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What is this almost xy thing?

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wapati

Joined: 12 Jun 2007

Posts: 622

Location: Canada

Items

Posted: Wed Apr 23, 2008 4:26 pm Post subject: What is this almost xy thing?

I posted this puzzle with an APE.

Code:

4 . .|. 3 6|8 . 7
. . 6|. 5 .|9 4 3
. . .|. . 4|6 1 .
-----+-----+-----
. . .|. 6 .|1 . .
5 6 .|. . .|. . 4
1 . 8|. 7 5|. 6 9
-----+-----+-----
7 2 9|6 4 .|5 . 1
6 . 1|. . 9|. . .
3 8 .|. 1 7|. 9 6

arkietech wrote:

My solver show this can be solved with many xy-wings, empty rectangles and kites.

I'd like to see that, I have tried with three solvers to get past this point and two (SE and SQ) find an APE while the other quits here.

Code:

.------------------.------------------.------------------.
| 4 19 25 | 19 3 6 | 8 25 7 |
| 28 17 6 | 178 5 128 | 9 4 3 |
| 289 3579 357 | 789 289 4 | 6 1 25 |
:------------------+------------------+------------------:
| 29 479 247 | 348 6 23 | 1 23578 258 |
| 5 6 237 | 1389 89 128 | 37 2378 4 |
| 1 34 8 | 24 7 5 | 23 6 9 |
:------------------+------------------+------------------:
| 7 2 9 | 6 4 38 | 5 38 1 |
| 6 45 1 | 35 28 9 | 347 37 28 |
| 3 8 45 | 25 1 7 | 24 9 6 |
'------------------'------------------'------------------'

2 in r4c8 could be gone (ER), it doesn't matter.

Code:

This is the APE, SE and SQ don't agree on r8c8 being included,
both look correct to me.

.------------------.------------------.-------------------.
| 4 19 25 | 19 3 6 | 8 25 7 |
| 28 17 6 | 178 5 128 | 9 4 3 |
| 289 3579 357 | 789 289 4 | 6 1 25 |
:------------------+------------------+-------------------:
| 29 479 247 | 348 6 23 | 1 *2578-3 258 |
| 5 6 237 | 1389 89 128 |*37 *2378 4 |
| 1 34 8 | 24 7 5 |*23 6 9 |
:------------------+------------------+-------------------:
| 7 2 9 | 6 4 38 | 5 *38 1 |
| 6 45 1 | 35 28 9 | 347 #37 28 |
| 3 8 45 | 25 1 7 | 24 9 6 |
'------------------'------------------'-------------------'

The ideas below are all wrong, mostly. I'll work on it some more as there is a little bit right, just not much!

Here is the fun part. At this same point and vicinity I see several patterns which solve the puzzle and I don't know what to call them, here they are, all seem related and resemble xy-wings (on steroids?).

Code:

Simplest.
.------------------.------------------.---------------------.
| 4 19 25 | 19 3 6 | 8 25 7 |
| 28 17 6 | 178 5 128 | 9 4 3 |
| 289 3579 357 | 789 289 4 | 6 1 25 |
:------------------+------------------+---------------------:
| 29 479 247 | 348 6 23 | 1 5-(2378) 258 |
| 5 6 237 | 1389 89 128 | 37 *2378 4 |
| 1 34 8 | 24 7 5 |*23 6 9 |
:------------------+------------------+---------------------:
| 7 2 9 | 6 4 38 | 5 *38 1 |
| 6 45 1 | 35 28 9 | 347 *37 28 |
| 3 8 45 | 25 1 7 | 24 9 6 |
'------------------'------------------'---------------------'

.------------------.------------------.-------------------.
| 4 19 25 | 19 3 6 | 8 *25 7 |
| 28 17 6 | 178 5 128 | 9 4 3 |
| 289 3579 357 | 789 289 4 | 6 1 25 |
:------------------+------------------+-------------------:
| 29 479 247 | 348 6 23 | 1 *23578 *258 |
| 5 6 237 | 1389 89 128 | 3-7 *2378 4 |
| 1 34 8 | 24 7 5 |*23 6 9 |
:------------------+------------------+-------------------:
| 7 2 9 | 6 4 38 | 5 38 1 |
| 6 45 1 | 35 28 9 | 347 3-7 28 |
| 3 8 45 | 25 1 7 | 24 9 6 |
'------------------'------------------'-------------------'
(Or you could use the 37 in r5c7 or the 37 in r8c8 for different eliminations.)

