Learning Path
Work through the techniques below from top to bottom if you are learning. Each group builds on the one before it, from obvious placements to harder note patterns.
- First
Start with sure numbers
Singles teach you to look for cells or digits that have only one place left.
- Next
Use notes to remove clutter
Locked candidates, pairs, triples, and quads help you erase notes before you place a number.
- Then
Look for larger shapes
Fish, wings, and chains are harder patterns that usually show up after the simple notes are cleaned up.
Basic Techniques
Intermediate Techniques
Locked Candidate
Box-line interactions
Candidates for one number inside a box all sit on the same row or column.
Naked Pair
Subsets
Two cells in one row, column, or box contain the same two notes.
Hidden Pair
Subsets
Two numbers can only go in the same two cells of a row, column, or box.
Naked Triple
Subsets
Three cells in one row, column, or box share only three possible numbers.
Expert Techniques
Naked Quad
Subsets
Four cells in a row, column, or box contain only four shared digits between them.
Hidden Quad
Subsets
Four numbers can only go in the same four cells of a row, column, or box.
Hidden Triple
Subsets
Three numbers can only go in the same three cells of a row, column, or box.
X-Wing
Fish
One number lines up in the same two columns across two rows, or the same two rows across two columns.
Skyscraper
Single-digit chains
Two two-choice lines for the same number point to a shared removal.
Two-String Kite
Single-digit chains
A two-choice row and a two-choice column connect through a box and force one removal.
Simple Coloring
Single-digit chains
Two colors mark a chain of one-or-the-other choices for one number.
W-Wing
Wings
Two matching two-note cells use a connecting one-or-the-other link to remove a shared note.
XY-Wing
Wings
One two-note pivot points to two wings that share a removable note.
XYZ-Wing
Wings
A three-note pivot and two wings remove a shared note from cells touching the whole pattern.
Swordfish
Fish
One number is locked across three rows and three columns.
Jellyfish
Fish
One number is locked across four rows and four columns.
Finned X-Wing
Finned fish
An almost X-Wing has one extra note that still allows a few removals.
Finned Swordfish
Finned fish
An almost Swordfish has an extra fin note that narrows where removals are allowed.
Finned Jellyfish
Finned fish
An almost Jellyfish has one or more extra fin notes that allow narrow removals.
Advanced Techniques
Want the shorter tour? Open the Sudoku Walkthrough.