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Jan 19 vh

 
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Sat Jan 19, 2008 2:19 pm    Post subject: Jan 19 vh Reply with quote

A simple UR (56) makes r6c7=9
a skyscraper (3:-r1c2=r8c2-r8c5=r2c5-) removes 3 from r1c4, r2c3
2 xwings (4: c14, 6: c16)
and a nice BUG+1
Code:

+--------------------------+--------------------------+--------------------------+
| 7       36      39       | 68      2       5        | 1       89      4        |
| 5       2       49       | 1       38      34       | 7       89      6        |
| 46      1       8        | 49      7       69       | 2       3       5        |
+--------------------------+--------------------------+--------------------------+
| 8       9       2        | 5       6       7        | 4       1       3        |
| 1       7       5        | 39      4       39       | 6       2       8        |
| 3       4       6        | 2       1       8        | 9       5       7        |
+--------------------------+--------------------------+--------------------------+
| 46      5       13       | 34      9       236      | 8       7       12       |
| 2       36      7        | 68      38      1        | 5       4       9        |
| 9       8       14       | 7       5       24       | 3       6       12       |
+--------------------------+--------------------------+--------------------------+

makes r7c6=3 (the "odd one out")

unconventional. nice.
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Sat Jan 19, 2008 2:33 pm    Post subject: Reply with quote

O.K., O.K.

there IS the conventional path.

After basics
Code:

+--------------------------+--------------------------+--------------------------+
| 7       36      39       | 3689    2       5        | 1       89      4        |
| 45      2       349      | 1       38      349      | 7       589     6        |
| 456     1       8        | 469     7       469      | 2       3       59       |
+--------------------------+--------------------------+--------------------------+
| 8       9       2        | 5       6       7        | 4       1       3        |
| 1       7       56       | 39      4       39       | 56      2       8        |
| 3       4       56       | 2       1       8        | 569     59      7        |
+--------------------------+--------------------------+--------------------------+
| 46      5       134      | 346     9       2346     | 8       7       12       |
| 2       36      7        | 368     38      1        | 59      4       59       |
| 9       8       14       | 7       5       24       | 3       6       12       |
+--------------------------+--------------------------+--------------------------+

The x-wing (6) c16 gets rid of 6 in r7c4,r3c4

Then later on

Code:
+--------------------------+--------------------------+--------------------------+
| 7       36      39       | 68      2       5        | 1       89      4        |
| 45      2       49       | 1       38      349      | 7       589     6        |
| 456     1       8        | 49      7       469      | 2       3       59       |
+--------------------------+--------------------------+--------------------------+
| 8       9       2        | 5       6       7        | 4       1       3        |
| 1       7       56       | 39      4       39       | 56      2       8        |
| 3       4       56       | 2       1       8        | 569     59      7        |
+--------------------------+--------------------------+--------------------------+
| 46      5       134      | 34      9       2346     | 8       7       12       |
| 2       36      7        | 68      38      1        | 59      4       59       |
| 9       8       14       | 7       5       24       | 3       6       12       |
+--------------------------+--------------------------+--------------------------+


xy(z)-wings galore:
xy: 34-46-36 (pivot r7c1) => r8c5 <>3
xyz: {1 3 4} ; r7c1<>4
xyz: {3 4 9} ; r3c6<>9
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Sat Jan 19, 2008 2:42 pm    Post subject: Reply with quote

I got the skyscraper. I had X-wings coming out my ears - for 4s, 6's and 9's in both columns and rows. I found the UR (56) leaving 79 in R6C7.
But I didn't reach any Bug+1 stage. (I had a Bug+2 - if there is such a thing). I finished with the xy-wing <346> with pivot R7C1.

(Also after learning about APE's from last VH - I couldn't find any here).
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Johan



Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium

PostPosted: Sat Jan 19, 2008 3:23 pm    Post subject: Reply with quote

There is a contradiction in R7, collapsing the grid in one move.

When R7C6=6 => R8C45=38 => R7C4=4 => R8C2=6 => R7C1=4 => R7C6 ≠ 6, solving the puzzle.

Code:

+--------------------------+--------------------------+--------------------------+
| 7         36        39   | 3689       2       5     | 1          89       4    |
| 45        2         349  | 1          38      349   | 7          589      6    |
| 456       1         8    | 469        7       469   | 2          3        59   |
+--------------------------+--------------------------+--------------------------+
| 8         9         2    | 5          6       7     | 4          1        3    |
| 1         7         56   | 39         4       39    | 56         2        8    |
| 3         4         56   | 2          1       8     | 569        59       7    |
+--------------------------+--------------------------+--------------------------+
| 46 =4     5         134  | 346 =4     9    6= 2346  | 8          7        12   |
| 2         36 =6     7    | 3-[6]8     38      1     | 59         4        59   |
| 9         8         14   | 7          5       24    | 3          6        12   |
+--------------------------+--------------------------+--------------------------+
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

PostPosted: Sat Jan 19, 2008 4:24 pm    Post subject: Reply with quote

Johan wrote:
There is a contradiction in R7, collapsing the grid in one move.

