Explore 20 Sudoku techniques from Sudoku Pro, from Naked Single to XY-Chain, with explanations and example grids.
Sudoku Pro gives you practice puzzles for every technique. If you get stuck, the trainer shows you how to reach the solution step by step on the puzzle you are playing.
Small digits are candidates. Crossed-out digits can be removed in this step.
When a cell has only one possible candidate left, that must be the answer. All other numbers are already used in the same row, column, or block.
| Given 1 | Given 2 | Given 3 | Pattern (purple). Candidates 4 |
| Empty | Empty | Given 1 | Given 2 |
| Empty | Empty | Empty | Given 3 |
| Empty | Empty | Empty | Given 1 |
When two cells in the same row, column, or block contain the exact same two candidates and nothing else, those two numbers are "locked" into those cells. You can remove them from all other cells in that shared unit.
| Pattern (purple). Candidates 1, 2 | Pattern (purple). Candidates 1, 2 | Affected cell (orange). Candidates 3. Eliminated 1 | Given 4 |
| Given 3 | Given 4 | Empty | Given 2 |
| Empty | Empty | Given 4 | Empty |
| Given 4 | Given 3 | Given 2 | Empty |
When a candidate within a block only appears in a single row or column, it must be placed somewhere in that line inside the block. You can eliminate that candidate from the rest of that row or column outside the block.
| Pattern (purple). Candidates 3, 4 | Pattern (purple). Candidates 3, 4 | Affected cell (orange). Candidates 2. Eliminated 3 | Given 1 |
| Given 1 | Given 2 | Empty | Given 4 |
| Given 2 | Given 1 | Given 4 | Empty |
| Empty | Empty | Given 1 | Empty |
The reverse of a Pointing Pair. When a candidate in a row or column only appears within a single block, it must go in that block. You can eliminate that candidate from all other cells in the block that are not in that row or column.
| Pattern (purple). Candidates 2, 3 | Pattern (purple). Candidates 2, 3 | Given 1 | Given 4 |
| Affected cell (orange). Candidates 1. Eliminated 3 | Given 4 | Given 2 | Empty |
| Empty | Given 1 | Empty | Empty |
| Given 4 | Empty | Empty | Empty |
When three cells in the same unit contain candidates from the same set of three numbers (and nothing else), those three numbers are locked into those cells. You can remove them from all other cells in that unit.
| Pattern (purple). Candidates 1, 2 | Pattern (purple). Candidates 2, 3 | Pattern (purple). Candidates 1, 3 | Affected cell (orange). Candidates 4. Eliminated 1 |
| Given 4 | Empty | Empty | Given 2 |
| Empty | Given 1 | Given 4 | Given 3 |
| Given 3 | Given 4 | Given 2 | Empty |
When a candidate appears in exactly two cells in each of two different rows, and those cells share the same two columns, the candidate must go in one of the two diagonal pairs. You can eliminate it from all other cells in those two columns.
| Pattern (purple). Candidates 1, 3 | Given 4 | Given 2 | Pattern (purple). Candidates 1, 3 |
| Affected cell (orange). Candidates 1, 2. Eliminated 3 | Empty | Empty | Affected cell (orange). Candidates 1, 4. Eliminated 3 |
| Pattern (purple). Candidates 3, 4 | Given 2 | Given 1 | Pattern (purple). Candidates 3, 4 |
| Affected cell (orange). Candidates 1, 4. Eliminated 3 | Empty | Empty | Given 2 |
A Skyscraper uses a candidate that appears in exactly two cells in each of two rows. The two base cells, one from each row, share a column; the two roof cells lie in different columns. The base cells cannot both hold the candidate, so at least one roof does. It can be eliminated from any cell that sees both roofs. The same works with columns instead of rows.
| Pattern (purple). Candidates 2, 4 | Given 3 | Given 1 | Pattern (purple). Candidates 2, 4 |
| Empty | Empty | Affected cell (orange). Candidates 3. Eliminated 4 | Empty |
| Empty | Empty | Given 2 | Affected cell (orange). Candidates 3. Eliminated 4 |
| Pattern (purple). Candidates 3, 4 | Given 2 | Pattern (purple). Candidates 3, 4 | Given 1 |
An extension of X-Wing to three rows. When a candidate appears in only two or three cells in each of three rows, and all those cells fall within three columns, you can eliminate that candidate from all other cells in those three columns.
