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A question from a Menneske

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keith

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

Posted: Fri Dec 03, 2010 4:27 am Post subject: A question from a Menneske

I am still working this one (feel free to post a solution!), but I do have a question:

Code:

Puzzle: M5694012sh(14)
+-------+-------+-------+
| . . 2 | . . . | 3 . . |
| . 3 7 | 6 9 . | 8 1 . |
| 6 . . | 1 . . | . . 9 |
+-------+-------+-------+
| . . 6 | 3 . 7 | 1 . . |
| . . . | . . . | . . . |
| . . 1 | 8 . 4 | 9 . . |
+-------+-------+-------+
| 3 . . | . . 1 | . . 7 |
| . 1 5 | . 8 6 | 2 9 . |
| . . 4 | . . . | 6 . . |
+-------+-------+-------+

After basics:

Code:

+-------------------+-------------------+-------------------+
| 1 9 2 | 57 47 8 | 3 467 456 |
| 45 3 7 | 6 9 25 | 8 1 245 |
| 6 45 8 | 1 347 235 | 57 247 9 |
+-------------------+-------------------+-------------------+
| 9 2458 6 | 3 25 7 | 1 24 2458 |
| 2458 2458 3 | 259 1 59 | 57 2467 24568 |
| 25 7 1 | 8 6 4 | 9 3 25 |
+-------------------+-------------------+-------------------+
| 3 6 9 | 25 25 1 | 4 8 7 |
| 7 1 5 | 4 8 6 | 2 9 3 |
| 28 28 4 | 79 37 39 | 6 5 1 |
+-------------------+-------------------+-------------------+

What is this? Note the pattern of 5.

Either the X-wing R26C19 is true, or R2C6 is true (5). Either way, R45C9 are not 5.

Kraken, franken, or something else?

Keith

Marty R.

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

Posted: Fri Dec 03, 2010 4:50 am Post subject:

Quote:

Kraken, franken, or something else?

Not sure, but based on terminology that's been used for what I consider similar situations, it may have been called an AX or Almost X-Wing.

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Fri Dec 03, 2010 5:23 am Post subject: Re: A question from a Menneske

keith wrote:

Kraken, franken, or something else?

I would call it a Kraken X-Wing as follows:

Code:

X-Wing r26\c19 => r1c9,r4c9,r5c19<>5

Kraken fin cell (5)r2c6 - r1c4 = r1c9 - r3c7 = (5)r5c7 => r4c9,r5c19<>5

Where r1c9 is not included in the final eliminations.

There are many fish present for eliminations on <5>. However, apparently only r2c9<>5 is critical to exposing the subsequent XY-Wings.

Code:

Franken Swordfish c67b1\r235 <> 5 r2c9,r5c1249

<45+2> XY-Wing r2c1/r2c9+r6c1 <> 2 r6c9 -complementary-
<24+5> XY-Wing r2c9/r2c1+r6c9 <> 5 r6c1

Note: the Franken Swordfish can be viewed as an inverted Kraken X-Wing using Keith's fin cell but reversing which condition is chained to the elimination:

Code:

Kraken fin cell (5)r2c6 => (5)r2c9

X-Wing c67\r35 - (5)r3c2 = (5)r2c1 => (5)r2c9

Last edited by daj95376 on Fri Dec 03, 2010 5:40 am; edited 1 time in total

Marty R.

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

Posted: Fri Dec 03, 2010 5:29 am Post subject:

W-Wing (25) X-Wing (5) XY-Wing (254) + two transports

Marty R.

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

Posted: Fri Dec 03, 2010 5:37 am Post subject:

Danny, I don't fully understand the notation, but is this something different from the other "almost" things? If you can't make an elimination just by virtue of the pattern, then you have to go on a fishing expedition to see where that fin takes you. And if that's the case, I just view it as a Forcing Chain except that a pattern led you to the chain as opposed to picking one at random.

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Fri Dec 03, 2010 5:45 am Post subject:

Marty R. wrote:

... is this something different from the other "almost" things?

Probably not. I just recall being exposed to Kraken for fish long before I was exposed to the almost terminology. So, I go with what I learned first.

peterj

Joined: 26 Mar 2010
Posts: 974
Location: London, UK

Posted: Fri Dec 03, 2010 9:18 am Post subject:

A nice ANP makes the same eliminations - but also includes r1c9 - which cracks it....

