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A very difficult 6x6

 
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Wed Oct 14, 2015 6:51 pm    Post subject: A very difficult 6x6 Reply with quote

6x6 puzzles are so easy I usually don't bother. But, I found this on another site:

Code:
+-------------+-------------+
| .   .   .   |   .   4   . |
| .   1   .   |   3   .   5 |
+-------------+-------------+
| .   .   .   |   2   .   . |
| .   .   3   |   .   .   . |
+-------------+-------------+
| 6   .   2   |   .   5   . |
| .   5   .   |   .   .   . |
+-------------+-------------+


Can you solve it? How?

Keith Razz
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JC Van Hay



Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium

PostPosted: Thu Oct 15, 2015 1:53 pm    Post subject: Reply with quote

r4c4=5
Analysis of the puzzle from R2 and R5 gives the following 2 steps :
Code:
+-------------------+--------------+
| 2(35) 2(3)6 (5)-6 | 1(6) 4   126 |
| 24    1     46    | 3    26  5   |
+-------------------+--------------+
| 145   46    1456  | 2    136 346 |
| 124   246   3     | 5    16  46  |
+-------------------+--------------+
| 6     (34)  2     | (14) 5   13  |
| 134   5     14    | 46   236 236 |
+-------------------+--------------+
AIC : [5r1c3=(5-3)r1c1=3r1c2-(3=4)r5c2-(4=1)r5c4-(1=6)r1c4]-(6=5)r1c3; r3c1=5
Code:
+---------------+-------------------+
| 23  (236) 5   | 1(6) 4      12(6) |
| 24  1     46  | 3    2(6)   5     |
+---------------+-------------------+
| 5   46    146 | 2    -1(3)6 (3)46 |
| 124 (246) 3   | 5    (16)   (46)  |
+---------------+-------------------+
| 6   (3)4  2   | 14   5      1(3)  |
| 134 5     14  | 46   236    236   |
+---------------+-------------------+
Kraken cell r1c2 : [1r4c5==3r3c5]-1r3c1; stte

2r1c2-(2=46)r4c26-(6=1)r4c5
||
3r1c2-3r5c2=3r5c6-3r3c6=3r3c5
||
6r1c2-6r1c46=6r2c5-(6=1)r4c5
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dongrave



Joined: 06 Mar 2014
Posts: 563

PostPosted: Thu Oct 15, 2015 10:28 pm    Post subject: Reply with quote

Two steps? I found a simple contradiction in no time that solved it in one step - and I usually have a heck of a time finding chains for 9x9s. This was the first 6x6 that I ever did - and it sure did seem simple. I don't know, maybe I screwed up (and didn't notice).
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Fri Oct 16, 2015 8:09 am    Post subject: Reply with quote

don,

Can you please post your solution?

Here is the thread where I found the original. I have still not solved it for myself.

http://forum.enjoysudoku.com/post12737.html#p12737

Keith
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dongrave



Joined: 06 Mar 2014
Posts: 563

PostPosted: Fri Oct 16, 2015 11:50 am    Post subject: Reply with quote

keith wrote:
don,

Can you please post your solution?

Here is the thread where I found the original. I have still not solved it for myself.

http://forum.enjoysudoku.com/post12737.html#p12737

Keith

If I can find it! I don't think I threw it out. I remember there was a bivalue cell (I think it was 1,4) and one value lead to the solution and the other lead to a contradiction (I think it was two 4's in column 1).
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JC Van Hay



Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium

PostPosted: Fri Oct 16, 2015 11:52 am    Post subject: Reply with quote

A simpler equivalent 2nd step :
Code:
+----------------+---------------+
| 23    236 5    | 16 4     126  |
| (24)  1   46   | 3  (26)   5   |
+----------------+---------------+
| 5     46  146  | 2  -1(3)6 346 |
| (1)24 246 3    | 5  (16)   46  |
+----------------+---------------+
| 6     34  2    | 14 5      13  |
| (134) 5   14   | 46 2(3)6  236 |
+----------------+---------------+
Kraken cell r6c1 : (1=6)r4c5-(6=2)r2c5-(2=4)r2c1-4r6c1=*[1r4c5=1r4c1-(1=*3)r6c1-3r6c5=3r4c5] -> [1r4c5==3r3c5]-1r3c1; stte
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dongrave



Joined: 06 Mar 2014
Posts: 563

PostPosted: Sat Oct 17, 2015 2:28 am    Post subject: Reply with quote

Hi Keith, I couldn't find my worksheet so I did the puzzle again tonight and I found that even though I did solve it in no time, it wasn't a one-stepper like I thought. After the basics, I ended up with the following:
Code:

 +----------------+---------------+
 | 23    236 5    | 16 4     126  |
 | 24    1   46   | 3  26    5    |
 +----------------+---------------+
 | 5     46  146  | 2  136   346  |
 | 124   246 3    | 5  16    46   |
 +----------------+---------------+
 | 6     34  2    | 14 5      13  |
 | 134   5   14   | 46 236    236 |
 +----------------+---------------+

Then, like I mentioned earlier, I took the 14 bi-value cell at r5c4 and assumed that it was a 4 which gave me the following:
Code:

 +-------------------+--------------+
 | 3     26    5     | 1    4   26  |
 | 24    1     46    | 3    26  5   |
 +-------------------+--------------+
 | 5     46    16    | 2    136 346 |
 | 12    246   3     | 5    16  46  |
 +-------------------+--------------+
 | 6     3     2     | 4    5   13  |
 | 14    5     14    | 6    23  23  |
 +-------------------+--------------+

Then at this point I used the 16-2 XY Wing with pivot at r4c5 so r2c1<>2 which solves it. I must have forgotten about this step when I posted my message earlier.