| Pattern (purple). Candidates 1, 2 | Pattern (purple). Candidates 2, 3 | Empty | Given 4 |
| Empty | Pattern (purple). Candidates 2, 4 | Pattern (purple). Candidates 1, 2 | Given 3 |
| Pattern (purple). Candidates 2, 3 | Empty | Pattern (purple). Candidates 2, 4 | Given 1 |
| Affected cell (orange). Candidates 4. Eliminated 2 | Affected cell (orange). Candidates 1. Eliminated 2 | Given 3 | Empty |
A 2-String Kite uses a candidate that appears in exactly two cells of one row and exactly two cells of one column. One cell from the row and one from the column share a block, and the two other ends lie outside it. The two cells in the block cannot both hold the candidate, so at least one end does. It can be eliminated from any cell that sees both ends.
| Pattern (purple). Candidates 1, 2 | Given 3 | Pattern (purple). Candidates 1, 2 | Given 4 |
| Given 4 | Empty | Empty | Pattern (purple). Candidates 2, 3 |
| Affected cell (orange). Candidates 1. Eliminated 2 | Empty | Empty | Pattern (purple). Candidates 2, 3 |
| Given 3 | Empty | Empty | Given 1 |
A W-Wing uses two cells with exactly the same two candidates that do not see each other. In a row, column, or block, one of these candidates appears in only two cells, one seeing each cell of the pair. One of those two cells must hold that candidate, so at least one cell of the pair holds the other one. The other candidate can be eliminated from any cell that sees both cells of the pair.
| Given 4 | Pattern (purple). Candidates 1, 3 | Pattern (purple). Candidates 1, 3 | Given 2 |
| Empty | Empty | Empty | Pattern (purple). Candidates 3, 4 |
| Given 1 | Pattern (purple). Candidates 3, 4 | Given 2 | Affected cell (orange). Candidates 3. Eliminated 4 |
| Empty | Empty | Empty | Given 1 |
A Y-Wing uses three cells each with exactly two candidates. One "hinge" cell can see two "wing" cells. The hinge shares one candidate with each wing, and the wings share a different candidate with each other. That shared wing candidate can be eliminated from any cell that sees both wings.
| Pattern (purple). Candidates 1, 2 | Cell related to the pattern. Empty | Cell related to the pattern. Given 4 | Pattern (purple). Candidates 1, 3 |
| Cell related to the pattern. Empty | Given 3 | Empty | Given 2 |
| Cell related to the pattern. Empty | Given 1 | Given 2 | Given 4 |
| Pattern (purple). Candidates 2, 3 | Given 4 | Empty | Affected cell (orange). Candidates 1. Eliminated 3 |
An XYZ-Wing works like a Y-Wing, but the hinge has exactly three candidates. It sees two wing cells with exactly two candidates each. All three cells share one candidate, and each wing also holds a different one of the hinge's other two. The shared candidate can be eliminated only from cells that see the hinge and both wings.
| Given 4 | Given 5 | Empty | Empty | Empty | Empty |
| Given 3 | Pattern (purple). Candidates 1, 6 | Given 2 | Empty | Empty | Empty |
| Empty | Empty | Given 5 | Empty | Empty | Empty |
| Empty | Empty | Empty | Empty | Empty | Empty |
| Empty | Pattern (purple). Candidates 1, 3, 6 | Given 4 | Empty | Given 2 | Empty |
| Empty | Affected cell (orange). Candidates 2, 3. Eliminated 6 | Pattern (purple). Candidates 3, 6 | Given 1 | Empty | Empty |
A Unique Rectangle uses four cells in two rows and two columns that lie in exactly two blocks. Three corners hold exactly the same two candidates, and the fourth holds both of them plus others. If the fourth corner were also reduced to that pair, the two candidates could be swapped around the rectangle and the puzzle would have two solutions. So the fourth corner loses both candidates of the pair.
| Pattern (purple). Candidates 2, 4 | Given 3 | Pattern (purple). Candidates 2, 4 | Given 1 |
| Affected cell (orange). Candidates 1. Eliminated 2, 4 | Empty | Pattern (purple). Candidates 2, 4 | Given 3 |
| Empty | Empty | Empty | Given 4 |
| Empty | Empty | Empty | Given 2 |
A Finned X-Wing is an X-Wing with extra cells. In one row, a candidate appears in only two cells. In a second row, it appears in the same two columns plus one or more fins, which all lie in the block of one of that row's two corners. If no fin holds the candidate, the X-Wing applies; if a fin holds it, no other cell in that block can. Either way, it can be eliminated from the cells of that corner's column that lie in the fin block, outside the two rows. The same works with columns instead of rows.
