dailysudoku.com

[David Bryant]

Ruud's "theme week" is officially over on his excellent "Nightmare" web site. I still haven't learned how to find those pesky "ALS" formations. But I'm happy to report that all 7 of the "ALS" puzzles in the "theme week" collection succumbed fairly easily to the "DIC" technique.

Here's an example: this is the "Nightmare" for Wednesday, August 30.

[David Bryant]

Here's a good one for practice with the "ALS XZ rule". This is the "tough" puzzle for today (September 8 in Australia already!) from http://www.sudoku.com.au.

[TKiel]

Some techniques are better left to computer solvers and IMO this is one of them. It is usually hard to spot a hidden triple in a puzzle: This is like spotting a hidden quad (quint, sextuple, etc...) that bends around a corner, then points to a cell somewhere else. If you told me that I would either have to find an ALS XZ or some kind of chain, give me the chain any day. (And I don't like to do chains.) I have no doubt that many puzzles could be solved with this techique, but I don't find it worth the time and mental energy that must be extended for a manual solver to use it, even with the aid of SS (or any program). And the fact that you find that the ALS seems to almost be a subset of the DIC, makes it all the more unattractive and unnecessary.

[AZ Matt]

I have this for boxes 6 and 9:

[David Bryant]

Matt:

The tricky thing about spotting an Almost Locked Set is that it doesn't have to lie entirely within one box, or column, or row. I had some trouble spotting this one, too. Here's that diagram of boxes 6 & 9.

[AZ Matt]

Well there was my problem, and it explains why some of Ruud's ALS's made perfect sense, while I couldn't grasp others. And now it all makes sense; I was stuck on ALS's in columns, rows, or boxes.

And I now see how this interlaces with DICs and my (for luck of a better term) "hunch" solving technique. I used to take credit for "big" solves involving 20 or so cells, and you'd point out it was really a two line DIC. But the cells were still interrelated, and I needed all of them to explain the "xx" I saw in the patterns of the numbers (how they didn't "fit" into the puzzle). Invariably the "xx" was either a DIC or an advance x-wing/swordfish thingy, but hey, we all solve differently. In my mind it is still simply a "xx" that exists because of the requirement of uniqueness (an inevitable imbalance).

And here we have 5 cells for 4/6/8 numbers to "fit" into = a "xx," aka a DIC, aka an ALS.

Now, how to convince Keith that you don't just randomly test for DICs, you discover them (or hunt for them?)? I think it has to do with strong links, but I am still working on that theory.

[David Bryant]

Hi, Matt!

I'm glad the "ALS XZ rule" is starting to make sense. I'm starting to catch onto it, too.

Here's another great example, where the "ALS" almost jumps right off the page at me. This is from Ruud's Nightmare web site -- it's the puzzle for today, Friday, 8 September, 2006.

[Ruud]

Hi David,

I'm afraid I have to correct you on this one. It is a mistake that I also made when I was first introduced into ALS.

Your Z-digit 9 does not appear in both sets. It is essential for the technique that it does. Here's why:

X-digit 7 must appear either in set A (5,6,7) or set B (5,7,9)
When it appears in set A, set B is locked to (5,9).
When it appears in set B, set A is locked to (5,6).

So, when set A is locked to (5,6), set B is still not locked, and the possibility exists that digit 9 will not be part of its solution. When digit 9 would appear in both sets, there will always be a digit 9 locked in one of the sets.

As compensation, I can offer you an alternative Z-digit 5, which can also be seen as an XY-Wing using 3 of the same cells:

[David Bryant]

You're right, Ruud. I was too quick to think I understand the ALS thing. But the "9"s are still out, because of the chain. :)

Maybe Tracy is right ... the chains are definitely easier for me to see. dcb

[AZ Matt]

David

Don't give yet. I think I am seeing ALS as a way to identfy a linked group of cells without being distracted by the plethora of other cells for which the numbers in the group could be a candidate. The z candidate is going to fit into the group one way or another. What might at first appear to be like seeing hidden quads around a corner (to quote Tracy) may be as simple as spotting a few x candidate linking possibilities and seeing if there are any ALS's attached.

PS: In your example, what jumped out at me was the interplay of r1c1, r2c3, and r7c1.

Either r2c3 = 5, or r7c1 = 5, or both
but in no event neither
so in any event, r7c3 cannot =5

I don't know what that is called, but I see it quite a bit.

[TKiel]

[AZ Matt]

Of course it's the xy-wing (doh!).

Which is an excellent example of why I get confused by all the names and rules. I can't just apply a rule, I have to understand it on an intuitive level and see how they all interrelate.

Tracy, in my experience, once you understand a technique (take the xy-wing for example) they become second nature (so much so that you take their names for granted, apparently). URs, remote pairs. I'll keep working on ALS and DICs and Type 8 URs, etc., and see if I can come up with a unified theory of Sudoky solving.

[TKiel]

[Mogulmeister]

I find the more I practice ALS the more they start to "jump out" of puzzles and I actuallly prefer them to chains.