dailysudoku.com

[David Bryant]

Ruud is running another theme week on his excellent Nightmare web site. This time the theme is Almost Locked Sets.

I've read quite a bit about the "ALS" technique, but I still don't think I really know how to use it. But in working these puzzles I've noticed that the double-implication chain technique works very well. I'm hoping somebody on this forum can help me understand why that is so. Maybe there's some connection between "ALS" and "DIC" that can be made more explicit.

Anyway, here's the Nightmare from Tuesday, August 29. I got through this one with one short chain that ended in a contradiction, plus one double-implication chain, and a little bit of coloring at the very end. I'll post my solution in a day or two.

[Marty R.]

[David Bryant]

[ravel]

As i said, i never found an ALS directly, but i found a chain and then constructed an ALS. For me it is a nice notation, but very hard to spot as 2 sets of almost locked sets. I give an example in this puzzle:

[Ruud]

Almost Locked Sets are more abundant in a sudoku than anything else. I was amazed to see how many could be found.

This is the grid in the state in which SudoCue reports the first ALS step:

[AZ Matt]

I found this thread from this very forum helpful:

http://www.sudoku.com/forums/viewtopic.php?t=2510

This is great stuff...

[David Bryant]

Thanks for the long list of almost locked sets, Ruud.

In the list Ruud posted, there are 254 distinct Almost Locked Sets. So there are 127 x 253 = 32,131 distinct pairs of "ALS"s. Ruud also shows us 21 different pairs that allow the XZ exclusion rule to be applied.

Perhaps that's why this technique is hard to master. In this puzzle, there are roughly 1,500 "duds" for every ALS pair that actually helps one make an exclusion. (i"m just guessing, but I suppose the ratio of useful ALS pairs to all ALS pairs is on the same order of magnitude in most puzzles where this technique -- or something similar -- is necessary.) I can see that many of the theoretically possible ALS pairs aren't logically connected (by lying in the same row / column, or by intersecting in an interesting way within one 3x3 box). Still, it seems that separating the wheat from the chaff is a fairly tall order. Or am I missing something obvious? dcb

[David Bryant]

Here's how I used the DIC technique to solve this "Nightmare." I'm starting from the position Ruud posted above.