Then I went back to the original grid after the basics:
Code:

 +----------------+---------------+
 | 23    236 5    | 16 4     126  |
 | 24    1   46   | 3  26    5    |
 +----------------+---------------+
 | 5     46  146  | 2  136   346  |
 | 124   246 3    | 5  16    46   |
 +----------------+---------------+
 | 6     34  2    | 14 5      13  |
 | 134   5   14   | 46 236    236 |
 +----------------+---------------+

and assumed that r5c4=1 and arrived at the following contradiction that r2c1=4 and r4c1=4.
If r5c4=1, then r1c4=6 so r2c5=2 so r2c1=4 and r6c5<>2. Also, if r5c4=1, then r6c4=4 so r6c3=1 so r6c1=3 so (r6c5<>3 so it's 6 so r4c5=1 so r4c1<>1) and (r5c2=4 so r3c2=6 so r4c2<>6 so r4c2=2 so r4c1<>2) so since r4c1<>1 and r4c1<>2, it must be 4; contradiction.

I can't believe someone of your caliber couldn't find a solution to this puzzle. I've seen you come up with solutions for 9x9's that I couldn't find in my lifetime so my guess would be that you're looking for the most elegant solution possible. (These 6x6's seem so easy!)
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Mon Oct 19, 2015 11:18 pm    Post subject: Reply with quote

dongrave wrote:
I can't believe someone of your caliber couldn't find a solution to this puzzle. I've seen you come up with solutions for 9x9's that I couldn't find in my lifetime so my guess would be that you're looking for the most elegant solution possible. (These 6x6's seem so easy!)


Thank you for the compliment. Every 6x6 I've seen in past has been trivial.

I think my brain is wired for 9x9, and I am also a patterns guy. I don't do chains, as a rule.

Looking at this 6x6 is, to me, like looking at an upside down map. Familiar, but not readable.

Keith
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dongrave



Joined: 06 Mar 2014
Posts: 563

PostPosted: Tue Oct 20, 2015 2:45 am    Post subject: Reply with quote

keith wrote:
dongrave wrote:
I can't believe someone of your caliber couldn't find a solution to this puzzle. I've seen you come up with solutions for 9x9's that I couldn't find in my lifetime so my guess would be that you're looking for the most elegant solution possible. (These 6x6's seem so easy!)


Thank you for the compliment. Every 6x6 I've seen in past has been trivial.

I think my brain is wired for 9x9, and I am also a patterns guy. I don't do chains, as a rule.

Looking at this 6x6 is, to me, like looking at an upside down map. Familiar, but not readable.

Keith

Keith, I hope someday to know HALF of what you or Marty have forgotten!
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Wed Oct 21, 2015 3:02 am    Post subject: Reply with quote

dongrave wrote:
Keith, I hope someday to know HALF of what you or Marty have forgotten!


Don,

That is quite generous, thank you.

Your comment did inspire me to write down a technique I have used for many years, but never seen explained. Take a look here:

http://forum.enjoysudoku.com/finding-the-possibility-of-single-candidate-eliminations-t32748.html

Gosh, it's been years and years since anyone has written such a basic tutorial on solving these devils!

(I put it on the other forum because I got frustrated with the formatting xx here.)

Keith
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dongrave



Joined: 06 Mar 2014
Posts: 563

PostPosted: Thu Oct 22, 2015 11:32 am    Post subject: Reply with quote

Very interesting Keith! Thanks for that! After a while I stopped spending time looking where there wasn't much available but I wasn't aware of the exact criteria as you explained. That was very informative! If you've got other insights like this that you'd like to share, I'd love to see them! Hey! You know what? You should write a book about advanced techniques like this! All I've ever seen out there are the same old run-of-the-mill books that go over the basics. Oh! And you know what I'd really like to see? A book dedicated to explaining Eureka notation for the simplest to the most complex examples along with detailed explanations! That would be great! Thanks again, Don.
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Fri Oct 23, 2015 3:42 pm    Post subject: Reply with quote

Don,

Do please try to use this. My method is:

If a box has candidates only in a row or in a column (Type A or B), it cannot participate in a single-digit elimination. If there are not at least four remaining (Type C) blocks arranged in a rectangle, don't bother looking for kites, skyscrapers, X-wings, swordfish, etc. in that digit.

