A Candidate Elimination Checklist for Stuck Sudoku Players

Eliminations from Placed Digits

The first and most fundamental checks involve removing candidates based on digits already placed on the grid. Every time you place a number, its influence extends across its entire row, column, and 3x3 box. This candidate elimination is the core rule of Sudoku, but it must be applied constantly and thoroughly. A common oversight is failing to scan all three units (row, column, box) for a newly placed digit, leaving stray candidates that block later logic. Always perform a full 'cross-hatch' scan after every placement. This step alone can reveal immediate placements, known as Naked Singles. For example, after several basic placements in a typical puzzle, a cell might be left with only one possible candidate because all others are eliminated by digits in its row, column, and box. Systematically clearing these basic eliminations is the essential foundation for all advanced solving.

• Check each placed digit: Eliminate that digit from all other cells in its row, column, and 3x3 box.
• Scan for Naked Singles: After basic eliminations, look for any cell with only one remaining candidate digit and place it.

Eliminations from a Single Box (Intersections)

Once basic eliminations are done, focus on interactions between boxes and rows or columns. These 'intersection' or 'locking' techniques are powerful intermediate steps. The first is the Pointing Pair/Triple. Look for a candidate digit that appears only in one row or column within a single 3x3 box. Because that digit must be placed within that line inside the box, you can eliminate it from the rest of that row or column outside the box. This is a crucial technique for removing candidates that are not immediately obvious. For instance, if the candidate for digit '5' in Box 5 appears only in cells that are all in row 4, then '5' cannot be elsewhere in row 4, even in Boxes 4 or 6. The converse technique is the Claiming Pair/Triple. Look for a candidate digit that is confined to one box within a row or column. Because the digit must go in that box, you can eliminate it from all other cells within that same box. Mastering these box-line interactions clears the way for more complex patterns to emerge.

• Look for Pointing Pairs/Triples: If a candidate is confined to one row/column within a box, eliminate it from the rest of that row/column.
• Look for Claiming Pairs/Triples: If a candidate is confined to one box within a row/column, eliminate it from the rest of that box.

Eliminations from a Line (Row or Column)

Now, examine individual rows and columns for patterns among remaining candidates. The most common are subsets like pairs and triples. A Naked Pair occurs when two cells in the same unit (row, column, or box) contain only the same two candidate digits. Since those two digits must occupy those two cells, you can eliminate them as candidates from all other cells in that unit. Finding a Naked Pair often creates a cascade of new eliminations. A Hidden Pair is slightly trickier. It occurs when two digits appear as candidates only in the same two cells within a unit, even if those cells have other candidates. This pattern reveals that those two cells must contain those two digits, so you can remove all other candidates from those two cells. Spotting a hidden pairs pattern requires checking the frequency of each candidate in a unit. These line-based eliminations simplify the candidate landscape significantly, making more advanced patterns visible.

• Look for Naked Pairs/Triples: Two or three cells in a unit sharing the same two or three candidates let you eliminate those candidates from the unit's other cells.
• Look for Hidden Pairs/Triples: Two or three candidates that appear only in the same two or three cells of a unit let you remove all other candidates from those cells.

Eliminations from Named Advanced Patterns

If the puzzle remains unsolved after the previous checks, it's time to search for advanced, multi-unit patterns. These patterns create elimination links that span across the grid. The X-Wing pattern looks for a candidate digit that is confined to two rows and two columns, forming a rectangle. If the candidate appears only twice in each of those two rows (and aligns in columns), you can eliminate that candidate from all other cells in the two involved columns. The Swordfish is a three-row, three-column extension of this idea. The Y-Wing (or XY-Wing) is a chain involving three cells with specific candidate relationships, allowing you to eliminate a candidate from a cell that sees both ends of the chain. These patterns are less common but are the final logical step before considering bifurcation or guessing. Successfully applying them requires a clear, clean candidate grid from all the prior elimination steps.

• Look for an X-Wing: A candidate forms a rectangle across two rows and two columns, letting you eliminate it from the rest of those columns.
• Look for a Swordfish: A candidate forms a pattern across three rows and three columns, letting you eliminate it from the rest of those columns.
• Look for a Y-Wing (XY-Wing): Three cells with a specific candidate relationship let you eliminate a candidate from cells that see both 'pincer' cells.

How to Apply This Checklist

This checklist is meant to be used iteratively. Start with the first category (Eliminations from Placed Digits) and apply it completely. This may reveal new Naked Singles; place them and immediately re-apply the first category. Only when no more progress is possible should you move to the next category. Work through each section in order: Single Box eliminations, then Line eliminations, then Named Patterns. After finding and applying an elimination from a later category, always loop back to the beginning. A new placement from an X-Wing, for example, triggers a new round of basic eliminations. This cyclical process is the essence of logical Sudoku solving. Sticking to this order prevents you from overlooking simpler techniques while searching for complex ones. It transforms a chaotic stare at the grid into a manageable, step-by-step procedure that reliably yields results.