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VH (+): Set A Puzzle 31

 
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Mon Nov 24, 2008 1:57 am    Post subject: VH (+): Set A Puzzle 31 Reply with quote

nataraj formatting tool. All rights reserved.

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

Play online

I plan to post puzzles with a variety of difficulty levels, so they won't all be this difficult/easy -- depending on the individual.

I'm particulary fond of this puzzle because it contains a Kraken X-Wing that performs 6/7 eliminations. Fortunately, you don't need it to solve the puzzle. If you get energetic, you can search for it after basics.
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Mon Nov 24, 2008 4:36 am    Post subject: Reply with quote

I had a two-stepper as follows:
Quote:
An xy-wing457 with pivot <57> at r7c1, and
A Type 1 UR15 at r56c37 to complete it.


I strongly suspect that a one-step solution is available, but I did not look for it. I did find a lot of basics after both VH steps.

Ted Smile
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re'born



Joined: 28 Oct 2007
Posts: 80

PostPosted: Mon Nov 24, 2008 7:12 pm    Post subject: Re: VH (+): Set A Puzzle 31 Reply with quote

daj95376 wrote:

I'm particulary fond of this puzzle because it contains a Kraken X-Wing that performs 6/7 eliminations. Fortunately, you don't need it to solve the puzzle. If you get energetic, you can search for it after basics.

I could use a hint/help. I found 2 Kraken X-wings on 5 that make 4 and 3 eliminations, respectively. Since 4+3=7, I ask, is this what you had in mind?
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Mon Nov 24, 2008 10:22 pm    Post subject: Re: VH (+): Set A Puzzle 31 Reply with quote

re'born wrote:
daj95376 wrote:

I'm particulary fond of this puzzle because it contains a Kraken X-Wing that performs 6/7 eliminations. Fortunately, you don't need it to solve the puzzle. If you get energetic, you can search for it after basics.

I could use a hint/help. I found 2 Kraken X-wings on 5 that make 4 and 3 eliminations, respectively. Since 4+3=7, I ask, is this what you had in mind?

Hint 1 wrote:
Candidate (5)

Hint 2 wrote:
rows 3 & 4

Hint 3 wrote:
Exterior fin cell [r4c9] indirectly eliminates seven cells by forcing: [r6c1]=5, [r7c7]=5, and [r8c3]=5

Hint 4 wrote:
X-Wing directly eliminates six of these cells, and indirectly eliminates the seventh cell

Hint 5 wrote:
[r6c4]<>5 and [r678c56]<>5
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re'born



Joined: 28 Oct 2007
Posts: 80

PostPosted: Tue Nov 25, 2008 3:22 am    Post subject: Reply with quote

Thanks, daj. The hints help and I think for the first time I'm getting what a kraken x-wing is. It is like transport. The indirect exclusion is a little shady for me. I get it, but only doing a little clearing of locked candidates in my head.

Incidentally, there is another kraken x-wing on 5.
Other Kraken wrote:
columns 1 and 7 eliminating 5 from r6c456.
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Tue Nov 25, 2008 5:18 am    Post subject: Re: VH (+): Set A Puzzle 31 Reply with quote

daj95376 wrote:


I'm particulary fond of this puzzle because it contains a Kraken X-Wing that performs 6/7 eliminations. .


Danny, I have looked at your hints but I am still lost. I believe I found the Kraken x-wing, but I thought that a candidate deletion must be "seen" by both the normal x-wing and the fin. I don't understand how the fin in r9c4 is transported to provide any deletions.

Here is my code after basics.
Code:

 | 3       1       8       | 7       6       2       | 9       5       4       |
 | 2       5       6       | 9       4       3       | 7       1       8       |
 | 4       9       7       | 1       58      58      | 2       6       3       |
 |-------------------------+-------------------------+-------------------------|
 | 9       237     4       | 6       12357   157     | 8       23      257     |
 | 6       8       1235    | 245     23579   4579    | 145     2349    257     |
 | 57      237     1235    | 2458    235789  45789   | 145     2349    6       |
 |-------------------------+-------------------------+-------------------------|
 | 57      6       25      | 3       2579    4579    | 45      8       1       |
 | 8       234     235     | 245     125     145     | 6       7       9       |
 | 1       47      9       | 458     578     6       | 3       24      25      |


Help please ......

Ted
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Tue Nov 25, 2008 8:47 am    Post subject: Re: VH (+): Set A Puzzle 31 Reply with quote

tlanglet wrote:
Danny, I have looked at your hints but I am still lost. I believe I found the Kraken x-wing, but I thought that a candidate deletion must be "seen" by both the normal x-wing and the fin.

I can understand your confusion. My head went TILT when I was introduced to a Kraken fish. As it turns out, the whole premise of a Kraken fish is that the exterior fin cell only results in overlapping eliminations by indirectly seeing the same eliminations as the fish.

Technically speaking, the exterior fin cell can force other candidates to contribute to the indirect eliminations, but I always use the same candidate as the fish.

