Sudoku Techniques

Sudokuno teaches techniques inside complete puzzles rather than through isolated diagrams. You get a real Sudoku, and the hints reveal the structure in three steps before they will make the move for you.

Every puzzle is graded by the technique it genuinely requires. The Specialist levels go one step further: the puzzle is built so that exactly one advanced technique must be used exactly once.

Specialist

Specialist contains advanced, candidate-based techniques. Each page explains the logic, shows it on a real Sudokuno puzzle and gives you a puzzle to practise on.

Recommended learning order

S1-S10 is a learning progression, not a ranking of technique families. It is the order in which Sudokuno recommends meeting the ten Specialist techniques.

The progression weighs four things:

  • X-Wing S1

    An X-Wing appears when one candidate has exactly two possible cells in each of two different rows, and both pairs sit in the same two columns. The four cells form a rectangle. The candidate must then occupy two opposite corners, one per row, so it can be removed from every other cell in those two columns.

  • Y-Wing S2

    A Y-Wing is three cells that each have exactly two candidates. The pivot sees both wing cells. It shares one candidate with each wing, and the two wings have a third candidate in common. That third candidate has to land in one of the wings, so it can be removed from any cell that sees both of them.

  • Chute Remote Pairs S3

    A chute is three boxes in a line - either three side by side or three stacked. If you find two cells in the same chute holding exactly the same candidate pair, and they share no row, column or box, then the three bridge cells in the unused line settle the matter. If one of the pair candidates is missing from the bridge, the other can be removed from the cells that see both ends.

  • Unique Rectangles S4

    A proper Sudoku has exactly one solution. That is a fact about the puzzle you can reason from, and Unique Rectangles is the technique that does. Four unsolved cells lying in two rows, two columns and exactly two boxes, all four holding the same two candidates, would be a disaster: the two digits could be swapped corner to corner and the grid would still be valid, so the puzzle would have two solutions rather than one. That arrangement is called a deadly pattern, and it can never occur. Whatever candidate would complete it can be removed.

  • Swordfish S5

    A Swordfish is the same idea as an X-Wing with three lines instead of two. One candidate has only two or three possible cells in each of three rows, and together those cells touch exactly three columns. The candidate is then confined to those three columns and can be removed from every other cell in them.

  • XYZ-Wing S6

    An XYZ-Wing is a Y-Wing whose pivot has three candidates instead of two. The two wings have two candidates each, both drawn from the pivot's three, and they share exactly one candidate with each other. That shared candidate must occupy one of the three cells - the pivot included - so it can be removed from any cell seeing all three.

  • Simple Colouring S7

    Simple Colouring looks at one digit at a time. When a row, column or box has exactly two places left for that digit, the two cells are strongly linked: exactly one of them holds it. Join such pairs together and you get a network that can be coloured alternately in two colours, and then exactly one of the colours is the true one. That is enough to remove candidates, even though you do not know which colour is which.

  • W-Wing S8

    A W-Wing starts with two cells that have exactly two candidates each, and the same two: say 7 and 9. Somewhere else on the board, one of those digits - say 7 - has exactly two places left in a single row, column or box, and each of the two cells sees one of those two places. That is enough to prove that at least one of the two cells holds 9, so any cell that sees both of them cannot.

  • Rectangle Elimination S9

    Rectangle Elimination follows one candidate around four boxes. Start with a hinge H whose row or column has exactly one other place for the digit, S. A possible target T lies on the perpendicular line through H. If T held the digit, H would be off and the strong side would force S on. When T and S then see every remaining place for that digit in the diagonally opposite box, the box would have nowhere to put it. T therefore cannot hold the digit.

  • BUG+1 S10

    BUG stands for Bi-Value Universal Grave: a position where every unsolved cell has exactly two candidates left and every digit has exactly two places left in every row, column and box. A position like that always has an even number of solutions, never one, so a proper Sudoku can never reach it. BUG+1 is that position with one exception - a single cell holding three candidates. One of those three is the only thing standing between the puzzle and the grave, and it can be placed straight away.

  • how easy the idea is to understand
  • how easy the pattern is to recognise on a fully pencilled board
  • how difficult the technique is to apply correctly
  • how naturally it builds on concepts introduced earlier

Families and learning order answer different questions. You do not need to finish one family before moving to the next step.

Technique families

A family groups techniques by the kind of logic they use. The boundaries are useful, but not absolute: some techniques draw on more than one family.

Fish

Fish confine one candidate across matching rows and columns.

Swordfish is the natural larger extension of X-Wing. Its core idea is not necessarily much harder, but finding a three-row or three-column fish on a full candidate grid is substantially more demanding. That is why it appears at S5 rather than directly after X-Wing.

Wings

Wing techniques combine small candidate sets so that different possibilities lead to the same elimination.

W-Wing overlaps Wings and Chains. It is filed under Wings because the pattern is most naturally introduced through its matching bivalue wing cells. The strong link connecting them is chain logic, so both viewpoints matter.

Chains

A link is one logical relationship between candidates; a chain is a sequence or network of links. Simple Colouring is the clearest example: alternating strong links form one connected network whose consequences can be followed.

Rectangle Elimination belongs here because its proof follows links and implications between candidates. The word ‘Rectangle’ in its name describes part of the geometry, not the family of its reasoning.

Uniqueness

Uniqueness techniques use the requirement that a well-formed Sudoku has exactly one solution.

Unique Rectangles is S4 because its deadly-pattern idea is local and fairly concrete. BUG+1 is S10: once seen, the move can be simple, but the explanation is more abstract. You must understand the board's global bivalue structure and why the extra candidate prevents a non-unique Bivalue Universal Grave.

The Foundations

These techniques underpin every puzzle in Sudokuno, and they keep appearing inside the Specialist puzzles too. They do not have pages of their own yet.

R1 - Naked single
A cell has only one value left.
R2 - Hidden single
A digit has only one possible cell in a row, column or box.
A1 - Naked pair
Two cells in a house share exactly the same two candidates.
A2 - Hidden pair
Two digits are locked into the same two cells.
A3 - Point & reduction
The link between a box and a line clears candidates from the other.
E1 - Naked triple
Three cells share three candidates between them.
E2 - Point & reduction
The same idea as A3, applied to triples.
E3 - Hidden triple
Three digits are locked into the same three cells.