GridWits
Extreme tier Technique 27 of 46 Used by Smart Hint

Grouped X-Cycles

X-Cycles generalized so a "node" can be a group of cells confined to one row-and-box or column-and-box intersection, not just a single cell.

How it works

  1. 1Row 1 has three 6s left — A1, B1 and G1 — so it is no ordinary conjugate pair. A1 and B1 both sit in the top-left box, so treat them as one group node: row 1's 6 is either somewhere in that group or at G1.
  2. 2Carry on with ordinary strong links: column G has only G1 and G5 left for 6, and row 5 has only G5 and A5. Alternating from the group gives teal, red, teal, red.
  3. 3If the group holds the 6, A2 can't — it sees both A1 and B1 through the box, which is what a group node demands.
  4. 4If G1 holds it instead, G5 is out, A5 takes row 5's 6, and A2 loses it down column A. Either colour rules 6 out at A2.

Play a Sudoku that needs this technique →

A 1 B 2 C 3 D 4 E 5 F 6 G 7 H 8 I 9 1 6 4 6 3 6 6 8 2 6 6 7 6 6 6 6 6 6
  • First colour in the chain
  • Second colour in the chain
  • Where the conclusion lands
  • Candidate ruled out
Next in the ladder Alternating Inference Chains (AIC) →

The most general chaining technique: follow a chain of candidates that alternates "at least one of these is true" with "at most one of these is true", hopping between digits as it goes. Whichever way it resolves, one of the two chain ends must be true.