===== ===== ===== ===== =====

I'm impressed with the interest in the Kraken X-Wings in (5) after basics. Let's strip away the excess candidates and look at the Kraken X-Wing that caught my attention.

Kraken X-Wing r34\c56 w/exterior fin cell [r4c9]:

Code:
 X-Wing eliminations
 +-----------------------------------+
 |  .  .  .  |  .  .  .  |  .  5  .  |
 |  .  5  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  . *5 *5  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  . *5 *5  |  .  .  5  |
 |  .  .  5  |  5 -5 -5  |  5  .  5  |
 |  5  .  5  |  5 -5 -5  |  5  .  .  |
 |-----------+-----------+-----------|
 |  5  .  5  |  . -5 -5  |  5  .  .  |
 |  .  .  5  |  5 -5 -5  |  .  .  .  |
 |  .  .  .  |  5 -5  .  |  .  .  5  |
 +-----------------------------------+

Code:
 X-Wing (+ Locked Candidate 1 indirect eliminations)
 +-----------------------------------+
 |  .  .  .  |  .  .  .  |  .  5  .  |
 |  .  5  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  . *5 *5  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  . *5 *5  |  .  .  5  |
 |  .  .  5  | -5 -5 -5  |  5  .  5  |
 |  5  .  5  | -5 -5 -5  |  5  .  .  |
 |-----------+-----------+-----------|
 |  5  .  5  |  . -5 -5  |  5  .  .  |
 |  .  .  5  | +5 -5 -5  |  .  .  .  |
 |  .  .  .  | +5 -5  .  |  .  .  5  |
 +-----------------------------------+

Code:
 eliminations resulting from [r4c9]
 +-----------------------------------+
 |  .  .  .  |  .  .  .  |  .  5  .  |
 |  .  5  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  5  5  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  . -5 -5  |  .  . +5  |
 |  .  . -5  |  5  5  5  | -5  . -5  |
 | +5  . -5  | -5 -5 -5  | -5  .  .  |
 |-----------+-----------+-----------|
 | -5  . -5  |  . -5 -5  | +5  .  .  |
 |  .  . +5  | -5 -5 -5  |  .  .  .  |
 |  .  .  .  |  5  5  .  |  .  . -5  |
 +-----------------------------------+

Code:
 Kraken X-Wing (common/overlapping) eliminations
 +-----------------------------------+
 |  .  .  .  |  .  .  .  |  .  5  .  |
 |  .  5  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  5  5  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  5  5  |  .  .  5  |
 |  .  .  5  |  5  5  5  |  5  .  5  |
 |  5  .  5  | -5 -5 -5  |  5  .  .  |
 |-----------+-----------+-----------|
 |  5  .  5  |  . -5 -5  |  5  .  .  |
 |  .  .  5  |  5 -5 -5  |  .  .  .  |
 |  .  .  .  |  5  5  .  |  .  .  5  |
 +-----------------------------------+

Since all of the exterior fin cell eliminations are indirect, I tend to cheat and allow indirect eliminations from the X-Wing as well. That's why [r6c4]<>5 is included as the seventh elimination.
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Tue Nov 25, 2008 1:18 pm    Post subject: Reply with quote

Idea Idea Idea

The light may have just turned on!

To restate the approach: "For the external fin, all of the "implications" of the fin being true (such as a naked single or lock candidate) are included in the set of cells for possible elimination. This set is then overlaid on the corresponding set for the normal x-wing to finally determine the actual eliminations."

I assume that this approach works for multiple external fins. Thus, in this example assuming external fins in both r4c89, I would determine the third set of implications due to r4c8 and overlay the other two sets.

I also assume this idea of using the implications of an external fin works for any other technique that admits a fin such as a finned xy-wing, but I have not given that any thought.

Thanks again Danny.

Ted
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re'born



Joined: 28 Oct 2007
Posts: 80

PostPosted: Tue Nov 25, 2008 2:19 pm    Post subject: Reply with quote

Thanks for the keen explanation, daj! Here is the process I'm using to find kraken eliminations:

Find a potential x-wing with one too many cells. Observe the potential eliminations of the x-wing. Then transport (in the sense of a weak inference followed by a strong inference) the extra cell around the grid until it sees some of the potential eliminations. These will be true eliminations.

In your example, I transport r4c9 to r9c45 (via r9c9) to kill the 5's in r78c56 and then I go back and transport r4c9 to r6c1 (via r9c9, r7c7 and r7c1) to kill the 5's in r6c56.

I don't have a good handle on the indirect eliminations yet.

tlanglet wrote:
I also assume this idea of using the implications of an external fin works for any other technique that admits a fin such as a finned xy-wing, but I have not given that any thought.

It is definitely true. The logic is exactly the same.
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Tue Nov 25, 2008 4:59 pm    Post subject: Reply with quote

Ted and re'born: I'm glad that my explanation was helpful to you Exclamation
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