And then, only look for the pattern in the Type C boxes.

As a further point, eliminations may occur in Type A or B boxes, but they are rare.

So far as the Eureka exposition is concerned, its like German to me. I can read it, but I cannot write it. As a winter project, I'll think about setting up some kind of Wiki or Google doc for people to collaborate on a definition of the Eureka language.

Best wishes,

Keith
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dongrave



Joined: 06 Mar 2014
Posts: 563

PostPosted: Sun Nov 01, 2015 7:06 pm    Post subject: Reply with quote

Hi Keith,

I tried your method today on the following Evil Sudoku1.net puzzle (#514872) and I think there's a chain hidden in there somewhere that I'm missing.

Code:

nš514872 Evil
 +-------+-------+-------+
 | . 4 . | 6 . 7 | . . . |
 | 1 9 . | . . . | 4 . . |
 | . . . | . 1 . | 8 5 . |
 +-------+-------+-------+
 | 9 . . | . 3 1 | . . 7 |
 | . . 3 | 5 . 6 | 1 . . |
 | 7 . . | 8 9 . | . . 5 |
 +-------+-------+-------+
 | . 7 2 | . 8 . | . . . |
 | . . 4 | . . . | . 9 8 |
 | . . . | 7 . 5 | . 3 . |
 +-------+-------+-------+


After the basics I checked the boxes for Type C patterns and I spent most of my time focusing on the 2's in boxes 3 and 6. I looked and looked but I still don't see it. Most of the Sudoku1.net Evil puzzles that I've solved in the past required a forcing chain but I didn't see that either. Does your method work for chains (or assumptions that lead to contradictions)? I went ahead and solved it by assuming that one of the bivalue cells was 2, and it lead to a contradiction but I don't see a nice translation of it to a forcing chain or anything. Is there something lurking in there that I'm missing? Thanks, Don.
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JC Van Hay



Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium

PostPosted: Mon Nov 02, 2015 8:30 am    Post subject: Reply with quote

Hi Don,

1. Only one solved cell for the digit 2, but only 3 Type C boxes, B356, for the digit 2. Therefore : no N>1-Fish(2).
2. An N>1-Fish can only be found for the digit 6 because of the rectangle B4679 of 4 Type C boxes for the digit 6.
3. 2-Fish(6R67)-6r9c2; 1-Fish(6B6)-6r3c1.
4. 6R6 or 6R7 -> r6c2=6

r6c2=6 or r6c8=6, r4c7=2=r5c2, r6c2=6
or
r7c1=6=r9c7, r4c7=2=r5c2, r6c2=6 or r7c8=6=r6c2

5. The 2-Fish(6R67) is therefore optional.
6. Synthesis :
Code:
+------------------+------------+------------------+
| 2358  4      58  | 6   25  7  | 9     12     123 |
| 1     9      56  | 3   25  8  | 4     7      26  |
| 236   36     7   | 49  1   49 | 8     5      236 |
+------------------+------------+------------------+
| 9     2568   568 | 24  3   1  | (26)  2468   7   |
| 4     8(2)   3   | 5   7   6  | 1     8(2)   9   |
| 7     -2(6)  1   | 8   9   24 | 3     24(6)  5   |
+------------------+------------+------------------+
| 36    7      2   | 19  8   39 | 5     16     4   |
| 35    135    4   | 12  6   23 | 7     9      8   |
| 68    168    9   | 7   4   5  | 26    3      12  |
+------------------+------------+------------------+
S-Wing : 6r6c2=6r6c8-(6=2)r5c2-2r5c8=2r5c2 :=> r6c2≠2, r6c2=6; stte

JC
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dongrave



Joined: 06 Mar 2014
Posts: 563

PostPosted: Mon Nov 02, 2015 10:32 pm    Post subject: Reply with quote

Oh! Of course! Thanks for explaining that JC! I can see that I need to work on recognizing the Type C boxes.
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Tue Nov 03, 2015 2:39 pm    Post subject: Reply with quote

Don,

A couple of other tips:

When I solve a puzzle I always write down a 3x3 grid like this:
Code:

123
456
789

And I black out each digit as it is solved in the puzzle.

The method I describe is for single-digit eliminations, so it will not help you find XY-wings or chains.

What I find very useful is to make small tic-tac-toe grids:
Code:

  |  |
--------
  |  |
--------
  |  |

or

...|...|...
...|...|...
...|...|...
-----------
...|...|...
...|...|...
...|...|...
-----------
...|...|...
...|...|...
...|...|...

and another

123
456
789

Now, for each digit, put a dot in the grid at each cell where it is a candidate. This is a quick way to identify box-line interactions. once you are done with those, you can quickly see if you have Type C cells in a rectangle so you should bother looking for Turbot Fish, etc. If not, black out the digit and move to the next one. with a little practice, you can make these diagrams without first doing the pencil marks. With a little more practice you can recognize the Type C cells without pencil marks or diagrams.

This is probably as clear as mud. I'll find an example.

Keith
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