| Empty | Empty | Empty | Empty | Empty | Empty |
| Empty | Empty | Empty | Empty | Given 3 | Empty |
| Empty | Affected cell (orange). Candidates 1, 3, 4, 6. Eliminated 2 | Empty | Empty | Empty | Empty |
| Given 5 | Pattern (purple). Candidates 1, 2, 6 | Pattern (purple). Candidates 1, 2, 6 | Given 4 | Pattern (purple). Candidates 1, 2, 6 | Given 3 |
| Given 1 | Pattern (purple). Candidates 2, 5 | Given 4 | Given 3 | Pattern (purple). Candidates 2, 5 | Given 6 |
| Empty | Empty | Empty | Empty | Empty | Empty |
Simple Coloring follows one candidate through strong links: rows, columns, or blocks where it appears in exactly two cells, so one of the two must hold it. Linked cells get alternating colors, and exactly one color is right. If two cells of the same color see each other, that color is wrong, and the candidate is removed from all its cells. An uncolored cell that sees both colors loses the candidate too.
| Empty | Empty | Given 3 | Given 1 | Empty | Empty |
| Given 6 | Empty | Empty | Empty | Empty | Given 4 |
| Given 3 | Empty | Empty | Empty | Pattern (purple). Candidates 1, 2, 6 | Given 5 |
| Pattern (purple). Candidates 1, 2 | Given 6 | Given 5 | Empty | Given 4 | Second pattern group (hatched). Candidates 1, 2, 3 |
| Given 5 | Empty | Empty | Empty | Empty | Empty |
| Second pattern group (hatched). Candidates 1, 2, 4 | Given 3 | Given 6 | Empty | Affected cell (orange). Candidates 2, 5. Eliminated 1 | Empty |
An extension of Swordfish to four rows. When a candidate appears in only two to four cells in each of four rows, and all those cells fall within the same four columns, you can eliminate that candidate from all other cells in those four columns.
| Given 4 | Affected cell (orange). Candidates 1, 5, 6. Eliminated 2 | Empty | Affected cell (orange). Candidates 1, 3, 5, 6. Eliminated 2 | Affected cell (orange). Candidates 1, 5, 6. Eliminated 2 | Empty |
| Affected cell (orange). Candidates 1, 5, 6. Eliminated 2 | Given 3 | Empty | Affected cell (orange). Candidates 1, 5, 6. Eliminated 2 | Affected cell (orange). Candidates 1, 4, 5, 6. Eliminated 2 | Empty |
| Pattern (purple). Candidates 2, 3, 6 | Pattern (purple). Candidates 2, 6 | Given 4 | Pattern (purple). Candidates 2, 5, 6 | Pattern (purple). Candidates 2, 5, 6 | Given 1 |
| Pattern (purple). Candidates 1, 2, 6 | Pattern (purple). Candidates 1, 2, 6 | Given 5 | Pattern (purple). Candidates 2, 6 | Given 3 | Given 4 |
| Pattern (purple). Candidates 2, 6 | Pattern (purple). Candidates 2, 4, 6 | Given 3 | Pattern (purple). Candidates 1, 2, 6 | Pattern (purple). Candidates 1, 2, 6 | Given 5 |
| Pattern (purple). Candidates 2, 5, 6 | Pattern (purple). Candidates 2, 5, 6 | Given 1 | Given 4 | Pattern (purple). Candidates 2, 6 | Given 3 |
A chain of bi-value cells (each with exactly two candidates). Adjacent cells in the chain share one candidate. The two endpoints share a common candidate. Any cell that sees both endpoints can have that candidate eliminated.
| Pattern (purple). Candidates 1, 2 | Given 4 | Empty | Empty |
| Empty | Pattern (purple). Candidates 2, 3 | Given 1 | Pattern (purple). Candidates 3, 4 |
| Affected cell (orange). Candidates 2, 4. Eliminated 1 | Empty | Given 3 | Pattern (purple). Candidates 1, 4 |
| Given 3 | Empty | Empty | Given 2 |