When R7C6=6 => R8C45=38 => R7C4=4 => R8C2=6 => R7C1=4 => R7C6 ≠ 6, solving the puzzle.



Johan, I follow the logic of the contradiction, but I fail to see how eliminating the 6 in r7c6 directly solves the puzzle.

Thanks .....

Ted
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Sat Jan 19, 2008 4:27 pm    Post subject: Reply with quote

I decided to use this for Medusa practice, after which an XY-Wing finished it off.

Quote:
(I had a Bug+2 - if there is such a thing)


Craig, there certainly is. There's also a BUG+3. But the +3 is the highest I've ever seen discussed.
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Johan



Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium

PostPosted: Sat Jan 19, 2008 4:33 pm    Post subject: Reply with quote

Quote:
Johan, I follow the logic of the contradiction, but I fail to see how eliminating the 6 in r7c6 directly solves the puzzle


Ted,

When <6> is eliminated in R7C6, then <6> must be placed in R3C6,

which eliminates <6> in R3C1
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Sat Jan 19, 2008 5:40 pm    Post subject: Reply with quote

Marty: This is as far as I got. Didn't reach Nataraj's Bug+1, so I assume I missed something obvious. (Actually- maybe I didn't - I shouldn't be so self-critical - maybe he did something he shouldn't have). But regardless!! Is there one of them Bug+2 s here that you alluded to. I can't find an explanation for these.

Cheers

Code:

+-----------+------------+---------+
| 7  36 39  | 68  2  5   | 1 89 4  |
| 5  2  49  | 1   38 34  | 7 89 6  |
| 46 1  8   | 49  7  69  | 2 3  5  |
+-----------+------------+---------+
| 8  9  2   | 5   6  7   | 4 1  3  |
| 1  7  5   | 39  4  39  | 6 2  8  |
| 3  4  6   | 2   1  8   | 9 5  7  |
+-----------+------------+---------+
| 46 5  134 | 34  9  236 | 8 7  12 |
| 2  36 7   | 368 38 1   | 5 4  9  |
| 9  8  14  | 7   5  24  | 3 6  12 |
+-----------+------------+---------+
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Sat Jan 19, 2008 6:04 pm    Post subject: Reply with quote

Craig,

the x-wing (4) takes out 4 in r7c3,
the triple (349) in c4 removes 3 from r8c4

the rest is BUG+1



Quote:
maybe he did something he shouldn't have


That is quite possible Smile
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Sat Jan 19, 2008 6:28 pm    Post subject: Reply with quote

cgordon wrote:
Marty: This is as far as I got. Didn't reach Nataraj's Bug+1, so I assume I missed something obvious. (Actually- maybe I didn't - I shouldn't be so self-critical - maybe he did something he shouldn't have). But regardless!! Is there one of them Bug+2 s here that you alluded to. I can't find an explanation for these.

Cheers

Code:

+-----------+------------+---------+
| 7  36 39  | 68  2  5   | 1 89 4  |
| 5  2  49  | 1   38 34  | 7 89 6  |
| 46 1  8   | 49  7  69  | 2 3  5  |
+-----------+------------+---------+
| 8  9  2   | 5   6  7   | 4 1  3  |
| 1  7  5   | 39  4  39  | 6 2  8  |
| 3  4  6   | 2   1  8   | 9 5  7  |
+-----------+------------+---------+
| 46 5  134 | 34  9  236 | 8 7  12 |
| 2  36 7   | 368 38 1   | 5 4  9  |
| 9  8  14  | 7   5  24  | 3 6  12 |
+-----------+------------+---------+

Craig,

I believe there is a valid BUG+3 pattern here. R7c3 must = 4 or r7c6 must = 3 or r8c4 = 3 to break up the Deadly Pattern. I haven't tried it, but at this point you could then try a triple-implication chain with those three numbers. This, I believe, is the Deadly Pattern:

Code:
+-----------+------------+---------+
| 7  36 39  | 68  2  5   | 1 89 4  |
| 5  2  49  | 1   38 34  | 7 89 6  |
| 46 1  8   | 49  7  69  | 2 3  5  |
+-----------+------------+---------+
| 8  9  2   | 5   6  7   | 4 1  3  |
| 1  7  5   | 39  4  39  | 6 2  8  |
| 3  4  6   | 2   1  8   | 9 5  7  |
+-----------+------------+---------+
| 46 5  13  | 34  9  26  | 8 7  12 |
| 2  36 7   | 68  38 1   | 5 4  9  |
| 9  8  14  | 7   5  24  | 3 6  12 |
+-----------+------------+---------+
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George Woods