Code:

*--------------------------------------------------------------------*
| 1 9 2 | 57 47 8 | 3 467 4-56 |
| (45) 3 7 | 6 9 25 | 8 1 (245) |
| 6 45 8 | 1 347 235 | 57 247 9 |
|----------------------+----------------------+----------------------|
| 9 2458 6 | 3 25 7 | 1 24 24-58 |
| 2458 2458 3 | 259 1 59 | 57 2467 24-568 |
| (25) 7 1 | 8 6 4 | 9 3 (25) |
|----------------------+----------------------+----------------------|
| 3 6 9 | 25 25 1 | 4 8 7 |
| 7 1 5 | 4 8 6 | 2 9 3 |
| 28 28 4 | 79 37 39 | 6 5 1 |
*--------------------------------------------------------------------*
ANP(25=4)r26c9 - (4=5)r2c1 - (5)r6c1=r6c9 ; r145c9<>5

keith

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

Posted: Fri Dec 03, 2010 10:25 pm Post subject: Re: A question from a Menneske

daj95376 wrote:

There are many fish present for eliminations on <5>. However, apparently only r2c9<>5 is critical to exposing the subsequent XY-Wings.

Code:

Franken Swordfish c67b1\r235 <> 5 r2c9,r5c1249

I don't see Danny's fish or the eliminations.

(My notion of fish is the old one, of aligned strong links.There is, I understand, a better interpretation in terms of constraint sets. So, as always, I am probably missing something.)

However:

The pattern of 5 is:

Code:

+-------+-------+-------+
| . . . | 5 . . | . . 5 |
| 5 . . | . . 5 | . . 5 |
| . 5 . | . . 5 | 5 . . |
+-------+-------+-------+
| . 5 . | . 5 . | . . 5 |
| 5 5 . | 5 . 5 | 5 . 5 |
| 5 . . | . . . | . . 5 |
+-------+-------+-------+
| . . . | 5 5 . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+

There is a Franken Swordfish, aka a cyclic coloring on 5:

Code:

+-------+-------+-------+
| . . . | 5 . . | . . 5 |
| 5A. . | . . 5 | . . 5 |
| . 5a. | . .-5 | 5B. . |
+-------+-------+-------+
| . 5 . | . 5 . | . .-5 |
|-5 5 . | 5 . 5 | 5b.-5 |
| 5c. . | . . . | . . 5C|
+-------+-------+-------+
| . . . | 5 5 . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+

The strong links are Aa, Bb, and Cc. Any cell that sees an upper and a lower case letter can be eliminated.

Which brings us here:

Code:

+-------+-------+-------+
| . . . | 5 . . | . . 5 |
| 5 . . | . . 5 | . . 5 |
| . 5 . | . . . | 5 . . |
+-------+-------+-------+
| . 5 . | . 5 . | . . . |
| . 5 . | 5 . 5 | 5 . . |
| 5 . . | . . . | . . 5 |
+-------+-------+-------+
| . . . | 5 5 . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+

Incredibly, there is now a Franken Squirmbag:

Code:

+-------+-------+-------+
| . . . | 5D. . | . . 5d|
| 5A. . | . . 5c| . .-5 |
| . 5e. | . . . | 5E. . |
+-------+-------+-------+
| . 5 . | . 5 . | . . . |
| .-5 . |-5 . 5C| 5b. . |
| 5a. . | . . . | . . 5B|
+-------+-------+-------+
| . . . | 5 5 . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+

(Yes, there is a complementary Franken Jellyfish that makes the same eliminations.)

I think I'll have steak for dinner. (Has anyone ever seen a Franken Squirmbag in the wild?)

(By the way, Marty is an avid fisherman, but not of the Sudoku kind!)

Best wishes

Keith

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Fri Dec 03, 2010 11:23 pm Post subject: Re: A question from a Menneske

keith wrote:

daj95376 wrote:

Code:

Franken Swordfish c67b1\r235 <> 5 r2c9,r5c1249

My fish() routine is based on constraint sets. I posted the complete description of a coloring mechanism in another forum a long time back. For this puzzle, I'll give an abbreviated description.

Load the grid into Simple Sudoku and select the <5> cells to be highlighted (light-green).

1) For every highlighted candidate cell in houses [c67b1], change the highlighted cells to (dark) Blue.

2) For every (non-Blue) highlighted candidate cell in houses [r235] change it to (hot) Pink.

3) For every Blue candidate cell in houses [r235], change its color to (dark) Green.

If there were any fin cells, they would still exist as Blue cells. There aren't any in this example, but I mention it because it's important to know.

4) The candidate <5> can be eliminated in all of the Pink cells.

Enjoy & Regards, Danny

keith

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

Posted: Sat Dec 04, 2010 12:53 am Post subject:

Quote:

Load the grid into Simple Sudoku and select the <5> cells to be highlighted (light-green)....

I was thinking along the lines:

Print puzzle. Get coffee and pencil ...

Keith

Marty R.

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

Posted: Sat Dec 04, 2010 12:56 am Post subject:

Quote:

(By the way, Marty is an avid fisherman, but not of the Sudoku kind!)

Well, there are X-Wings. Laughing

keith

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

Posted: Sat Dec 04, 2010 2:06 am Post subject:

Marty R. wrote:

Quote:

(By the way, Marty is an avid fisherman, but not of the Sudoku kind!)

Well, there are X-Wings. Laughing

But, for multi-step Marty, they are a rare catch! Razz

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