A Grouped AIC is an Alternating Inference Chain in which at least one node represents a group of candidates rather than a single candidate in one cell.
The logic does not change: Strong and Weak inferences still alternate. What changes is the size of a node.
Instead of saying:
candidate 7 in r3c4
one node might mean:
candidate 7 is somewhere in r3c4/r3c5 inside this row-box intersection.
That grouped statement can participate in a Strong Link just like an individual candidate when the Sudoku constraints justify it.
Why group nodes exist
Suppose a row has digit 7 candidates in two regions:
- one individual cell outside a box;
- several cells clustered inside the row's intersection with that box.
If the individual 7 is false, at least one of the grouped 7s must be true.
That is a Strong inference between:
- one candidate node;
- one group node.
The group does not claim which cell contains 7. It claims that the group as a whole contains 7.
The most common group: a box-line intersection
Group nodes frequently appear where a digit's candidates are restricted to a row/box or column/box intersection.
A group can contain two or three candidate cells in that intersection.
For chain purposes, treat the statement “X is somewhere in this group” as one Boolean node when the rest of the house provides the corresponding Strong relationship.
This is closely related to the logic behind Locked Candidates.
Strong and Weak Links with a group
A Strong group link means:
if the candidate is not true in node A, it must be true somewhere in group B.
A Weak group link means:
if the candidate is true in node/group A, it cannot be true in node/group B.
For Weak Links, every member involved must obey the relevant visibility constraint. You cannot treat two partially overlapping groups as weakly linked merely because one pair of cells sees each other.
Grouped AIC follows ordinary AIC rules
Once the nodes are valid, the chain is read exactly like a normal AIC:
- Strong;
- Weak;
- Strong;
- Weak;
- ...
The usual endpoint deductions still apply.
If an AIC starts and ends with Strong inference for the same digit, the digit must be true at one end or the other. Targets seeing all candidates represented by both endpoints can be eliminated.
If the endpoints involve different digits in seeing structures, Type 2-style endpoint eliminations may apply.
Worked Grouped AIC
Grouped AIC vs ordinary AIC
Ordinary AIC uses individual candidate nodes.
Grouped AIC adds nodes such as:
- two candidates in a row-box intersection;
- three candidates in a column-box intersection;
- other valid same-digit groups supported by house logic.
The group can shorten a chain dramatically because several equivalent candidate locations no longer need separate branches.
Grouped AIC vs Locked Candidates
Locked Candidates is a local intersection technique.
Grouped AIC can use the same intersection restriction as one link inside a longer chain.
So the grouped node does not replace Pointing or Claiming; it generalizes the restricted-position information into chain language.
Grouped AIC and ALS nodes
Expert chain systems can go further and use Almost Locked Sets as nodes. HoDoKu groups that discussion with grouped Nice Loops/AICs because an ALS can provide a Strong relationship between its candidate states.
For VeyraPlay, keep the learning sequence clean:
- ordinary AIC;
- Grouped AIC with simple group nodes;
- ALS and ALS-XZ;
- only later, chains that use ALS nodes directly.
Why group nodes are powerful
Real expert puzzles often contain useful inference that is almost visible as an AIC but appears to “break” because a Strong Link ends in two or three cells instead of one.
Grouping preserves the true logical statement:
one of these candidates must be true.
That lets the chain continue without guessing which one.
Common mistakes
Treating arbitrary candidates as a group
A group needs one coherent Boolean meaning, usually “digit X is in one of these cells.”
Forgetting all members in target visibility
A target that sees only one member does not necessarily see the group state.
Mixing a group with a net
A group is one node representing alternatives. A net branches through independent consequences and later reconverges. Those are different structures.
Assuming group links are automatically Strong
The underlying house restriction must prove the Strong inference.
Hiding an invalid link inside notation
Always expand the group and test the inference in ordinary Sudoku terms.
FAQ
What is a group node in Sudoku?
It is a set of candidate occurrences treated as one logical statement, such as “digit 5 is somewhere in these two cells of a box-line intersection.”
Is Grouped AIC harder than AIC?
Usually. The alternation rules are unchanged, but validating a group requires reasoning about all member candidates.
Is Grouped AIC the same as a Forcing Net?
No. A grouped node compresses alternatives into one valid node. A net involves branching consequence paths whose logic cannot be represented as a simple linear chain.
Can ALS be used as AIC nodes?
Yes in more advanced chain systems, but learn ordinary candidate groups and ALS separately first.
What to learn next
Almost Locked Sets are the natural next step. They explain how multi-cell candidate structures can act like Strong inference nodes and lead directly to ALS-XZ.