X-Chain in sudoku

single-digit AIC · how it fits

Unfair · rating cost 260 · Chains and Loops · also called X-Chains

Four or more cells with candidate X in a chain whose links alternate between conjugate pairs (strong) and cells that see each other (weak), starting and ending strong.

Why it works

If one end is not X, the strong links force X and the weak links forbid it in turn, making the other end X. At least one end is therefore X, so X is removed from every cell outside the chain that sees both ends.

How to spot it

Filter the grid to one digit, mark its conjugate pairs, and join pairs end to end wherever two of their cells see each other.

Worked example

X-Chain example on a sudoku board. X-Chain on 1: r8c3 → r8c6 → r6c6 → r6c7 → r4c8 → r9c8; one end must be 1, so 1 is removed from cells seeing both ends. So 1 is removed from r9c3. — remove the chain on 1

X-Chain on 1: r8c3 → r8c6 → r6c6 → r6c7 → r4c8 → r9c8; one end must be 1, so 1 is removed from cells seeing both ends. So 1 is removed from r9c3.

Step 35 of this puzzle's solution, found and verified by the sudokUI engine. Cells are named by row and column: r2c3 is row 2, column 3. Play this puzzle from the start.

Practise it on a real puzzle. sudokUI generates a puzzle that needs X-Chain and takes you straight to the position where it applies. Hints draw the pattern on the board and explain the step.

Practice X-Chain Open in the app's guide

In a puzzle's rating

Each time the solver needs X-Chain, the puzzle's difficulty rating grows by 260. Its class is Unfair. It is needed in 1 in 260 puzzles that sudokUI generates. How the rating works.

More chains and loops

Remote Pair · Chute Remote Pair · X-Cycles (loops) · Grouped X-Cycles · XY-Chain · Twinned XY-Chains · Nice Loop · Grouped Nice Loop · Alternating Inference Chain · AIC with Groups · AIC with ALSs

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