Naked Single
A Naked Single is a cell where only one digit is possible, because all the other eight digits are already in the cell's row, column or box.
Learn the technique with interactive examplesSudoku techniques: learn all techniques from easy to brutal
Here you will find all the techniques you need to solve sudoku, ordered by difficulty level. Each technique has its own page with interactive examples you can work through step by step, a procedure you can follow on your own puzzles, and the most common mistakes to avoid. Start at the level that suits you, or test the techniques directly in the Sudoku Solver.
Easy: the basic techniques
The easiest sudokus are solved with two techniques that both build on the same rule: each digit can only appear once in each row, column and box. If you learn these two, you can solve all puzzles on Easy level.
Hidden Single
A Hidden Single is a digit that only fits in one cell within a box, row or column. This is true even if the cell could also take other digits.
Learn the technique with interactive examplesMedium: pairs and blocking
At Medium level it is no longer enough to place digits directly. Now it is about removing candidates: when you can prove that a digit cannot go in a cell, the rest of the puzzle becomes easier. Write candidate notes, because that is the key to all techniques from here on.
Naked Pair
A Naked Pair is two cells in the same unit that have exactly the same two candidates. The two digits must share these cells between them, so they can be removed from the rest of the unit.
Learn the technique with interactive examplesHidden Pair
A Hidden Pair is two digits that can only go in the same two cells in a unit. Then the two cells must contain exactly these digits, and all other candidates in them can be removed.
Learn the technique with interactive examplesPointing Pair
A Pointing Pair is a digit that within a box can only go in one row or one column. The box then points: the digit can be removed from the rest of the row or column outside the box.
Learn the technique with interactive examplesHard: patterns across the puzzle
At Hard level you must see multiple units in context: digits that form rectangles across multiple rows, chains of linked cells and boxes that lock each other. The techniques still only remove candidates, but these are exactly the eliminations that open up the puzzle.
Box/Line Reduction
Box/Line Reduction is the Pointing Pair turned inside out: when a digit within a row or column can only go in one box, the digit can be removed from the rest of that box.
Learn the technique with interactive examplesX-Wing
An X-Wing is four cells that form a rectangle: in two rows or columns a digit can only go in the same two places. Then the digit can be removed from the rest of the crossing lines.
Learn the technique with interactive examplesSwordfish
Swordfish is X-Wing extended to three lines: a digit that in three rows can only go in the same three columns can be removed from the rest of the columns.
Learn the technique with interactive examplesSimple Coloring
Simple Coloring follows a chain of cells linked in pairs for one specific digit and colors every other cell. One color must be correct, and that can be used to eliminate candidates.
Learn the technique with interactive examplesExtreme: wings and advanced coloring
Puzzles at Extreme level require techniques that combine three or more cells in logical reasoning of the if-then type. Try your way through the examples below, step by step, using the same tools the solver uses on your own puzzle.
XY-Wing
XY-Wing uses three cells with two candidates each: a pivot with candidates XY and two wings with XZ and YZ.
Learn the technique with interactive examplesXYZ-Wing
XYZ-Wing is like XY-Wing, but the pivot has all three candidates: XYZ.
Learn the technique with interactive examplesJellyfish
Jellyfish is the fish above Swordfish: four rows where a digit can only go in the same four columns.
Learn the technique with interactive examples3D Medusa
3D Medusa is coloring in multiple dimensions: the chains link both cells with the same digit and the two candidates inside the same cell.
Learn the technique with interactive examplesBrutal: chains and almost locked sets
The hardest puzzles require techniques that follow long logical chains through the entire puzzle. They are in practice proof by contradiction: assume something, follow the consequences and see what does not hold. Try your way through the examples below, step by step, using the same tools the solver uses on your own puzzle.
BUG+1
BUG+1 exploits the fact that a valid sudoku puzzle cannot end in a state where all empty cells have exactly two candidates. That state is called a Bivalue Universal Grave.
Learn the technique with interactive examplesALS (Almost Locked Sets)
ALS stands for Almost Locked Sets and links two groups of cells that are almost locked, that is, n cells with n+1 candidates, via a common digit.
Learn the technique with interactive examplesKraken Fish
Kraken Fish is here an X-Wing or Swordfish with one fin, that is, an extra candidate that almost ruins the regular fish pattern.
Learn the technique with interactive examplesAIC (Alternating Inference Chains)
AIC stands for Alternating Inference Chains and consists of chains that alternate between strong and weak links across the puzzle.
Learn the technique with interactive examplesForcing Chains
Forcing Chains test both candidates in a cell and follow the consequences of each of them.
Learn the technique with interactive examplesTest the techniques on your own puzzle
The Sudoku Solver finds the next step on your puzzle and explains which technique is used and why it works.
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