Hidden XY Chains Are Reverse XY AIC

This post demonstrates that every hidden XY chain has a recognizable AIC counterpart on the normal grid, nrc space. That means it is not necessary, if you are AIC literate,  to generate and maintain the grid spaces in which hXY chains hide.   Besides that, I have a highlight reel for you after dinner, showing some of the delights you would miss if you stay on the SudoRules resolution path with the very puzzles selected to promote hidden XY chains in The Hidden Logic of Sudoku.

First, I have a couple of  17-35802-xy-235802 nrc XY chains to checkpoint for you.

Here is the second, . . .




. . . and the third, for the collapse.

17-35802-xy-3Now,  with all of the THLS evidence of XY success in nrc space, should we spend the effort to be ready to apply the XY chain rules on the symmetry grids?   

Forget it, pilgrim.

Also, don’t expect the same degree of XY chain success in symmetry land.  None of the 35802 chains we just found would be possible on the symmetry grids, because all three depend on weak links with boxes as the “seeing” unit. In the symmetry spaces, remember, there are no boxes.

xy-wing-in-crnAnd as Berthier himself illustrates in THLS, an XY chain in a symmetry space transforms into an AIC in standard nrc space with corresponding eliminations. Here is a properly numbered version of Berthier’s hidden XY wing example, Figure 2 in Chapter XV, with slinks and winks explicitly shown between candidates. In crn space the 1231 XY chain has a victim seeing both end candidates, forming what my mentor Andrew Stuart calls, an almost nice loop, or ANL.

In standard nrc space, the bv are stretched into row slinks and the row winks condensed into bv.

xy-wing-in-nrcThe corresponding 2-candidate is eliminated, but in the process, a corresponding 5-candidate is confirmed.  Perhaps not in THLS, where confirming ANL are politically incorrect.

It’s true that such AIC are more advanced in the SOB, and  may be more logically complex than XY chains. But we manage with the help of AIC hinges.

Bottom line,  we can do without the laborious symmetry grid maintenance burden of hidden XY chains because we have a richer solving repertoire than THLS.

This is demonstrated further in the next post with a report on the Sysudoku resolution of the hidden XY example puzzles.

In the course of preparing that report, I did come across one puzzle for which I found no other solution than the AIC corresponding a hidden XY chain. Your homework Royle 17-7295, diligent sysudokie, makes a concrete, supersymmetry example. Here is your basic trace checkpoint:

17-7295-basic-tr17-7295-aicIn the resulting line marked grid, none of the five UR delivered results. I struck out with the bv scan, the C-panels and coloring as well. Perhaps I wasn’t looking hard enough, because I kept thinking about the hidden XY chain to nrc AIC example above, and its THLS companions. I wrote in my AIC hinges, and the reversed XY AIC came right out and saluted.

The AIC hinge is a cell with more than two candidates, with two or more forming slinks. Such cells allow an alternating chain to pass through. It’s a reversed XY chain, with slinks added on each end. The elimination brings an immediate collapse.

But wait! Is this the transformed XY chain in the THLS trace for 7295? Berthier does say that 7r1n4 is eliminated in crn space by his XY chain, corresponding to 4r1c7 on our planet. Oops, we eliminated 4r7c1. Is that a typo or did he find something different?

I know it sounds ridiculous if you’re not a THLS reader, but Berthier announces the cells of his XY chain in cnr space, with no grid diagram. Remember, he shows no candidates in any space.  I’m not willing to convert the whole grid, or even all remaining candidates, but I can convert chain’s cell list onto a nrc grid and see what we have. I think you should try it and check me out on the following diagram.

17-7295-aic-to-crnIn crn space, my AIC looks like an ANL confirming 7r7n4, but that is something SudoRules appears to know nothing about. This something has the same effect as the THLS trace’s hXY removal of 7r1c4.


The puzzle has some wiggle room and we don’t have an exact match.


17-7295-thls-in-crnIt seems likely that this is the XY ANL that SudoRules came up with, but when I modify my AIC to get that 4r1c7 elimination, I need the NE4m slink below to make it work. That slips an irrelevant 8 into r1n4 here.

Notice the absence of box slinks in both of these hXY’s. They don’t exist in crn space.


17-7295-mod-aicAnyway, I trust you are satisfied that you see what comes with the hidden XY merchandize that Berthier promotes without the price list. I’m not buying any for my human solver friends. Computer solver buddies with sweet routines for XY chains might be interested, but we human solving advocates are not the drudges that  computers are. We’re in it for fun.


royle-17-1020In the next two posts,  I’m showing the alternative sysudokie solution highlights for all the other puzzles that THLS claims to require hidden XY chains.  The purpose is to show that the value of hidden chains lags far below the price in human effort. Here is the capstone puzzle in this series, Royle 17-1020.  Basic solving is tough. You’ll have two weeks for this assignment.  Go!


About Sudent

I'm John Welch, a retired engineering professor, father of 3 wonderful daughters and granddad to 7 fabulous grandchildren. Sudoku analysis and illustration is a great hobby and a healthy mental challenge.
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