My Sudoku

Extreme Used in extreme puzzles.

Grouped Chain (AIC)

Chains through groups

A group is a digit's places where a box and a row (or a column) cross, two or three of them, taken as one: it is true when one of them holds the digit, false when none does.

Groups link as single places do. When a digit's places in a unit split into two groups, or a group and a cell, one of the two holds it: a strong link. A group and a place of the same digit that sees all its cells cannot both hold it: a weak link.

A grouped AIC is an AIC, as in the chapter before, with groups among its nodes. One of its two ends is true, so a candidate that cannot stand with either goes: with the same digit at both ends, it goes from every cell that sees all the cells of both.

What to look for

Find a box where a digit's places line up: as a group, they link to the digit's other places along that line, as one place would.

Example

61793814751421243124762475198498512412491246731396147134147825181234123513898967785121262694319341781247124626737955617914731824892348514737146 112233445566778899
Grouped AIC: if R3C4 is not 1, then one of R1C6, R3C6 is 1 (box 2), so R9C6 is not 1 (column 6), so R9C8 is 1 (row 9), so R9C8 is not 4 (same cell), so R1C8 is 4 (column 8), so R2C9 is not 4 (box 3), so R2C9 is 9 (the cell's other candidate), so R6C9 is not 9 (column 9), so R6C9 is 1 (the cell's other candidate). Either R3C4 or R6C9 is 1: remove 1 from R6C4.
  • The cells the technique relies on
  • Cells where it removes candidates, struck out in red
  • Strong link (solid line) and weak link (dashed)

Practise it

In the app, Learn › Grouped Chain (AIC) sets exercises on real positions, then a full puzzle that needs this technique and nothing harder.

Practise in your browser