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.
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.
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.
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).
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.
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.
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.
Forcing chains
The deepest technique used here. 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. Only Insane puzzles need this.
Which techniques each difficulty needs
Betty Bee Sudoku generates every puzzle by checking which techniques are required to solve it, so a difficulty label describes the reasoning involved rather than simply how many digits were removed.
- 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.