Sudoku techniques · Master
X-Chain in Sudoku
An X-Chain is a chain built on one number whose links alternate strong, weak, strong and so on, beginning and ending with a strong link. If either end were not the number, the alternation would force the other end to be, so at least one end holds it, and every cell seeing both ends loses the candidate.
Also known as: Turbot Fish (short cases).
Why it works
In an X-Chain, strong and weak links on a single number alternate, starting and ending with strong links, so at least one of the two chain ends must hold that number, and any cell that sees both ends loses it.
How to spot it
Skyscrapers and Two-String Kites are X-Chains of a fixed shape. This is the general version.
- Pick a number and list every unit where it has exactly two spots: those are your strong links.
- Join them end to end through cells that see each other; those joins are the weak links.
- The chain must have an odd number of links, so the count of cells is even: 4, 6, 8 or 10.
Builds on
Worked example
These are the app's own lesson boards. Step through them the same way a hint does.
- 1
These 6 cells all hold the candidate 7 and form a chain. The first link, the last link, and every second link between them are strong links: the two cells in each strong link are the only spots for 7 in one row, column, or box. If either end cell were not 7, the links would force the other end to be 7.
- 2
At least one of the two end cells must be 7, so we can remove the candidate 7 from any other cell that sees both ends.