Sudoku Techniques in Order of Difficulty (With Data)

Here are the sudoku techniques in order of difficulty, easiest first: naked single, hidden single, pointing, claiming, naked pair, X-Wing, hidden pair, naked triple, Swordfish, hidden triple, XY-Wing, simple colouring, and Jellyfish. Past those come the patterns you only meet in the hardest puzzle books: skyscraper, two-string kite, unique rectangle, W-Wing, XYZ-Wing, BUG+1, and chains. Those 13 main techniques are enough for every puzzle in Sudoku Royale's library of 457,000 graded puzzles.

Most lists, including our own complete technique list in learning order, stop at the order. This one adds how often each technique is actually needed, measured by grading every puzzle we serve and recording the hardest step each one requires. The numbers change which techniques are worth learning first. The X-Wing, for example, is famous, but it is the hardest step in fewer than 1 in 100 Expert puzzles, while the naked pair is the hardest step in 1 in 4.

The ranked list

The difficulty score is the one our grader uses, on the same scale as the Sudoku Explainer rating: the higher the number, the harder the step is to find. The level column shows the first of Sudoku Royale's six Classic levels that can require the technique.

Two notes on the order. First, a hidden single scores lower than a naked single on this scale, but beginners learn the naked single first because you can see it by looking at one cell. We rank it first for that reason. Second, the X-Wing sits between the pairs because the logic is short, but it is hard to spot, since its four cells are spread across the grid.

What each difficulty level actually needs

We graded every puzzle Sudoku Royale serves and recorded the hardest step each one requires. This table shows the result by level. It answers a question most technique lists skip: if you are stuck on a puzzle at this level, which technique is it most likely to be?

Some Expert and Master puzzles top out at an easy technique. That is not a mistake: Sudoku Royale sets a level by the harder of two things, the hardest technique and the total amount of searching the puzzle takes. A puzzle that needs only hidden singles but hides every one of them well still plays like an Expert puzzle.

Three things stand out. The hidden single does most of the work all the way up to Hard. Pairs and locked candidates (pointing and claiming) are what Expert is about. And the XY-Wing, not the X-Wing, is the technique that defines Master.

Tier 1: singles

Singles place digits directly. A naked single is a cell with only one possible digit. A hidden single is a digit with only one possible cell in a row, column, or box. You can solve every Easy and Medium puzzle with these two alone, and you can find both without pencil marks.

• 5 clue
• 5 already solved
• 5 new digit
• 5 pattern candidate
• 5 candidate to remove

Tier 2: locked candidates (pointing and claiming)

Both use the overlap between a box and a line. Pointing: a digit confined to one line inside a box can be removed from that line outside the box. Claiming, also called box-line reduction: a digit confined to one box inside a line can be removed from the rest of that box. These are the techniques that make Hard puzzles hard. Our guide to pointing pairs and box-line reduction covers both directions.

Tier 3: pairs and the X-Wing

A naked pair is two cells in one group that hold the same two candidates and nothing else. A hidden pair is two digits that fit only the same two cells of a group. The hidden version is ranked higher because the pair cells usually carry other candidates that disguise it.

The X-Wing follows one digit. If it has exactly two possible cells in each of two columns, and those cells line up on the same two rows, the digit must take one cell in each of those rows. It can be removed from the rest of both rows. (The same works with rows and columns swapped.)

Tier 4: triples, Swordfish, and the XY-Wing

Triples are pairs with three cells and three digits. A naked triple does not need every cell to hold all three digits: 12, 23, and 13 is a valid triple. Hidden triples are the mirror image. The Swordfish is the X-Wing on three rows and three columns.

The XY-Wing is the one to learn at this tier, because it is the hardest step in 72% of our Master puzzles. It uses three cells with two candidates each: a pivot with XY, and two pincers the pivot can see, with XZ and YZ. One pincer must be Z, so any cell that sees both pincers loses Z. There is a worked XY-Wing example in what to do when you are stuck and another in how to solve sudoku when there are two options.

Tier 5: simple colouring and the Jellyfish

Simple colouring follows a single digit through a chain of conjugate pairs: groups where the digit has exactly two possible cells, so one of them must hold it. Colour the cells of the chain in two alternating colours. One colour is all true and the other all false. If two cells of the same colour see each other, that colour is false. If a cell outside the chain sees both colours, it cannot hold the digit.

The Jellyfish is the X-Wing on four rows and columns. It is so rare that 17 of our 457,000 puzzles need one, so learn it last, if at all.

Beyond the list: techniques for the hardest puzzles

About 9% of the puzzles our generator produces need something beyond the 13 techniques above, and we leave those out of the app. You will still find them in newspaper "fiendish" tiers and puzzle books. These are the usual next steps, roughly in order:

The unique rectangle and BUG+1 have worked examples in what to do when you are stuck with only pairs, and forcing chains are covered in whether you can solve sudoku without guessing.

How to learn them in order

Learn one tier at a time and play puzzles that need it before moving on. Sudoku Royale's Classic levels are built on this ladder: Easy and Medium are open from the start, Hard unlocks after 2 Medium solves, Expert after 4 Hard solves, Master after 10 Expert solves, and Extreme after 14 Master solves. When you stall, the lightbulb hint names the technique the board needs without giving away the digit. For drilling, the Dojo has a short lesson and a timed drill for every technique in tiers 1 to 5 except the Jellyfish: open Pointing, Claiming, Naked Pair, Hidden Pair, X-Wing, XY-Wing, or Simple Colouring on your iPhone. For how the levels feel in play, see the guide to sudoku difficulty levels.