Elimination is the core principle behind every Sudoku technique. Remove impossible candidates from cells until the solution emerges through logic.
Elimination in Sudoku refers to the process of removing candidates (possible digits) from cells based on logical deductions. The basic form of elimination is straightforward: if a digit already appears in a cell's row, column, or box, that digit cannot be placed in that cell and is eliminated as a candidate.
This simple principle is the foundation upon which every Sudoku solving technique is built. From the most basic crosshatching to the most advanced chain-based methods, every technique ultimately works by proving that certain candidates are impossible and removing them. For a complete overview of strategies, visit our strategies guide.
At the most basic level, elimination works through the three Sudoku constraints. When you place a digit in a cell, that digit is immediately eliminated as a candidate from every other cell in the same row, column, and box. This cascade of eliminations often triggers further placements, creating a chain reaction.
For example, consider a row where eight of nine cells are filled. The remaining cell has only one possible candidate - the missing digit. This is elimination at its simplest. More complex scenarios involve naked pairs, where two cells in a house share exactly two candidates, allowing those candidates to be eliminated from all other cells in that house.
Beyond basic constraint-based elimination, advanced techniques use more complex logical reasoning to prove eliminations. The X-Wing pattern, for instance, uses the alignment of candidates across two rows and two columns to eliminate candidates from intersecting cells.
The key to mastering advanced elimination is understanding that every technique follows the same core logic: if you can prove a digit cannot go in a cell, you eliminate it. The techniques differ only in how they construct that proof. Simple techniques use direct observation; advanced techniques use chains of logical implications.
Explore more Sudoku concepts in the complete glossary.
Elimination is the process of removing impossible candidates from cells. By identifying digits that cannot go in a cell because they already exist in its row, column, or box, you narrow down the possibilities until each cell has only one valid option.
Elimination is the core mechanism behind solving, but they are not identical. Solving means determining the final digit for a cell. Elimination reduces the candidates for a cell but may not immediately solve it. However, all solving techniques ultimately work by eliminating candidates.
The most common elimination techniques are crosshatching, naked singles, hidden singles, naked pairs, pointing pairs, and box-line reduction. More advanced techniques include X-Wing, Swordfish, and XY-Wing, which eliminate candidates across multiple rows or columns simultaneously.
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