Hard sudoku techniques
Our sudoku books start where most puzzle books stop. Every puzzle needs the advanced and expert moves below, usually several of them, and each one is explained the moment it is used in the walkthrough. Here is the whole ladder, with a one-sentence explanation and real puzzles to see it in.
Classic 9 × 9 sudoku, solved by logic alone: every puzzle in the books has exactly one solution and never needs a guess. At most one forcing chain per puzzle, and most puzzles need none.
Expert
Long chains, almost-locked sets, colouring and (at most one per puzzle) a forcing chain. The steps that make the books extreme.
- Jellyfish
- An X-Wing with four rows and four columns. Used in 8 of our sudoku walkthroughs.
- Finned Fish
- An X-Wing or Swordfish with one extra candidate (the fin). Cells that are in the fish pattern and also see the fin lose the digit. Used in 394 of our sudoku walkthroughs, the key move in 9.
- XY-Chain
- A chain of two-candidate cells, each linked to the next. Whichever way the start cell goes, one end of the chain holds the digit, so cells seeing both ends cannot. Used in 439 of our sudoku walkthroughs, the key move in 83.
- WXYZ-Wing
- Four cells holding four digits between them, where only one digit is not confined. That digit is removed from cells that see all its copies. Used in 376 of our sudoku walkthroughs, the key move in 5.
- Sue de Coq
- Cells where a box meets a row or column hold a set of digits that must split between the box and the line. That rules digits out of both. Used in 174 of our sudoku walkthroughs.
- Coloring/Multi-coloring
- Following one digit’s strong links, cells get two colours: one colour is true and the other is false. A cell that sees both colours cannot hold the digit. Used in 37 of our sudoku walkthroughs.
- ALS-XZ
- Two almost-locked sets (n cells with n+1 candidates) share a restricted digit X. Then a digit Z common to both must be in one of them, so cells seeing all of its copies cannot be Z. Used in 450 of our sudoku walkthroughs, the key move in 169.
- Nice Loops/AICs
- An alternating chain of strong and weak links. Whichever end is true, the conclusion holds, so the digit at the marked cell is ruled out. Used in 443 of our sudoku walkthroughs, the key move in 184.
- Cell Forcing Chains
- Try each candidate of one cell in turn. Every choice leads to the same result, so that result must be true. Used in 337 of our sudoku walkthroughs.
Advanced
Fish, wings and short chains. In an Extreme book these come up many times in a single puzzle.
- X-Wing/Swordfish
- A digit fits in only two (or three) places in each of two (or three) rows, and those places line up in the same columns (or the other way round). The digit can be removed from the rest of those columns. Used in 180 of our sudoku walkthroughs.
- Skyscraper
- Two rows each have a digit in exactly two places, with one end lined up. One of the two free ends must hold the digit, so any cell that sees both free ends cannot. Used in 152 of our sudoku walkthroughs.
- 2-String Kite
- A row and a column each have a digit in exactly two places, linked through one box. One of the two far ends holds the digit, so a cell seeing both ends cannot. Used in 290 of our sudoku walkthroughs.
- Empty Rectangle
- In one box a digit is confined to an L or cross shape. Combined with a strong link outside the box, it rules the digit out of one cell. Used in 199 of our sudoku walkthroughs.
- XY-Wing
- Three two-candidate cells: a pivot {X,Y} sees two wings {X,Z} and {Y,Z}. Whichever digit the pivot takes, one wing becomes Z, so any cell seeing both wings cannot be Z. Used in 236 of our sudoku walkthroughs.
- XYZ-Wing
- Like an XY-Wing, but the pivot holds all three digits {X,Y,Z}. A cell that sees the pivot and both wings cannot be Z. Used in 137 of our sudoku walkthroughs.
- W-Wing
- Two cells with the same pair {X,Y} are joined by a strong link on X. One of them must be Y, so cells seeing both cannot be Y. Used in 247 of our sudoku walkthroughs.
- Unique Rectangles
- Four cells in two rows, two columns and two boxes cannot all share the same pair, or the puzzle would have two solutions. That rules out a candidate. Used in 12 of our sudoku walkthroughs.
- BUG+1
- Every unsolved cell but one has exactly two candidates. The odd cell must take the digit that would otherwise leave the grid with two solutions. Used in 3 of our sudoku walkthroughs.
Intermediate
Pairs, triples and box-line interactions. Routine in our books; they clear the ground for the hard steps.
- Naked Pairs/Triples
- Two (or three) cells in one row, column or box share the same two (or three) candidates between them. Those digits must go in those cells, so they can be removed from the rest of that row, column or box. Used in 428 of our sudoku walkthroughs.
- Hidden Pairs/Triples
- Two (or three) digits can only go in the same two (or three) cells of a row, column or box. Those cells can hold nothing else. Used in 158 of our sudoku walkthroughs.
- Naked/Hidden Quads
- The same idea as pairs and triples, with four cells and four digits. Used in 2 of our sudoku walkthroughs.
- Pointing Pairs/Triples
- Inside a box, a digit is confined to one row or column. It must go in that box, so it can be removed from the rest of that row or column. Used in 445 of our sudoku walkthroughs.
- Box-Line Reduction
- Inside a row or column, a digit is confined to one box. It must go in that line, so it can be removed from the rest of the box. Used in 311 of our sudoku walkthroughs.
Basic
The moves every solver makes without thinking. Our books assume them.
- Naked Singles
- A cell with only one possible digit left must take it. Used in 450 of our sudoku walkthroughs.
- Hidden Singles
- When a digit fits in only one cell of a row, column or box, it goes there. Used in 450 of our sudoku walkthroughs.
The books
Step-by-step solutions: Extreme Sudoku 1 · Extreme Sudoku 2 · Extreme Sudoku 3.