AIC Hinges

X-chains, including grouped chains, and XY-chains, including remote pairs, are particular forms of Alternate Inference Chain, or AIC. If we refer to a chain as an AIC, we generally mean it is a mix of these forms. After all, the elimination and confirmation effects of chains depends on the alternating sequence of slinks and winks, and not their particular forms.

The mix of AIC forms has consequences for human solving technique. Instead of the channeled search that can be aided by a bv map or and X-panel, the search for ANL, nice loops and inference chain winks, its more a matter of finding any way to keep the chain going, until  closure on a value occurs.

This AIC example comes from section I of Rebecca Bean’s Extremely Hard Sudoku, # 41. The chain starts with a reversed bv node based on the internal wink, becoming  a grouped 9-chain, to an XY  node, and ending in a grouped 1-chain. One ANL is completed when the AIC reaches 1r7c3, but going on to net an unanticipated bonus of two more eliminations.

Now about that reversed bv node r6c8. The AIC node does not depend on having only two candidates in the cell. Any cell with more than one slink partnering candidate is similar material for an AIC node.

In Sysudoku, such cells as r3c7 and r5c3 above, are marked before the AIC scan as AIC hinges, by drawing a weak link curve between the slink partnering candidates.

The “keep it going” construction of AIC is deferred until the lower hanging fruit of the single form chains is completed. Coloring clusters are another resource for this search, so AIC is also deferred past coloring as well. Pattern analysis does follow AIC, except that  the edges of X-panels have been examined for easy pattern eliminations described a little later in this Guide.

So after coloring, when it is time for “Hail Mary” AIC construction, The AIC hinges are added to the grid. Its another Sysudoku feature in support of human solving. You’re welcome.

AIC hinges make some ANL’s much easier to spot. Take this ANL from Royle 17-7295(1/3/17), from a vast collection of 17-clue puzzles, and  cited in Berthier’s The Hidden Logic of Sudoku.

You just don’t get to this simple ANL without the hinges.

 

 

Also among Berthier’s selected Royle puzzles is Royle 1020(1/17/17), in which a hinge cell competes the victim’s view of the toxic set. Yes, the pre-set hinges make the loop drawing a little more challenging, but that’s part of the fun.

Note how the hinges point the way in a monster-like sea of candidates.

For more than 2 partnering candidates a closed curve suffices for the AIC hinge. It doesn’t need to be redrawn for different chains through the cell.

For  exaggerated illustration, let’s say a cell of 6 candidates, has three slink partners a, b and c, respectively. Two slink paths,  a to b and b to c, are represented by the attachment curvatures.

 

AIC hinges can extend already productive chains. In the MegaStar Maestro puzzle 47 (6/12/12) introducing AIC, a 49 to 4 chain combination ANL is extended through a reversed bv and three hinges for one ANL (green), and an extension from that chain grabs another, more decisive one

 

 

Earlier in Maestro 47, the AIC hinge field produced two confirmation ANL’s in a row.

First, an XY to X combination was extended into a loop to confirm 3r5c8.

 

 

 

 

 

Then, the XY is switched earlier to a 2-chain for a 2 confirmation ANL.

It’s AIC flexibility supplementing  uniform chains, via AIC hinges.

 

 

 

 

 

 

In a more recent review, Manuel Castillo’s Only Extreme 218 (11/14/17) brings a similar example. The AIC hinge field rescues a pair of stalled clusters with a nice loop.

 

 

 

 

 

The hinge corner includes a trap, and the nice loop removal also enables a skyscraper, but there is something much more decisive afoot.  The cluster expansions produce the bridge:

Not(green and red) =>

blue or orange,

but more decisively, both of the South band hinges make a slink between blue and orange. This brings a merge. It can’t be right, unless red is blue and orange is green. The merged cluster quickly wraps green.

To summarize,  the flexibility of AIC’s makes the AIC scan a challenging task for human solvers. It is well to undertake it after more structured methods are completed. AIC hinges, placed on the grid beforehand, provide visual guidance and additional logical resources for the AIC scan.

The ALS Node

A rare resource for the AIC scan is the ALS Node. It uses an Almost Locked Set, an ALS, as if it were a bv, providing a connecting slink and changing the value. It requires the entering and exit candidates or groups to “see” the entire group of like value candidates in the ALS. The internal slink is between value groups. Because the removal of an ALS value locks the remaining groups, there is a group slink between every pair of ALS value groups.

The ALS node is rarely needed, but ALS are so numerous that chains of nodes are described in Sudoku literature and built into digital solvers. The problem for human solvers is the low return on investment in time, for individual ALS nodes or chains of them.

Here is an excellent ALS node example, Figure 30.1,  from Andrew Stuart’s The Logic of Sudoku, translated into Sysudoku graphics.

Only after you put together an XY from 7 to 2 with a 2-chain would you realize that the ordinary ALS in NW links up a confirmation ANL.

As a practical matter, sysudokies only consider such AIC combinations with AIC hinges.

In deference to reality, here’s what happens to the available AIC hinges in this case. Each one reaches a point of failed alternation on both ends.

In deference to reality, here’s what happens to the available AIC hinges in this case. Each one reaches a point of failed alternation on both ends.

 

Looking back, the ALS node enabled confirmation ANL above ignores all of the hinges.

But looking ahead, there’s a puzzle to solve, and more to learn about ALS nodes in AIC.

Following the 2-chain in the opposite direction, a surprising grouped elimination ANL appears. Did Andrew’s solver do it this way? Does it matter? Not to me.

 

 

After the modest follow up of

(NW1, NW5m, r3s56),

can you usefully reconnect the chain with that innocent looking ALS that started all of this?

Yes, it has to be a nice loop, doesn’t it?

The full disclosure of the 30.1 “before and after” is for an upcoming post. You have it all to work it yourself. There’s some X-panel work before you get to Andrew’s Figure 30.1, and after this grid, a neat finishing judo chop recently covered in this Guide.

Meanwhile, my other ALS node example is also courtesy of Andrew Stuart. This time, from his solver’s solution of World’s Hardest (just kidding) Sudoku, puzzle 200.

This confirming ANL  looks appropriately unlikely as a human solver finding.

 

Keep your hinges happy when it’s time for AIC.

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