A short AIC is the shortest X-chain: a strong link, a weak link and a second strong link, all on one digit. It has four cells and three links. One of the two outer cells holds the digit, so a cell that sees both loses it.
How to spot it
You don't need to walk a long path. Pick a digit and list the houses where it has exactly two places. Each of those is a strong link.
Now compare the strong links two at a time. If a cell of one sees a cell of the other, those two cells form the weak link in the middle. The two cells left over are the ends.
Any other cell holding the digit that sees both ends loses it. The grid below has two of them.
List the strong links on the 1
Take the 1. Row two has only two places for it, columns one and six. So does row seven, in columns two and six. That gives two strong links, one in each row.
Join them with a weak link
Row two, column six and row seven, column six share column six. That column has four places for the 1, so the two cells are not a strong pair. They do see each other, and only one of them can be the 1. A dashed line joins them, and the chain is complete.
Read it from one end
Suppose row two, column one is not the 1. Row two then puts it in row two, column six. Column six rules out row seven, column six. Row seven puts the 1 in row seven, column two. A miss at one end means a 1 at the other.
Strike the 1s that see both ends
Row three, column two shares box one with row two, column one and column two with row seven, column two. Row eight, column one shares column one with the first end and box seven with the second. Whichever end holds the 1, each of these cells is in a house with it, so the 1 comes out of both.
Collect the singles
Row three, column two is left with only an 8, a naked single. Column two and box seven now each have one place for the 1, row seven, column two, a hidden single. The grid had no single anywhere until the strike.
Why three links are enough
The walk in step three used only three houses. Row two moved the 1 to column six, column six took it away from row seven, column six, and row seven moved it to column two. Run it from row seven, column two and the same houses work in reverse, so at least one end holds the 1.
In the solution it is row seven, column two. Row two, column one is a 6, and the 1 of row two sits in column six.
How it differs from an X-chain
An X-chain can run as long as it needs to, and the one on the X-chain page has six cells. A short AIC stops at four. Fewer links can't work. A chain must start and end on a strong link, and one strong link alone is just two places in a house.
Being short changes how you search. Instead of building a path one link at a time, hold two strong links side by side and ask whether a cell of one sees a cell of the other. The in-game hint uses the same split, calling a four-cell chain a short AIC and a longer one an X-chain.
AIC stands for alternating inference chain. Every link here is on one digit. Later in this chapter, longer AICs also link two candidates inside one cell.
Two places. If row seven, column six is not the 1, row seven, column two is.
Four places. Rows three and seven cannot both hold the 1, but neither has to, because rows two and eight are left.
The same shape, standing up
Turn the chain on its side and look for it in columns. Column two has two places for the 1, rows three and seven, so that is a strong link. Row seven joins row seven, column two to row seven, column six. Column six seems to give a second strong link, up to row three, column six.
It doesn't. Column six has four places for the 1. Treat it as strong anyway and the ends are row three, columns two and six. Row three, columns one and five see both, so you would strike their 1s. In the solution the 1 of row three is in column one.
Count the places in both outer houses before you strike anything. The middle link only needs two cells that see each other.
Shapes with names
Other sites call this pattern a turbot fish and name its shapes. Two strong links in parallel rows, with their near ends in one column, make a skyscraper, as on this grid. Turned sideways it works in columns too. One strong link in a row and one in a column, joined inside a box, make a two-string kite. A third shape puts one strong link inside a box.
List the houses where a digit has exactly two places. Look for two of those strong links where a cell of one sees a cell of the other. The two cells left over are the ends, and any cell that sees both of them loses the digit.
Where this sits on the path
A short AIC places nothing. It removes candidates, and the singles do the placing. Here one chain opened two of them.
It is the fourth step of the chapter on chains and coloring, after X-chains with cell groups. On this grid nothing earlier on the path removes a candidate.
Short AICs with cell groups come next.
This chain runs from row two, column six to row seven, column two. Which 1 does it remove?
Start with the ends. You want a 1 that shares a house with each of them.
Итог
- Ищите
- Two houses where one digit has exactly two places, with a cell of one seeing a cell of the other.
- Область
- One digit. The four cells of the chain, and any other cell holding that digit that sees both ends.
- Результат
- The digit comes out of every cell that sees both ends.
- Признак
- Two strong links on the same digit that come close to each other, often in parallel rows or columns.
- Если не сработало
- Count the places in each outer house again. Both must have exactly two. If no cell sees both ends, try another pair of strong links.