Sudoku Solving Techniques
Every Sudoku is solvable by logic alone; the difference between an easy grid and a brutal one is which techniques you need to get there. These are the techniques in the order you will meet them.
Solving techniques, easiest first
Naked single
A cell has exactly one candidate left, because the other eight digits already appear in its row, column, or box. Fill it in. Easy puzzles can be finished with nothing else.
Full guide: Naked single
Hidden single
A digit has only one cell it can go in within a row, column, or box — even though that cell still looks like it has several options. Scan a unit one digit at a time and ask where that digit could possibly live.
Full guide: Hidden single
Naked pair and hidden pair
Two cells in the same unit share exactly the same two candidates, so those two digits are locked to those cells and can be removed everywhere else in the unit. A hidden pair is the mirror image: two digits that can only go in the same two cells, which lets you strip every other candidate from them.
Full guide: Naked pair · Hidden pair
Pointing pair and box/line reduction
These connect a box to a line. If a digit inside a box is confined to one row or column, it can be eliminated from the rest of that row or column outside the box (pointing pair). If a digit in a row or column only appears inside one box, it can be eliminated from the rest of that box (box/line reduction).
Full guide: Pointing pair · Box/line reduction
Naked triple and hidden triple
The same idea as pairs, extended to three cells and three digits. The three cells do not each need all three candidates — between them they must use exactly those three.
Full guide: Naked triple · Hidden triple
X-Wing
The first technique that spans the whole grid. When a digit is limited to the same two columns in two different rows, it forms a rectangle; that digit can then be eliminated from those two columns everywhere else. Hard puzzles start to require this.
Full guide: X-Wing
Swordfish and XY-Wing
Swordfish is an X-Wing across three rows and three columns instead of two. XY-Wing uses a pivot cell with two candidates linked to two others, so that whichever value the pivot takes, one specific digit is eliminated from the cells both wings see.
Chains
Follow a sequence of strongly linked candidates through the grid — if this cell is a 5, that one is not, so the next one must be. Any cell that gives the same answer along both branches can be resolved. Tiers 8 and 9 are defined in the solver but never applied by it, so nothing here is graded on them.
Full guide: Chains and forcing chains
Forcing chains
The deepest technique in ordinary Sudoku. Take a cell with two candidates, follow the consequences of each assumption, and look for a conclusion both paths share — that conclusion is true regardless of which assumption is correct. Useful on the lowest clue counts, though the generator here never requires it.
Full guide: Chains and forcing chains
Every technique, one page each
Each technique below has its own page with a worked example, how to spot the pattern, and exactly what it lets you eliminate.
- Naked Single Sudoku Technique — The first technique anyone learns and the one that finishes most of every grid. A cell has one candidate left, so that candidate is the answer.
- Hidden Single Sudoku Technique — The most useful technique in Sudoku, and the one most beginners never learn. Instead of asking what a cell can be, ask where a digit can go.
- Naked Pair Sudoku Technique — The first technique that eliminates candidates instead of placing digits — and the gateway to everything above it.
- Hidden Pair Sudoku Technique — The mirror image of a naked pair, and much easier to miss: the two cells can be carrying four or five candidates each and still be locked.
- Pointing Pair Sudoku Technique — The first technique that reasons across two different units at once: what a box knows, it tells the row.
- Box/Line Reduction Sudoku Technique — A pointing pair run backwards: what the row knows, it tells the box.
- Naked Triple Sudoku Technique — The same logic as a naked pair, one size up — and much easier to miss, because the three cells rarely look alike.
- Hidden Triple Sudoku Technique — Among the hardest patterns to see by eye, because the three cells can be carrying five or six candidates and look nothing like a set.
- X-Wing Sudoku Technique — The step where Sudoku stops being local. Everything before this works inside one unit; the X-Wing needs four cells in four different ones.
- Swordfish Sudoku Technique — An X-Wing across three lines instead of two, with one wrinkle that makes it far harder to see.
- XY-Wing Sudoku Technique — The first technique built on hypothetical reasoning: you do not learn what the pivot is, only that either way, one digit dies.
- Forcing Chains Sudoku Technique — The deepest reasoning in ordinary Sudoku, and the point at which the puzzle stops rewarding pattern recognition and starts rewarding bookkeeping.
What each difficulty actually changes
Difficulty here is set by how many clues are left in the grid — Easy starts from 46, Medium 40, Hard 34, with Extreme and Insane stripped further still. Fewer clues is what makes the deeper techniques necessary in practice: the tiers below are the reasoning each level is designed to demand, not a guarantee enforced on every grid.
- Easy — naked and hidden singles only.
- Medium — adds pairs, pointing pairs, and box/line reduction.
- Hard — adds triples and X-Wings.
- Extreme — adds Swordfish and XY-Wing.
- Insane — adds chains and forcing chains.