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VH+ 082521

 
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immpy



Joined: 06 May 2017
Posts: 455

PostPosted: Wed Aug 25, 2021 5:06 pm    Post subject: VH+ 082521 Reply with quote

Hello all, enjoy the puzzle...

Code:

+-------+-------+-------+
| . . . | . . . | 9 . 2 |
| . 5 4 | . 1 . | . . . |
| . . . | . . 6 | . 5 . |
+-------+-------+-------+
| . . 6 | . . 9 | 3 . 7 |
| 9 1 7 | 4 3 8 | 5 2 . |
| 8 . 3 | 6 . . | 4 1 . |
+-------+-------+-------+
| . 8 . | 3 . . | . . . |
| . . 1 | . 7 . | 2 9 . |
| 7 . 5 | . . . | . . . |
+-------+-------+-------+

Play this puzzle online at the Daily Sudoku site

cheers...immp
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TomC



Joined: 30 Oct 2020
Posts: 109
Location: Wales

PostPosted: Thu Aug 26, 2021 1:43 pm    Post subject: Reply with quote

Nice puzzle immpy!

Code:

+------------+-----------+-------------+
| 1   67  8  | 57 4  35  | 9   367 2   |
| 26  5   4  | 9  1  23  | 678 367 38  |
| 23  379 29 | 27 8  6   | 1   5   4   |
+------------+-----------+-------------+
| 5   4   6  | 1  2  9   | 3   8   7   |
| 9   1   7  | 4  3  8   | 5   2   6   |
| 8   2   3  | 6  5  7   | 4   1   9   |
+------------+-----------+-------------+
| 24  8   29 | 3  69 15  | 67  467 15  |
| 346 36  1  | 58 7  45  | 2   9   358 |
| 7   39  5  | 28 69 124 | 68  346 138 |
+------------+-----------+-------------+

Play this puzzle online at the Daily Sudoku site

At this point r9c8<>3 as then r9c2=9 r7c3=2 r7c1=4 leads to no 4's in box 9 and basics then to finish
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dongrave



Joined: 06 Mar 2014
Posts: 443

PostPosted: Thu Aug 26, 2021 3:19 pm    Post subject: Reply with quote

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.
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immpy



Joined: 06 May 2017
Posts: 455

PostPosted: Thu Aug 26, 2021 5:40 pm    Post subject: Reply with quote

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

Grid now looks like this:
Code:

+------------+-----------+-------------+
| 1   67  8  | 57 4  35  | 9   36  2   |
| 26  5   4  | 9  1  23  | 678 367 38  |
| 23  379 29 | 27 8  6   | 1   5   4   |
+------------+-----------+-------------+
| 5   4   6  | 1  2  9   | 3   8   7   |
| 9   1   7  | 4  3  8   | 5   2   6   |
| 8   2   3  | 6  5  7   | 4   1   9   |
+------------+-----------+-------------+
| 24  8   29 | 3  69 15  | 67  467 15  |
| 346 36  1  | 58 7  45  | 2   9   358 |
| 7   39  5  | 28 69 124 | 68  346 138 |
+------------+-----------+-------------+

Play this puzzle online at the Daily Sudoku site
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immpy



Joined: 06 May 2017
Posts: 455

PostPosted: Thu Aug 26, 2021 5:47 pm    Post subject: Reply with quote

Then there is a beautiful ALS XZ Rule:

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



Joined: 06 May 2017
Posts: 455

PostPosted: Thu Aug 26, 2021 6:00 pm    Post subject: Reply with quote

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

Code:

+----------+---------+-----------+
| 1  7  8  | 5 4  3  | 9  6  2   |
| 6  5  4  | 9 1  2  | 78 37 38  |
| 23 39 29 | 7 8  6  | 1  5  4   |
+----------+---------+-----------+
| 5  4  6  | 1 2  9  | 3  8  7   |
| 9  1  7  | 4 3  8  | 5  2  6   |
| 8  2  3  | 6 5  7  | 4  1  9   |
+----------+---------+-----------+
| 24 8  29 | 3 69 15 | 67 47 15  |
| 34 6  1  | 8 7  45 | 2  9  35  |
| 7  39 5  | 2 69 14 | 68 34 138 |
+----------+---------+-----------+

Play this puzzle online at the Daily Sudoku site
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immpy



Joined: 06 May 2017
Posts: 455

PostPosted: Thu Aug 26, 2021 6:14 pm    Post subject: Reply with quote

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

cheers...immp
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immpy



Joined: 06 May 2017
Posts: 455

PostPosted: Thu Aug 26, 2021 6:17 pm    Post subject: Reply with quote

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
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Mogulmeister



Joined: 03 May 2007
Posts: 873

PostPosted: Fri Aug 27, 2021 9:06 pm    Post subject: Reply with quote

TomC wrote:
Nice puzzle immpy!


