dailysudoku.com

[immpy]

Hello all, enjoy the puzzle...

[TomC]

Nice puzzle immpy!

[dongrave]

Starting with TomC's grid, I used the following chain:
(9=6)r7c5 - (6=7)r7c7 - (67=4*)r7c8 - (4=2)r7c1 - (2=6)r2c1 - r2c78 = r1c8 - (4*6=3)r9c8 - (3=9)r9c2 => r7c3 <> 9; stte.

[immpy]

After basics: Just one slight change to Tom's grid; the Claiming 7s in Box 3 leaves r1c8<>7.

Grid now looks like this:

[immpy]

Then there is a beautiful ALS XZ Rule:

A=r2c6789 {23678}, B=r9c47 {268}, X=6, Z=2 =>r3c4, r9c6<>2.

[immpy]

That alone does not completely solve the puzzle, but it takes you quite deep. The grid (after a good rinse) now looks like this:

[immpy]

One may then choose either the XY-Wing: 3-45 r8c69,r9c8 =>r9c6<>4, or the BUG+1: r9c9=3.

cheers...immp

[immpy]

Another HUGE Thank You to Mogulmeister for enlightening me and showing the way on the ALS XZ Rule!! I absolutely love having this in my arsenal of solving skills.

cheers...immp

[Mogulmeister]

[Mogulmeister]

Great puzzle Impp!

Your wonderful ALS XZ is a bit more special than you might think.

[Mogulmeister]

OK. Your two sets:

A = {2,3,6,7,8} which is Green
B = {2,6,8} which is Purple

As you say, X=6 and Z(red) = 2

Your restricted common (X) is 6 which causes a slight problem. I've shown the problem cell in pink.
You will notice that there are two sixes at r2c78. Unfortunately only the 6 at r2c7 obeys the restricted common rule. Remember that the restricted common can only end up in one or other of A and B.

As currently configured, you could end up with 6 in r2c8 and r9c7 so the ALS XZ is busted.

But is it ? NO.

Logically, either your XLS XZ is true or the pink 6 is true.

The good news is if the pink 6 is true we have a chain......

(37=6)r2c8-(6=2)r2c1-(2=4)r7c1-(4=67|67)r7c78-(6=8)r9c7-(8=2)r9c4

Means r3c4,r9c6 <>2 - the same eliminations as the ALS XZ.

Either way your eliminations of 2 still stand!

What you inadvertently did Immp, is produce a very good AALS XZ!!

[immpy]

Wow!! Didn't see this until you illustrated it! I now think my logic was a bit faulty. I was pushing too hard to find an ALS. Luckily it didn't mess this puzzle up. Happy for my inadvertent good fortune. Must be a bit more careful going forward. I can say this though, this technique has become one of my pet solving skills now. I am always looking for it. It un-muddies so many difficult (and not so difficult) grids. It suits my mind's eye better than some of the various wings that may be available as well. Thanks again many times for all of your insight Mogulmeister.

cheers...immp

[immpy]

OH MY!!! I just revisited this puzzle and I found what I did...and stupidly forgot to include...along my solving path. THE HIDDEN RECTANGLE!! I employ it so casually sometimes that I don't even think about it, as if it were a basic solving skill. So I completely forgot to include it in my steps.

Hidden Rectangle: 6/7 in r2c78,r7c78=>r2c8<>6. This removes that 6 from the pink cell, which I had already done on paper as I solved the puzzle. But as I posted the grids of my progress, I left this very important step out, and I jumped to my grid with that 6 still in there at r2c8!!

That's why I was so puzzled by your finding of the extra 6 in my ALS. I thought, how could I have identified it as an ALS?? When it clearly wasn't.

It sucks getting old, eh? In my case, yes!! LOL

Apologies for my screw-up, but glad I figured this out.

cheers...immp

[Mogulmeister]

Immp

No need for apologies. I thought your AALS was a great thing and a good exercise. Congratulations are due imho. We never learn unless we push forward. Well done. I liked the double elimination too.

[immpy]

Well, all is well and good, but I really am not familiar with the AALS. Not at this time, anyway. My intent was the ALS and I did indeed find it. Using it now and practicing with it. Getting pretty good with it too. But thanks for the kind words Mogulmeister. Try my newly posted puzzle for today. Enjoy.

cheers...immp

[Mogulmeister]

Remember this other AALS from a little while ago. Same principle as yours Immp.

[immpy]

Thanks Mogulmeister. I am just going to stick with honing my skills with the ALS for now. That extra candidate just muddies the whole thing up for me somehow. And then I get confused and can't accurately keep things straight. Mistakes ensue. Or I think I see something similar in another puzzle, and not being precise or sure of the technique, again, mistakes ensue. Besides, I have already opened many new avenues just by learning this new (to me) ALS-XZ Rule. I am going to get more familiar with IT and as I get more comfortable through repetition, I will surely begin to understand more about the AALS. You might bet a chuckle out of knowing that when I first discovered the XY-Wing technique it took me many puzzles to become adept at finding them, and adapting them correctly to the particular puzzle. At present, they are second nature to me, almost a "basic skill" in their ease of use. That is the process I must go through to level up to a newly learned technique. And it is a joy, and why I love doing Sudoku puzzles, or else I would have quit long ago.

One last note...in your last grid with the AALS, my eye would have already found the U.R. Type 1 of 67 r39c45 in which r3c5<>67=8! and which neatly solves from here without the need of the AALS.

cheers...immp

[Mogulmeister]

Thanks Immp

You will see the almost strategies throughout sudoku. Sometimes it’s shown as a fin in an x wing or swordfish. An extra candidate which is tolerated because it makes the same elimination as the orthodox structure OR the fin shuts down the puzzle also (see below).

In your case the AALS did not confer any advantage but in the example it was a one stepper.[as was the <67> UR].

[Mogulmeister]

Here's an "almost" solve of an extreme that I did with an "almost" XY wing from the old days! (2010)

[Mogulmeister]

Incidentally Immp,

You will find the overlapping <13> URs interesting too.