Joined: 28 Mar 2006
Posts: 304
Location: Dorset UK

PostPosted: Sat Jan 19, 2008 6:49 pm    Post subject: bugs and XY wings Reply with quote

As I understand the Bug +1 logic ,, it says that wrong value in the 3candidate cell leaves nothing but doublets (going around in perpetuity - and no solution) and that just leaves one valid candidate there BUT what if the doublets have an XY wing included - as they clearly do here - is the BUG+1 logic valid? What is shown above as a "Deadly Pattern" is suceptible to the XY wing!
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Clement



Joined: 24 Apr 2006
Posts: 935
Location: Dar es Salaam Tanzania

PostPosted: Sat Jan 19, 2008 7:03 pm    Post subject: Daily Sudoku: Sat 19-Jan-2008 VH Reply with quote

Interesting. It begins with a UR of 5,6 in Blocks 4 and 6 leaving 9 in r6c7. This leads to two X-Wings of 4,s in columns c1&4 and 6,s in c1&6 respectively, removing the 4,s in r7c3 and r7c6 and 6 in r7c4.After these reductions an XY-Wing appears with {1,3}r7c3 as a pivot and {3,4}r7c4; {1,4}r9c3 as pincers eliminating 4 in r7c1. This solves the puzzle.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Sat Jan 19, 2008 7:10 pm    Post subject: Re: bugs and XY wings Reply with quote

George Woods wrote:
As I understand the Bug +1 logic ,, it says that wrong value in the 3candidate cell leaves nothing but doublets (going around in perpetuity - and no solution) and that just leaves one valid candidate there BUT what if the doublets have an XY wing included - as they clearly do here - is the BUG+1 logic valid?

Yes it is. All that means is that--as is very often the case--there are multiple techniques that are available.

Quote:
What is shown above as a "Deadly Pattern" is suceptible to the XY wing!


If I understand you correctly, you are saying that the Deadly Pattern grid contains XY-Wings. But you would never get to that grid because it is indeed the Deadly Pattern and thus no longer has a unique solution.
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Sat Jan 19, 2008 7:23 pm    Post subject: Reply with quote

Nataraj: You're absolutely right. There's a triple in C4 that leaves a Bug+1.

Marty: I don't really follow the Bug+3 thing. I think that a Bug+1 is when you just have one triple left - which forms an xyz wing with an xy and an xz. For some reason, which I've long forgotten, you make the triple equal x. But what you are implying here is that I can't do the same for the three xyz wings available. I have to do some work !!
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Sat Jan 19, 2008 7:32 pm    Post subject: Reply with quote

UR {56},

x-wing on 6,

then after a naked triple in col 4 which takes out the 3 that the skyscraper takes out

an x-wing on 4

then xy-wing on {3,4,9} pincers in r5c4 and r3c6
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keith



Joined: 19 Sep 2005
Posts: 3340
Location: near Detroit, Michigan, USA

PostPosted: Sat Jan 19, 2008 8:27 pm    Post subject: Reply with quote

There is a discussion of a BUG+3 in this thread:

http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=2171

While you are there, you can also learn about Medusa coloring.

Keith
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Sat Jan 19, 2008 9:12 pm    Post subject: Reply with quote

other than Johan's one step approach. this was a very nice "VH" to solve, considering that the puzzles have had a history of one step moves lately.
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Sat Jan 19, 2008 11:09 pm    Post subject: Reply with quote

I sussed out Keithís thread for Medusa colouring and BUG+3ís. Wasnít Medusa the one who had snakes growing out of her head. She was probably OK until she took up the colouring thing. The BUG+3s would have probably killed her. Definitely too much work for this loafer.
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keith



Joined: 19 Sep 2005
Posts: 3340
Location: near Detroit, Michigan, USA

PostPosted: Sun Jan 20, 2008 12:10 am    Post subject: Reply with quote

cgordon,

Medusa coloring was invented / discovered by Bob Hanson, a Chemistry Professor in Minnesota.

He has an interesting 3D way of looking at Sudoku puzzles. Imagine a 9x9x9 cube. Each layer contains information about each candidate. Layer 1 is <1>, layer 2 is <2>, etc.

So, if you go coloring on <1>, it is all in the first layer. But, when he saw that you could also color cells that have only two candidates, his 3D visualization reminded him of the intertwined snakes in Medusa's hair. Hence, the name.

Go here:

http://www.stolaf.edu/people/hansonr/sudoku/index.htm

and click on 3D view it the top right of the page. Wait for it to load. Then, drag on the image with your mouse. How cool is that??

Keith
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