The New Sudoku Players' Forum

[Instinct]

Hi, I'm new to this forum, I don't need help with a certain puzzle, rather with how to improve my technique. I've always liked sudokus but only got deeper into it recently. It started when I found a puzzle on some website when I was bored and I couldn't solve it(which used to be quite rare, I could solve most of them in newspapers). I found an online solver and when I loaded it the solver started pointing out answers using terminology that was unknown to me, like XY-Chains and Jellyfish and the others. I understood its logic though and found it fascinating so I've decided to read up more about sudoku solving techniques and I've also found a few websites which offer quite difficult puzzles, well, at least for me.

My main problem is that with these very hard/diabolic puzzles, at some point I always get stuck. Sometimes it's because I'm searching for too difficult stuff and I fail to notice a simple XY-Wing or even just simple pointing pairs. However, more often than not, what I'm missing are some kinds of chains. Simple colouring or XY-Chains, etc. I have a really hard time finding these because I don't know where to search for them because sure there are many chains at any point on a grid, but most of them are not really useful.

I mean, an X-wing is really easy to find, I just go through the grid line-by-line and column-by-column, and if I find a number with only 2 instances in a unit, I will look for another wing in other units, it also turns out pretty fast whether it's a useful X-wing for elimination or not.

But with these chains, how do I know that a chain will turn out to be useful? Is it just trial and error, like "Well, here's a chain, let's see if it eliminates something"? Or, is it more like "Damn, it'd be so good if X wouldn't be possible in this cell, maybe there's a chain to kill it"? Either way, there seems to be quite an amount of intuitive factors involved. Do I just need to start solving a mass of puzzles so I get a bit more experience with the more difficult ones, or is there a shortcut, like some theory about in what kind of circumstances should I be looking for a chain?

Here's a quick example:


On Diagram A, you can see the point where I got stuck. I loaded the position into a solver, and it pointed out an XY-chain, demonstrated by Diagram B. The chain starts from r7c7 and ends at r8c3. A 4 from r8c7 and another from r8c8 can be eliminated which will lead to naked pairs and basically almost solves the entire puzzle, only an X-wing and a couple of XY-wings are left before the grid is reduced to a bunch of naked singles eliminating each other. On Diagram C, there's a set of chains, originating from r5c9, but they're completely useless for the moment, unless I'm planning on solving half of the puzzle in my head.

So basically my question is, how should I know that r8c7 is a critical cell and r5c9 is not? As far as my newbie knowledge goes, both seem to be reasonable options at first glance.

Thanks, in advance.

[JasonLion]

First, it is fairly easy to get a rough idea of when chains are going to help and when they aren't worth the trouble. Chains build off of cells with two pencil marks and houses with two occurrences of a candidate. If there aren't enough of those around, which is easy to see, then chains are not likely to help. This is especially true at the start of solving, when chains are normally going to be rare.

Beyond that, it varies. A good learning technique is to try every possible chain you can spot. That isn't usually practical/fun for routine solving, but it is a great way to learn.

Some people identify a target elimination, and then check to see if there are chain end points that can make that elimination, and then see if they can connect those end points together.

Another approach is to visualize where the possible links in the chain are, and get a sense of what can be chained to what. This takes some visualization skills, but can quickly show you what areas hold promise, and you can then explore those areas in more detail. When learning this approach, it is often best to start with a simple kind of chain, say only consider remote pairs, and play with puzzles known to contain remote pair moves and get a sense of how that goes, then move up to more complex chains. Another approach is to make bi-value/bi-location plots for some practice puzzles that are known to be at the point of a complex chain move and study them for a while. Drawing those plots can be a big help in building visualization skills.

It takes time to build up skills in this area. The more time you put in, the more quickly you will spot things. Sudoku seems to involve learning certain very specific kinds of pattern matching at an intuitive level, which leaves your conscious mind free to work at a higher level. The main way you develop that is to just keep working at it. You start by searching methodically, and with enough practice things will start to just kind of "jump out" at you and more and more of it becomes automatic.

[Instinct]

Thanks very much for your reply, I now have a better understanding of when to look for chains, your advice actually helped me with solving one of the puzzles I have been working on today.

