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VH Plus

 
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Earl



Joined: 30 May 2007
Posts: 546
Location: St Louis MO

PostPosted: Tue Jul 24, 2007 6:39 pm    Post subject: VH Plus Reply with quote

Today's VH did not confuse me enough.
This one has. What am I missing?

Earl


Code:

+---------------+-----------------+-------------+
| 1278 15  9    | 2578 125   1258 | 4    3  6   |
| 6    3   28   | 278  4     9    | 78   1  5   |
| 178  4   158  | 6    15    3    | 9    2  78  |
+---------------+-----------------+-------------+
| 9    7   2356 | 235  8     256  | 256  4  1   |
| 123  156 125  | 9    12356 4    | 2578 58 278 |
| 4    8   1256 | 25   7     1256 | 256  9  3   |
+---------------+-----------------+-------------+
| 38   9   4    | 1    35    7    | 258  6  28  |
| 5    2   368  | 38   9     68   | 1    7  4   |
| 18   16  7    | 4    256   258  | 3    58 9   |
+---------------+-----------------+-------------+

Play this puzzle online at the Daily Sudoku site


Last edited by Earl on Tue Jul 24, 2007 10:53 pm; edited 1 time in total
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Tue Jul 24, 2007 8:50 pm    Post subject: Reply with quote

Earl,

You've selected quite a tough one this time! It's got some nice stuff in it.

First, examine <2>s in Box 9 and Row 7 for some cleanup. This opens up a fairly evident 4-cell XY-Chain.

There is also an X-Wing available. After that, things get more complicated... unless I overlooked something.

There is a very interesting ER that eliminates a <5>. In fact there are two of them that eliminate the same <5>. That is a clue for something more valuable than the ER, however: a Color-Wing.

If you can find that, then the rest of the puzzle can be solved with a sequence of three longish XY-Chains. (You will want to focus on C5.)

Note: There is a very interesting implication chain approach that also does the work of the first two of those last three XY-Chains. I don't want to spoil things now. But, I might post more later. Some of the real toughie sudokus lead me to resort to such implication chain-type solutions.
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Wed Jul 25, 2007 12:37 pm    Post subject: Reply with quote

Iím sure that Asellusís approach is the rational way to proceed but, just for fun, Iíve marked the cells open to 5 in the four rows 3, 4, 6 and 7.

Code:
+----------------+--------------------+--------------+
| 1278 15   9    |  2578  125    1258 |  4    3  6   |
| 6    3    28   |  278   4      9    |  78   1  5   |
| 178  4   F158  |  6    F15     3    |  9    2  78  |
+----------------+--------------------+--------------+
| 9    7   F2356 | F235   8     F256  | F256  4  1   |
| 123  156  125  |  9     12356  4    |  2578 58 278 |
| 4    8   F1256 | F25    7     F1256 | F256  9  3   |
+----------------+--------------------+--------------+
| 38   9    4    |  1    F35     7    | F258  6  28  |
| 5    2    368  |  38    9      68   |  1    7  4   |
| 18   16   7    |  4     256    258  |  3    58 9   |
+----------------+--------------------+--------------+

You will see that these cells also have a transverse cover of four houses: box 5 and columns 3, 5 and 7. This 4-fish eliminates 5 from all other cells in the box and columns.

I think some call the pattern a franken jellyfish. Whatever itís called, it reveals an xy-wing pivoted on the (26) in r9c5 with pincers r15 and r9c2 which eliminates 1 from r1c2 and solves the puzzle.

Steve
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Wed Jul 25, 2007 8:09 pm    Post subject: Reply with quote

A Franken Jellyfish, eh? I'm going to have to mull that one over to figure it out! It does resemble an X-Wing merged with a sort of Swordfish-Jellyfish "hybrid". (I've lately been learning "Sashimi" Fish! It's all pretty fishy!)

I'll show the Color Wing using those <5>s. But first, I'll apply the XY-Chain with pincers R9C1 and R3C5 that eliminates <1> in R3C1 and produces a bit more simplification. (It is not necessary for the Color Wing but comes in handy later.) This gets us here:

Code:
+----------------+--------------------+-----------------+
| 278  1R5  9    |  2578  125    1258 |  4       3  6   |
| 6    3    28   |  278   4      9    |  78      1  5   |
| 78   4    1G5  |  6    B1R5    3    |  9       2  78  |
+----------------+--------------------+-----------------+
| 9    7    2356 |  235   8      256  |  256     4  1   |
| 123 #1G56 12-5 |  9     123-56 4    |  2-578 #g58 278 |
| 4    8    1256 |  25    7      1256 |  256     9  3   |
+----------------+--------------------+-----------------+
| 38   9    4    |  1    B3r5    7    |  2g58    6  28  |
| 5    2    368  |  38    9      68   |  1       7  4   |
| 18   16   7    |  4     256    258  |  3      r58 9   |
+----------------+--------------------+-----------------+


The Color Wing is marked as follows. The Bridge cells are B. The two color chains are red/green, one lower case and one upper case. The Bridge is red. The green pincers are #. Three <5>'s are eliminated.

After that, there are various XY-Chains as I noted before. However, there is some interesting implication stuff.

