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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Wed Oct 14, 2015 6:51 pm Post subject: A very difficult 6x6 |
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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  |
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Thu Oct 15, 2015 1:53 pm Post subject: |
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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 |
+-------------------+--------------+
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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 |
+---------------+-------------------+
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Kraken cell r1c2 : [1r4c5==3r3c5]-1r3c1; stte
2r1c2-(2=46)r4c26-(6=1)r4c5
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3r1c2-3r5c2=3r5c6-3r3c6=3r3c5
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6r1c2-6r1c46=6r2c5-(6=1)r4c5 |
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dongrave
Joined: 06 Mar 2014
Posts: 568
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| Posted: Thu Oct 15, 2015 10:28 pm Post subject: |
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| 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
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dongrave
Joined: 06 Mar 2014
Posts: 568
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| Posted: Fri Oct 16, 2015 11:50 am Post subject: |
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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
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| Posted: Fri Oct 16, 2015 11:52 am Post subject: |
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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 |
+----------------+---------------+
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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: 568
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| Posted: Sat Oct 17, 2015 2:28 am Post subject: |
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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
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| Posted: Mon Oct 19, 2015 11:18 pm Post subject: |
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| 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: 568
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| Posted: Tue Oct 20, 2015 2:45 am Post subject: |
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| 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
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| Posted: Wed Oct 21, 2015 3:02 am Post subject: |
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| 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: 568
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| Posted: Thu Oct 22, 2015 11:32 am Post subject: |
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| 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
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| Posted: Fri Oct 23, 2015 3:42 pm Post subject: |
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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: 568
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| Posted: Sun Nov 01, 2015 7:06 pm Post subject: |
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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 . |
+-------+-------+-------+
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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
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| Posted: Mon Nov 02, 2015 8:30 am Post subject: |
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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 |
+------------------+------------+------------------+
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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: 568
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| Posted: Mon Nov 02, 2015 10:32 pm Post subject: |
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| 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
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| Posted: Tue Nov 03, 2015 2:39 pm Post subject: |
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Don,
A couple of other tips:
When I solve a puzzle I always write down a 3x3 grid like this:
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: |
| |
--------
| |
--------
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or
...|...|...
...|...|...
...|...|...
-----------
...|...|...
...|...|...
...|...|...
-----------
...|...|...
...|...|...
...|...|...
and another
123
456
789
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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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