Grouped AIC
An alternating inference chain that links through box/line groups.
An Alternating Inference Chain links candidates through alternating strong and weak inferences until its two endpoints prove at least one of them must be true. The grouped AIC sudoku technique extends this by letting a group node — two or three cells of a single digit that share both a box and a line — stand in for a single candidate as one link in the chain. That extra reach lets the chain make box-to-line jumps a single-cell AIC can never make, exposing eliminations that ordinary chains walk straight past.
Worked example
Working on digit 1, cells R1C1 and R3C1 share box 1 and column 1, so they act together as one group node. The chain opens at R5C6, whose strong link across row 5 (its only 1s) forces the 1 into R5C1; a weak link down column 1 reaches the group {R1C1, R3C1}; then box 1's strong link — its only 1s are that group plus R1C2 — jumps to R1C2. The endpoints are now R5C6 and R1C2, so at least one of them holds the 1. R1C6 sees R1C2 along row 1 and R5C6 down column 6, so it can never be the 1, and that candidate is eliminated.
When to use it
Reach for a grouped AIC when an ordinary single-cell chain almost lands but stalls on a box that holds three copies of the digit. Scan each box for a digit whose candidates line up two or three to a single row or column while sharing that line with the box — that aligned set is your group node. Treat it as one link and keep the chain going; the box-to-line strong link it supplies has no single-cell equivalent.
How to use it
- Allow group nodes. A group is the two or three cells of one digit that share a box and a line. The group is "on" when the digit lands in any of those cells, so it can stand in for a single node in a chain.
- Alternate strong and weak links. Chain strong links (a unit whose digit cells split exactly between two nodes) with weak links (two nodes that cannot both hold the digit), beginning and ending on a strong link.
- Eliminate what sees both ends. As with any AIC, at least one end is true, so a candidate that sees both ends — every cell of a group end included — is removed.
Frequently asked questions
What is a Grouped AIC in Sudoku?
A Grouped AIC is an Alternating Inference Chain that includes at least one group node — two or three cells of a single digit that share both a box and a line and behave as one link in the chain. The alternating strong/weak logic is identical to a plain AIC; the group node simply lets the chain reach links a single cell cannot. In the worked example, the group {R1C1, R3C1} on digit 1 is what carries the chain out of column 1 and into box 1.
How do I spot a group node on the grid?
Look inside one box for a digit whose remaining candidates all fall in the same row or the same column — usually two or three cells. Because they share a box and a line, that cluster acts as a single node: any link that would touch one of them touches the whole group at once. On this board, digit 1's R1C1 and R3C1 sit together in box 1 and column 1, forming exactly such a node.
How is a grouped AIC different from a plain AIC?
A plain AIC uses only single-cell nodes, so every strong and weak link runs from one candidate to one candidate. A grouped AIC adds multi-cell group nodes, which unlock box-to-line strong links no single cell can provide. That is what makes eliminating the 1 from R1C6 possible here — the strong link out of box 1 needs the whole {R1C1, R3C1} group, not any lone cell.