Advanced Sudoku Techniques

Advanced Sudoku does not require arithmetic. It requires candidate relationships that span more than one cell. Before using these techniques, record candidates accurately and exhaust all naked and hidden singles. Complex patterns are reliable only when the candidate list is current.

Locked candidates

If every possible position for a digit inside one 3×3 box lies on the same row, that digit cannot appear elsewhere on that row outside the box. The same rule applies to a column. This is often called pointing. The reverse pattern, sometimes called claiming, occurs when all candidates for a digit in a row lie inside one box, allowing that digit to be removed from other cells in the box.

Naked pairs

When two cells in the same row, column, or box contain the same two candidates, those digits must occupy those two cells in some order. Remove both digits from every other cell in that region. A naked pair is useful even though you do not yet know which cell receives which value.

Hidden pairs

If two digits appear as candidates in exactly the same two cells of a region, those cells are reserved for the pair. Other candidates can be removed from those two cells. Hidden pairs are harder to see because the cells may initially contain three or four notes, so search by digit rather than by cell.

X-Wing

Suppose a candidate appears in exactly two positions in one row and exactly the same two columns in another row. The four positions form the corners of a rectangle. The digit must occupy opposite corners, so it can be removed from every other cell in those two columns. The pattern also works with rows and columns reversed.

Swordfish

Swordfish extends the X-Wing idea across three rows and three columns. If a candidate in three rows is confined to the same three columns, that candidate can be removed from other cells in those columns. Confirm the pattern carefully: each participating row must contain two or three candidates, and their combined columns must total exactly three.

Candidate chains

A strong link exists when a digit has only two possible positions in a region: if one is false, the other must be true. Connecting strong links can reveal that a candidate at the end of a chain must be removed or placed. Chains are powerful but easy to misread, so use them only after simpler eliminations stop producing progress.

How to work without losing the thread

1. Choose one candidate digit.
2. Mark regions where it has only two positions.
3. Look for pairs, locked candidates, or aligned rows and columns.
4. Make only eliminations justified by the pattern.
5. Rescan for singles after every elimination.

Difficulty note: a low clue count does not alone determine difficulty. The order and interaction of deductions matter more than the number of given digits.