atrotta wrote:HI Space, can you give some hint on how you are able to spot AICs so easily? I'm astonished that you do that in paper also. Please advice
Well, about a year and half ago I would have been astonished too!
That's when I started studying non-basic techniques (of which X-Wing was the only thing I'd ever used before). When I first looked at some of the more complicated chains found by the SudokuWiki solver (the only solver I knew at the time) back then, I was pretty certain it wasn't humanly possible to find them manually, at least for me. I was obviously wrong, and it didn't even take very long to start spotting them, which surprised myself too. It has taken quite a bit of studying, practicing, and developing spotting aids, though, and it's a work in progress. I can share the process which I've gone through and has helped me, but I can't know what works for others.
First, I might recommend learning coloring if you haven't already. That's how I started, and it helped me find chaining eliminations before I even understood how chains really worked. In a quick succession I studied Simple Coloring, 3D-Medusa, Multi-Coloring, Weak Colors, and X-Colors (none of which I actually used) until I found David Bird's GEM which was exactly what I was looking for. It's the most powerful humanly applicable coloring technique I know. It's especially powerful for a pencil-and-paper solver, even though David doesn't present it as such. In fact, I think his spreadsheet-based way of presenting it has probably been an epic marketing blunder, because it makes it seem more complicated than it is. I'm probably one of the very few people who actually uses GEM besides David himself, and it's because I'd had similar (but not as fully developed) ideas which made me see its value immediately despite the not-so-attractive interface. Once I created a human-friendly way to apply it on paper, it's been an invaluable tool. At first it worked as training wheels for chaining stuff, but I still use it as a backup in tough spots or when I want to find effective eliminations faster. It's also possible to use with a software solver that has candidate coloring, like Hodoku, but it's a bit painful as it requires so many color mappings.
There's one caveat about using coloring methods, and especially GEM. They're easy to use without thinking (and I admit to having used GEM without thinking early on, because it allowed me to solve puzzles I couldn't have dreamed of solving otherwise at that time). However, to actually learn something, you should always build a chain (or a net) for each elimination you find. You can do that mentally, but even better, I highly recommend learning the Eureka notation and writing down all the chains you find (if you don't already). I'm pretty sure that actually helps understanding chains better and thus spotting them also. When I started using GEM, I couldn't explain many of the eliminations it found, so it seemed a bit like magic. Some of those eliminations were actually based on nets, which is another thing to be aware of as GEM makes using them easy as well (a matter of personal preference if such eliminations are accepted or not -- I think nets are fine and fun as long as the player understands and can explain them).
Another problem with coloring methods is that they work a bit backwards by finding eliminations first, after which the player should construct chains (or nets) to prove them. What about finding chains and their eliminations directly? That's a bit tougher but also more rewarding. It's especially tough with a standard pencil mark grid without any visual clues about the strong links. For that reason I've created my own candidate mark-up system which shows all bilocation strong-links, including group links. I recommend something like that to any serious p&p solver. It makes visualizing AICs a lot easier, and it also helps applying GEM if need be. Early on I experimented a bit with external B/B plots, but quickly figured they just produced useless spaghetti. With harder puzzles I might draw a couple of helper plots, though: one for single digits (easier to see X-Chains and fishes) and sometimes one for bivalue cells (mostly useless). If none of those help enough (or fast enough), then I resort to using GEM. If that doesn't help either, then it's probably an SE 9+ puzzle for which my tools aren't sharp enough.
One last generic piece of advice is to deepen your understanding of chains by simply looking at them and studying them a lot, which makes it easier to see them as well. For example, I've learned a lot from the solutions in the Puzzles section of this forum. Studying chains found by software solvers, such as Hodoku, helps too. It might be a good exercise to try to see (and write!) some variants of those chains yourself. Eventually, especially with good visual aids for the strong links, it's possible to start seeing at least simpler chains or chain fragments as patterns on the grid. It's also important to recognize the different AIC types and their differing elimination possibilities to know what to look for. There are four main types, as far as I know:
AIC Type 1: End nodes have the same digit and don't see each other: eliminate any candidate of that digit weakly linked to both ends.
AIC Type 2: End nodes have different digits and see each other (but aren't in the same cell): each end eliminates its own digit from the opposite end node.
AIC-Loop: End nodes are weakly linked to each other. Every weak link eliminates in its scope.
AIC-Loop with ALS nodes: In addition to the previous, ALS bystanders get locked and also eliminate in their scopes.
I don't know if this helped at all as it's all pretty generic, but I'm happy to answer any specific questions. Like I said, it's a work in progress for me too, and communicating helps to organize one's thoughts and sometimes figure out new ideas.
Let's see...
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