Code:
+----------------+--------------------+---------------+
| 278  15   9    |  2578  125    1258 |  4     3  6   |
| 6    3    28   |  278   4      9    |  78    1  5   |
| 78   4    15   |  6     15     3    |  9     2  78  |
+----------------+--------------------+---------------+
| 9    7    2356 |  235   8      256  |  256   4  1   |
| 123  156  12   |  9     1236   4    |  278   58 278 |
| 4    8    1256 |  25    7      1256 |  256   9  3   |
+----------------+--------------------+---------------+
| 38   9    4    |  1     35     7    |  258   6  28  |
| 5    2    368  |  38    9      68   |  1     7  4   |
| 18   16   7    |  4     256    258  |  3     58 9   |
+----------------+--------------------+---------------+


The {125} ALS in Box 2 C5 got my attention. If R5C5 is <2> then R5C3 is <1>. But also, R9C5 is <6> and R9C2 is <1>. This is impossible since it eliminates all candidates for <1> from Box 1 (or causes two <5>s). A similar result occurs if R5C5 is <1>.

Another way of seeing it notes that in both cases R7C5 would be <3> which pivots to <1> in R9C1 resulting in two <1>s in Box 7.

So, either way, <1> and <2> can be eliminated from R5C5.

It isn't necessarily the most elegant option. But, it shows how ALS can be used in chaining.


Last edited by Asellus on Thu Jul 26, 2007 7:30 am; edited 1 time in total
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Earl



Joined: 30 May 2007
Posts: 546
Location: St Louis MO

PostPosted: Wed Jul 25, 2007 8:59 pm    Post subject: Truly VH Reply with quote

Asellus,

Regarding the Color Wing: since the wings are symetrical, could the bridge be green as well, and all other 5 candidates removed from C5?

Also I do not understand the Franken Fish.
If someone has the patience, please explain how a box mixes with rows and columns and subsequent eliminations are made.

Thanks

Earl
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Wed Jul 25, 2007 9:51 pm    Post subject: Reply with quote

The fish is childís play. It helps if you stand back and empty your mind. Forget the pattern. Forget the size of the puzzle. Ready?

We have four lines in which 5 is to be entered. The available places in these lines make up a set of cells. Call this set of cells C. All that matters is that four 5s must be entered into C.

Now suppose C is covered by (= forms part of) four houses distinct from the four lines you began with. As each house can contain only one 5, there must be one in each house. The conclusion is that no cell outside C in these houses can contain a 5.

The argument is just the same for the familiar classical x-wing, a 100-fish in a 225 x 225 puzzle Ö

Steve
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Thu Jul 26, 2007 8:16 am    Post subject: Reply with quote

Earl,

I think you are right! But, I don't think it is because of the symmetry. Rather, it is because the two pincers in the Color Wing are themselves "buddies" (i.e. they can "see" each other). After the other <5>s in R5 are eliminated, there is now a strong link between the pincer <5>s. In essence, one of the arms of the Color Wing "flips" color. Take the lower case red/greens and reverse them into upper case colors (g become R and r becomes G). We then get a basic Color Wrap back to the bridge cells, which are now R and G and thus elliminate the other <5>s in C5. So, the Color Wing that collapses to a Color Wrap causes exactly the same elliminations as the Franken Jellyfish. There is probably a very good reason for this. But, don't ask me to tell you what it is!

Steve,

That is the clearest explanation you've given of the Franken Fish concept. I get it now. I didn't actually get it in your Franken Swordfish (or whatever species it was!) post in the other section of this board because the example was also a straightforward Color Wrap. The statement that a Box can serve as one of the limiting houses as well as a Row or Column is now clear.

Probably, it was your instruction about clearing my mind that did it!

Earl,

Perhaps Steve's explanation made it as clear to you as it did to me. But, if not, I'll reiterate in my own way, now that I've grasped it.

In a conventional "fish", say a swordfish, a candidate is limited to 3 Rows within 3 Columns (or vice versa). It is important to see that Rows and Columns are just "Houses" that intersect in an obvious way. But, each of them also intersects with Boxes, the "other" sort of House. Any House, no matter the type, can serve as a constraint.

In a "Franken" fish, a Box provides one of the alternate constraining houses.

In the Franken Jellyfish case in this puzzle, we started with 4 Rows as the initial constraints. Now, if you look at the cells Steve marked "F," they are in 5 Columns, C34567. That is one too many Column( House)s for a conventional Jellyfish. But, the "F" values in C46 are all contained within Box 5. So, we can "replace" the two Houses C46 with the single House Box 5. Seen this way, there are now just four "alternate" Houses, C357 and Box 5, as Steve explained. Since this fully determines the possible placements, all other candidates in C357 and Box 5 can be eliminated.

If you still don't see it, try clearing your mind some more! (You'll certainly need to get experienced at clearing your mind in order to find the dang things on your own!)
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Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Fri Jul 27, 2007 9:13 am    Post subject: Reply with quote

Earl,

I have added a link below from the very lucid Havard who I think gives a good overview on fish (including frankenfish).

http://www.sudoku.frihost.net/forum/viewtopic.php?t=990

Mogul
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Earl



Joined: 30 May 2007
Posts: 546
Location: St Louis MO

PostPosted: Fri Jul 27, 2007 5:04 pm    Post subject: Truly lVH Reply with quote

Thanks to all of you for the explanations of FISH.

I am still digesting some of it and trying to expand my thinking beyond intersecting lines.

Hope to say "Eureka!" soon.

Earl
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Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Sat Jul 28, 2007 9:01 am    Post subject: Reply with quote

I found it helps to start with x-wing which I guess you're totally happy with then learn about swordfish - then sashimi swordfish. You get past the original simple idea of a 3x3 or 4x4 grid. Once you have understood those general principles then upsizing the pattern is no problem.

PS Steve, I like the way you used the word "transverse" - you're not a motoring enthusiast as well are you ?
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