Here we link back to advanced solving posts as we enjoy sysudokie solving snapshots from the review table puzzles 0f Frank Longo’s Absoutely Nasty Level 4 (AN4) collection. Did you ever get trapped looking at a neighbor’s vacation slides ? You may feel that way late in this post, but I don’t think you will want to pass anything up. This is sysudoku magic at work.
Although the first XY-chain of AbNasty4 #1 produces three almost nice loops , I really want to show you first the bv map which leads to their discovery. This is a network of curves emerging from one bi-value cell (bv) and entering another bv via any link, weak or strong . The colors mark different curves that can be drawn. You try to start where there is an emerging curve but no entering one, and with a candidate with matching candidates for a toxic set and a victim. You go as far as you can on curves, then draw connecting curves to form a network. This network organizes a comprehensive search for XY-chains.
On the grid, you can see how the first XY-chain follows this network. I show bv connecting links as winks, even if they are slinks, because in an XY-chain, they function as winks. Usually I omit the internal slink between close candidates of the bv.
My comments on this slide identify the chain as 9274129-chain =>(W9,NW4). The beginning and ending 9’s form the toxic set. Or you can connect the chain with any victim “seeing “ the toxic 9’s, forming an almost nice loop(ANL).
FolIowing the curves network, it’s easy to find dramatically long XY chains. That is why XY- chains come early in the advanced solving order of battle.
Our next exhibit AbNasty4 #11 has four biggies. How about an ALS assisted AIC forcing chain confirming an APE removal? No, I’ve never seen, or even thought about that, until it came up.
The APE, or Aligned Pair Exclusion, was unsuccessful, as most are. The possible combinations of these two cells I describe as
APE r6c13 = 17+19+29+39+13+23 .
The 7-candidate appears in only one term. By any chance, could this combination be impossible? To find out, we start forcing chains stepping away from candidates 1 and 7, looking for some clash. It occurs in r3, where the chains force 1 and 9 out of two bv, leaving 8 in both of them. Can’t happen, so the combination 17 is eliminated, and with it, candidate 7.
But wait. Isn’t an ALS node in an AIC a very advanced technique, compare to an APE? Yes, and this fact elevates the sysudoku grade level of this puzzle, but I didn’t have to search for the ALS node. It hit me as a way to extend the forcing chain. All I had to do was to be aware of it.
This is a significant example of a forcing chain used as a supporting tool. The specific opportunity to remove the 7-candidate means that the forcing chains are not the least bit arbitrary. They support APE fact, not an arbitrary guess. To me, this marks the proper boundary between logical solving and trial-and-error (T&E).
I would forbear showing off the finned swordfish , it being the boxed fin variety, except that the removal triggers a naked triple. The enabled triple promptly eliminates three candidates. The picture reminds us that we need to react comprehensively to every advance, and update all our solving information with every removal or confirmation.
OK, can you hold on for more? #11 also wants to show us its kraken jelly. The 6-panel reveals the kraken analysis, and I will try to explain it briefly.
First there is the blank line marking of the potential fish. The bars show the potential fish columns and the plus signs show the rows they cover. The f in c8 marks the candidate which is out of place, spoiling the jellyfish. It becomes the fin. The o’s in the victim rows were v’s at first, standing for victim. But these victims, if true, make the fin true. Only one makes the fin false. It “sees” the fin and therefore remains a victim of this crippled fish.
An interesting feature of AbNasty #11 is that it contains not only a kraken jellyfish, but also a much more ordinary nice loop off the 8-panel which collapses the puzzle, and does not depend on the jellyfish removal.
It just so happens that, following my SSOB, I look at the 6-panel before the 8-panel, applying all X-panel techniques to each number in turn. I’m just glad it worked that way, and I didn’t miss the trophy fish.
Did you know which 8 is eliminated? If not, brush up on nice loops. It is any link that sees both ends of any link, weak or strong. I think we’d better make this AbNasty4 Snaps I and do AbNasty4 Snaps II next post.
You may have too much to think about right now, but in case you’d like to start a puzzle for the next collection review, here is something to box mark for the next post. It’s Super Tough #5, from volume 5, book 1 of the ST download on www.KrazyDad.com . It’s gonna be a great illustration of high powered Medusa coloring, if you’d care to brush up.