the "extra" candidate numbers from those two cells, effectively turning the Hidden Pair into a Naked Pair.

X-Wing

The X-Wing is an advanced technique used to eliminate candidates in very hard puzzles. It requires looking at the grid globally rather than just focusing on a single block.

How it Works

An X-Wing occurs when a specific candidate number can only be placed in exactly two cells in a row, and this same pattern is repeated in another row, perfectly aligned in the exact same two columns.

Think of it as a rectangle. Because the rules of Sudoku dictate that the number must appear once in each row and once in each column, the true placements must form a diagonal across that rectangle (the "X").

Consequently, the number cannot appear anywhere else in those two vertical columns outside of our four corner cells. You can safely erase it from the pencil marks of all other cells in those columns!

Swordfish

The Swordfish is an expert-level technique that is essentially an expanded version of the X-Wing pattern. While an X-Wing uses two rows and two columns, a Swordfish uses three.

How it Works

A Swordfish pattern exists when you find a specific candidate number that is restricted to two or three cells in exactly three different rows. Crucially, those candidate cells must all align perfectly into exactly three columns.

Because the number must be placed exactly three times across those three rows, and can only fall into those three specific columns, the three resulting placements will completely "fill" the requirements for those columns.

Therefore, you can confidently eliminate that candidate number from any other cell in those three columns!