A grouped AIC is an alternating inference chain where one node can be a cell group: two or three cells in one box, along one row or column, that share a candidate. The group acts as one candidate, so a house with three places for a digit can still give a strong link. When both ends carry the same digit, a cell that sees both ends loses it.
How to spot it
Start as for any AIC: the cells with two candidates and the houses with two places for a digit give the strong links.
Then look for the houses with three places for a digit, where two of the three sit in the same box and share a row or column. Those two cells can act as one node. The house then splits into the lone cell and the group, which is a strong link a plain AIC can't use.
Build the chain as before, alternating strong and weak links. When a strong link lands on the starting digit somewhere else, that is the second end. Strike the digit from every cell that sees both ends.
Assume the first end is not the 7
Row six, column eight has only a 2 and a 7. If it is not the 7, it is the 2. The solid line inside the cell stands for that.
Follow the 2 along row six
Row six, column three shares row six with that cell, so it is not the 2. The link is weak, since row six has a third 2 at column nine.
Land on the group in column three
Column three has three places for a 2. Row six, column three is one. The other two, rows seven and nine, both sit in box seven. Take them as one node. With row six ruled out, the 2 is in that group, and the chain doesn't need to know which cell.
Leave the group through box seven
Row nine, column two sees both cells of the group. It shares box seven with each and row nine with one of them. Wherever the group's 2 is, this cell can't be a 2. It has only a 2 and a 7, so it is the 7.
Close on a 7 in column six
Row nine, column six shares row nine with that cell, so it is not the 7. Column six has only two places for a 7, and the other is row seven, column six. So that cell is the 7. Put together, if row six, column eight is not the 7, row seven, column six is.
Remove the 7 from row seven, column eight
Row seven, column eight shares column eight with the first end and row seven with the second. Whichever end turns out to be the 7, this cell shares a house with it, so its 7 goes.
Why one end holds the 7
Run the chain from the far end. If row seven, column six is not the 7, column six puts it at row nine. Row nine then takes the 7 away from row nine, column two, so that cell is the 2. That cell sees both cells of the group, so neither of them is the 2. Column three has only one place left, row six, column three, which takes the 2 out of row six, column eight. That cell is then the 7. From either end, if that end is not the 7, the other one is.
The solution puts a 7 at both ends. The chain alone guarantees one. Neither cell of the group is the 2: the group only had to hold it if the first end was not the 7.
The two-ends rule
The ends follow the plain AIC rule: one digit at both, and a strong link into each. A cell you strike must see every cell of both ends. Row six, column nine has a 7 and shares row six with the first end, but nothing with the far end, so its 7 stays.
How group nodes work in an AIC
A group is two or three cells that hold the same candidate, sit in one box, and share one row or one column. It stands for "the digit is in one of these cells", without saying which.
A strong link to a group needs a house whose places for the digit split into exactly two parts, the group being one of them. Column three works that way here: one 2 in box four and two in box seven. A weak link to or from a group needs a candidate that sees all of its cells. Row nine, column two does, through box seven.
A group can also be an end. Then a cell has to see every cell of the group as well as the other end, so fewer cells qualify. The quiz below has a chain like that.
How it differs from AIC and X-chain with groups
An AIC uses single candidates only. On this grid the plain AICs all remove a 3, and none of them touches a 7. Without the group, column three has three places for a 2 and gives only a weak link, so the chain stalls at row six, column three.
An X-chain with cell groups uses groups too, but it stays on one digit and every link runs between cells. This chain changes digit twice: from 7 to 2 inside row six, column eight and from 2 back to 7 inside row nine, column two. On this grid no X-chain removes anything, with groups or without.
Both links inside cells here are in cells with two candidates, so they are strong. In a cell with three or more, a link inside the cell is weak only. The quiz chain has one.
Two places, if one of them is the group. Rule out row six, column three and the 2 is in box seven's part of the column.
Point the link at one cell and there is still a third 2 at row nine, column three. Ruling out row six doesn't put the 2 at row seven, so the link is weak and the chain can't go on.
Other chains on this grid
Box four gives a second route between the same ends. Its 2s are row six, column three and a group in rows four and five of column two, so the chain can enter that group instead. Row nine, column two shares column two with both its cells, and the chain carries on as before.
From row nine, column two the 7 can also run up column two to row eight and along row eight to column nine. That chain ends in another cell, so it strikes one more 7, at row six, column nine.
The in-game hint shows a different grouped chain, on the 3s, which removes the 3 from row nine, column nine. Several chains can be right on one grid.
When a house has three places for a digit and two of them share a box and a line, treat those two as one node. Alternate strong and weak links as in any AIC. A cell that sees every cell of both ends loses the end digit.
Where this sits on the path
With that 7 struck, row six, column eight is the only place left for a 7 in column eight, so it is a hidden single.
Grouped AICs follow AICs in the chapter on chains and coloring. On this grid nothing earlier on the path removes a 7.
3D Medusa comes next.
On a different grid, this chain runs from row three, column four to a group of two cells in row three, columns eight and nine. Both ends carry a 4. Which 4s does it remove?
A cell has to see the single-cell end and both cells of the group.
Recap
- Look for
- A house with three places for a digit where two of them share a box and a line, next to the cells with two candidates and houses with two places that make up an AIC.
- Scope
- The candidates and groups in the chain, and any cell holding the end digit that sees every cell of both ends.
- Result
- Every cell that sees both ends, all of a group's cells included, loses the end digit.
- Tell-tale
- An AIC that stalls at a house with three places for its digit, two of them in one box.
- If it fails
- Check that each group sits in one box and one line, that a weak link out of a group sees all of its cells, and that both end links are strong.