A complete logic toolkit — from beginner singles to advanced X-Wing techniques
A 9×9 Sudoku grid must be filled with digits 1–9 so that:
These three constraints overlap and interact — that interaction is what makes Sudoku solvable by logic without any guessing. Every valid Sudoku has a unique solution.
Before solving complex puzzles, pencil in candidates — the digits that could legally go in each empty cell based on its row, column, and box. A cell where 1, 2, 5, 8 do not appear in its row, column, or box has candidates {3,4,6,7,9}. Write them small in the cell. Eliminating candidates is how all advanced techniques work.
A Naked Single (also called a "sole candidate") occurs when a cell has only one candidate remaining. All other digits from 1–9 already appear in the cell's row, column, or box. Place that digit immediately.
Naked Singles often cascade: placing one digit reveals another Naked Single, which reveals another. On Beginner puzzles, Naked Singles alone are sufficient to solve the entire board if you scan diligently.
A Hidden Single occurs when a digit appears as a candidate in only one cell within a row, column, or box — even though that cell has other candidates too. Since the digit must appear exactly once in that row/column/box, it must go in the only cell where it's a candidate.
Scan for Hidden Singles in all three unit types: rows, columns, and boxes. A digit hidden from easy view in one row may jump out immediately when you scan the box containing it.
A Naked Pair occurs when exactly two cells in the same row, column, or box both have exactly the same two candidates — and only those two. Since one cell will contain one digit and the other will contain the other, you can eliminate both candidates from all other cells in that shared row/column/box.
Naked Pairs are the most common intermediate technique and appear in virtually every puzzle rated Medium or harder. Always check for pairs when Naked Singles and Hidden Singles run dry.
Extension of Naked Pairs: three cells in the same unit share exactly three candidates between them (the three candidates don't all have to appear in every cell — just no cell has a 4th candidate outside those three). Eliminate those three digits from all other cells in the unit.
Two digits appear as candidates in exactly two cells of a unit, but those cells also have other candidates. Since the two digits must fill those two cells, you can eliminate all other candidates from those two cells. Effectively turns them into a Naked Pair.
If a candidate in a 3×3 box appears only in one row or column of that box, then that candidate can be eliminated from the rest of that row or column outside the box. The candidate must go somewhere in the box, and it can only go in that row/column — so it cannot appear outside the box in that row/column.
An X-Wing occurs when a candidate appears in exactly two rows, and in those two rows it only appears in exactly the same two columns. The candidate must occupy two of the four cells at the corners of an imaginary rectangle. You can therefore eliminate that candidate from all other cells in those two columns.
X-Wings unlock expert-level puzzles that resist all simpler techniques. They require full candidate notation to spot reliably.
The game offers 3 hint tokens per puzzle. Use them wisely:
1. Fill all Naked Singles. 2. Fill all Hidden Singles. 3. Mark candidates if needed. 4. Look for Naked/Hidden Pairs. 5. Try Box-Line Reduction. 6. Try X-Wings. Repeat from step 1 after each discovery. Most Medium puzzles need only steps 1–4; Hard puzzles may need steps 5–6.
Apply these techniques on a live puzzle!
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