Solving techniques
Every technique here is one the hints of My Sudoku use. Each comes with the explanation of the app's lessons, what to look for, and a real example on a board: the cells it relies on in green, the candidates it removes struck out in red. They come simplest first: the easiest puzzles need only the first few, the hardest the chains at the end.
The rules
A Sudoku is a 9 × 9 grid divided into nine 3 × 3 boxes. Some cells are filled in from the start: the clues.
Fill every empty cell with a digit from 1 to 9 so that each row, each column and each box holds every digit exactly once. A digit can never appear twice in the same row, column or box.
A proper puzzle has exactly one solution, and it can be reached by reasoning alone: no guessing is needed.
The small digits in an empty cell are its candidates: the digits it can still hold. Each technique in the chapters ahead is a way to rule candidates out, until every cell has one left.
- The cells the text is about
How to go about a puzzle
- Start with the digits, not the cells: take each digit in turn and look, in every box, row and column, for the one place it can go (Hidden Single). Units with a single gap fill themselves (Full House).
- When that runs dry, write the candidates: in each empty cell, the digits its row, column and box still allow. A cell with one left is a Naked Single.
- Then look for digits locked together: a digit confined to one line inside a box (Locked Candidates: Pointing), two cells sharing the same two candidates (Naked Pair), and their larger cousins. They place nothing, but remove candidates, until a single appears.
- Each time a digit is placed, take it out of its row, column and box, and look again for singles around it: that is where the next one usually is.
- Only when nothing simpler works, turn to patterns across the grid: the X-Wing and the other fish for one digit, the XY-Wing for cells with two candidates, and last of all the chains.
- Never guess: a proper puzzle can always be solved by reasoning. If you are stuck, a hint of the app shows you where to look first, then the technique, then the whole step.
The techniques, level by level
Very easy
Very easy puzzles need only the singles that fill a unit's last cell or a digit's last place, without writing a single candidate.
Easy
Easy puzzles add the Naked Single: a cell with one candidate left.
Medium
Medium puzzles need candidates removed before a digit appears: locked candidates, pairs and triples.
Hard
Hard puzzles bring the patterns: quads, fish, wings, coloring, and the uniqueness of the solution.
- Naked QuadFour cells, four candidates
- Hidden QuadFour digits, four cells
- X-WingTwo rows, two columns
- SwordfishAn X-Wing over three lines
- JellyfishAn X-Wing over four lines
- XY-WingA pivot and two wings
- XYZ-WingA three-candidate pivot
- Simple ColoringChains of strong links
- Unique RectangleAvoiding a second solution
- SkyscraperTwo strong links on one base
- Finned X-WingAn X-Wing with a fin
- BUG+1One cell away from two solutions
Extreme
Extreme puzzles call for chains, followed link by link across the grid, and almost locked sets.
A few words used here
- Cell names
- R1C1 is the cell in row 1, column 1, top left; R9C9, bottom right. Boxes are numbered 1 to 9, left to right and top to bottom.
- Unit
- A row, a column or a box: nine cells that must hold every digit once.
- Candidates
- The digits an empty cell can still hold. Every technique ends by placing a digit or removing candidates.
- Seeing
- Two cells see each other when they share a row, a column or a box: they cannot hold the same digit.
- Strong link
- Two candidates of which at least one is true: if one is false, the other is true. A digit with only two places in a unit makes one; so does a cell with only two candidates.
- Weak link
- Two candidates that cannot both be true: if one is true, the other is false. The same digit in two cells that see each other, or two digits of one cell.