Peace

[SteveG48]

Building on what Jason said, a chain will often be useful if there's a candidate with many unsolved cells, but which is "highly connected". That is, if you solve one instance of the candidate, most or all of the other instances will be solved. (In technical terms, it has many strong links). If you have this situation, look for a bivalue cell containing this candidate and another candidate which can "see" two or more instances of itself in the same house. These instances will be your targets. (The connected candidate is not your target!) Assume that the second candidate is not true in your bivalue cell- meaning that the "connected" candidate is. This will set/reset the connected candidate in many other cells, often leading to a "set" value for your target candidate in a location that sees one of your target cells. It sounds complicated, but it's easy to do and it works.

[Instinct]

Hi, thank you for the reply, I'm well aware of strong links and how the chain works, I've read a lot about it, I just had a bit of difficulties actually finding them in a puzzle. For example, now I'm smashing my head because I've missed an easy X-Cycle which could have saved me quite a LOT of time instead of colouring half of the puzzle and coming to the same conclusion, lol.

[SteveG48]

Hi, thank you for the reply, I'm well aware of strong links and how the chain works, I've read a lot about it, I just had a bit of difficulties actually finding them in a puzzle. For example, now I'm smashing my head because I've missed an easy X-Cycle which could have saved me quite a LOT of time instead of colouring half of the puzzle and coming to the same conclusion, lol.

I was trying to answer your question "How do I know if a chain will be useful?". I don't know if I managed that. In my experience, if a candidate can see more than one instance of itself in the same house, and if that candidate is paired in a bivalue cell with another candidate that has many strong links, then a chain starting in that bivalue cell is likely to be useful and give you eliminations.

[Instinct]

Hi, thank you for the reply, I'm well aware of strong links and how the chain works, I've read a lot about it, I just had a bit of difficulties actually finding them in a puzzle. For example, now I'm smashing my head because I've missed an easy X-Cycle which could have saved me quite a LOT of time instead of colouring half of the puzzle and coming to the same conclusion, lol.

I was trying to answer your question "How do I know if a chain will be useful?". I don't know if I managed that. In my experience, if a candidate can see more than one instance of itself in the same house, and if that candidate is paired in a bivalue cell with another candidate that has many strong links, then a chain starting in that bivalue cell is likely to be useful and give you eliminations.

If I understand correctly, you are talking about a situation like this:



Here r9c4 is paired with r8c5. It can also see many X-s in column 5, and also a couple of Y-s, and r8c5 has many strong links. Am I correct?

[SteveG48]

Yes! If you start a chain assuming r9c4 <> X, then the links provided by the Y's will likely result in a cell where X is set and can see one of the X's in column 4. That will give you an elimination. Or you may find an X that is reset in column 4. In fact, if r9c4 <> X, then r5c4 must be Y, so you can eliminate the X in r5c4 in your example.

[Instinct]

In fact, when I posted that figure it was just an example based on your description, I didn't even think about actually putting a useful chain in it, and it turns out, that two of the X-es can be eliminated.



If r9c4=X then it directly sees the X at r3c4 and r6c4 and if r9c4=Y then a chain will set r5c4=X, so this means either r5c4 or r9c4 is in fact an X, therefore, neither r3c4 nor r6c4 can be an X.

Funny, this just shows how useful chains are, even in a completely arbitrary and imaginary scenario. Now I only need to find them on actual puzzles without colouring the whole stuff

[SteveG48]

Funny, this just shows how useful chains are, even in a completely arbitrary and imaginary scenario. Now I only need to find them on actual puzzles without colouring the whole stuff

Indeed. Remember, though, the scenario isn't completely arbitrary. I described a configuration that I've found to be likely to produce useful chains, and you nailed it with your diagram.

[Instinct]

Yeah but this sort of set-up is pretty common when solving puzzles. At least something similar occurs almost always after finding the naked singles, pairs and triples. The puzzles I do now are not the really devilish ones, usually after the stage of finding the pairs and triples, an X-wing, XY-wings, and 2-3 eliminations by Simple colouring and XY-chains reduce the puzzle to single-land. I know because when I'm stuck for more than an hour I just put it into a solver, though this is required less and less, as I'm getting more comfortable with these simple chains. I'll bother with 3D Medusas and Death Blossoms later, when I know what I'm doing