At this point r9c8<>3 as then r9c2=9 r7c3=2 r7c1=4 leads to no 4's in box 9 and basics then to finish


Nice contradiction forcing chain Tom which is also a loop

When you plug 3 into r9c8 the loop removes it so r9c8<>3

(46=3)r9c8-(3=9)r9c2-(9=2)r7c3-(2=4)r7c1-(4=36|367|67)r127c8-(3)r9c8
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Mogulmeister



Joined: 03 May 2007
Posts: 873

PostPosted: Sat Aug 28, 2021 3:33 pm    Post subject: Reply with quote

Great puzzle Impp!

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



Last edited by Mogulmeister on Sat Aug 28, 2021 3:54 pm; edited 1 time in total
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Mogulmeister



Joined: 03 May 2007
Posts: 873

PostPosted: Sat Aug 28, 2021 3:51 pm    Post subject: Reply with quote

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!!
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immpy



Joined: 06 May 2017
Posts: 455

PostPosted: Sat Aug 28, 2021 4:52 pm    Post subject: Reply with quote

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
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immpy



Joined: 06 May 2017
Posts: 455

PostPosted: Sat Aug 28, 2021 5:12 pm    Post subject: Reply with quote

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
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Mogulmeister



Joined: 03 May 2007
Posts: 873

PostPosted: Sat Aug 28, 2021 6:22 pm    Post subject: Reply with quote

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.
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immpy



Joined: 06 May 2017
Posts: 455

PostPosted: Sat Aug 28, 2021 7:35 pm    Post subject: Reply with quote

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
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Mogulmeister



Joined: 03 May 2007
Posts: 873

PostPosted: Sat Aug 28, 2021 8:04 pm    Post subject: Reply with quote

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

Mogulmeister wrote:
As a post script there is another way using an ALS (Almost Locked Set) or to be accurate an AALS (Almost Almost Locked Set).



We have two ALS interacting:

Green {1,3,6,8} in (n-1=) 3 squares

Beige {1,2,3,4,8} in (n-1=) 4 squares

The restricted common should be 3 with the common candidate being 1 which can be removed from r2c8 because it can "see" all the other 1's in both ALS.

There's a wrinkle though.

The restricted common definition is bust because there's another 3 in r3c7. Otherwise it would fit and all would be well.

So logically we have a situation:

Either the ALS xz is true or the 3 is true in r3c7.

IF ALS is true then r2c8 <>1

If 3 is true (3)r3c7-(3=7)r3c3-(7=4)r2c3-(4=1)r2c9-r2c8 so r2c8 <>1

Makes the same elimination so all good.
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immpy



Joined: 06 May 2017
Posts: 455

PostPosted: Sun Aug 29, 2021 1:41 am    Post subject: Reply with quote

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
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Mogulmeister



Joined: 03 May 2007
Posts: 873

PostPosted: Sun Aug 29, 2021 6:41 am    Post subject: Reply with quote

Thanks Immp

You will see the almost strategies throughout sudoku. Sometimes itís 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].


Last edited by Mogulmeister on Tue Aug 31, 2021 8:19 am; edited 4 times in total
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Mogulmeister



Joined: 03 May 2007
Posts: 873

PostPosted: Sun Aug 29, 2021 9:43 am    Post subject: Reply with quote

Here's an "almost" solve of an extreme that I did with an "almost" XY wing from the old days! (2010)
Mogulmeister wrote:
Quote:
OK an almost XY wing (asterisks) <189> which has a fin (3) in r1c8

IF FIN false then r1c9, r3c4<>8 solves puzzle

otherwise

FIN true (19=3)r1c8-(3=1)r6c8-(1)r6c7; r6c7<>1 solves puzzle

Code:
+----------------+----------------+----------------+
| 2    6    13   | 5   *89   7    | 4   *139 139-8 |
| 5    89   13   | 6    4    189  | 7    2    1389 |
| 7    89   4    | 19-8 3    2    |*18   6    5    |
+----------------+----------------+----------------+
| 1    3    89   | 2    89   5    | 6    4    7    |
| 468  7    68   | 48   1    3    | 9    5    2    |
| 49   2    5    | 49   7    6    |8-1   13   138  |
+----------------+----------------+----------------+
| 689  5    689  | 189  2    1489 | 3    7    149  |
| 3    1    2    | 7    6    49   | 5    8    49   |
| 89   4    7    | 3    5    189  | 2    19   6    |
+----------------+----------------+----------------+
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Mogulmeister



Joined: 03 May 2007
Posts: 873

PostPosted: Sun Aug 29, 2021 11:22 am    Post subject: Reply with quote

Incidentally Immp,

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