.------------------.------------------.------------------.
| 4 19 25 | 19 3 6 | 8 25 7 |
| 28 17 6 | 178 5 128 | 9 4 3 |
| 289 3579 357 | 789 289 4 | 6 1 25 |
:------------------+------------------+------------------:
| 29 479 247 | 348 6 23 | 1 *23578*258 |
| 5 6 237 | 1389 89 128 |*37 *2378 4 |
| 1 34 8 | 24 7 5 | 3-2 6 9 |
:------------------+------------------+------------------:
| 7 2 9 | 6 4 38 | 5 *38 1 |
| 6 45 1 | 35 28 9 | 347 37 28 |
| 3 8 45 | 25 1 7 | 24 9 6 |
'------------------'------------------'------------------'
(You could use the 37 in r8c8 instead, or the 23 in r6c7 instead of the 37.)

I'm seeing this as line-box interaction and I spot it when looking for xy-wings, or xyz-wings. What is it?

TIA.

Last edited by wapati on Thu Apr 24, 2008 2:55 am; edited 1 time in total

wapati

Joined: 12 Jun 2007

Posts: 622

Location: Canada

Items

Posted: Wed Apr 23, 2008 5:43 pm Post subject:

To clarify a little better, I see this as a "bent" locked set, rather than two nearly locked sets interacting. An xy-wing is the simplest example. By definition, that leaves out APE, ALS and sue de coq.

humble_programmer

Joined: 27 Jun 2006

Posts: 69

Location: Colorado Springs, USA

Items

Posted: Wed Apr 23, 2008 6:18 pm Post subject:

My 2 cents worth:

Code:

NAKED PAIR IN r1c3 AND r1c8:
   r1c2 => not 5
   r1c4 => not 2
POINTING PAIR IN r4c1 r4c2:
   r4c4 => not 9
NAKED PAIR IN r8c5 AND r8c9:
   r8c4 => not 2 8
   r8c7 => not 2
   r8c8 => not 2 8
X-WING BY ROW: r6c4 r6c7 - r9c4 r9c7:
   r2c4 => not 2
   r3c4 => not 2
   r4c4 => not 2
   r5c4 => not 2
   r5c7 => not 2
Y-WING (Pivot r8c2 Wings r6c2 - r8c4):
   r6c4 => not 3
SIMPLE COLORING r4c9-r7c8-r8c5:
   r4c6 => not 8
Y-WING (Pivot r6c4 Wings r4c6 - r6c2):
   r4c2 => not 3
   r4c3 => not 3
Y-WING (Pivot r7c6 Wings r4c6 - r8c5):
   r5c5 => not 2
CHAIN: r2c1-r1c3-r9c3-r9c7-r6c7-r6c2-r6c4-r4c6-r7c6:
   r2c6 => not 8
CHAIN: r3c9-r8c9-r8c5-r9c4-r9c3-r9c7-r6c7-r6c2-r8c2:
   r3c2 => not 5
HIDDEN SINGLE IN c2:
   r8c2 => 5
NAKED SINGLE:
   r8c4 => 3
   r7c6 => 8
   r7c8 => 3
   r8c5 => 2
   r8c8 => 7
   r8c7 => 4
   r8c9 => 8
   r9c3 => 4
   r9c4 => 5
   r9c7 => 2
   r6c7 => 3
   r5c7 => 7
   r6c2 => 4
   r6c4 => 2
   r4c6 => 3
   r5c6 => 1
   r2c6 => 2
   r2c1 => 8
HIDDEN SINGLE IN c2:
   r3c2 => 3
HIDDEN SINGLE IN c3:
   r5c3 => 3
HIDDEN SINGLE IN c4:
   r4c4 => 4
HIDDEN SINGLE IN r4:
   r4c8 => 8
NAKED SINGLE:
   r5c8 => 2
   r1c8 => 5
   r1c3 => 2
   r3c1 => 9
   r1c2 => 1
   r1c4 => 9
   r2c2 => 7
   r2c4 => 1
   r3c3 => 5
   r3c5 => 8
   r3c4 => 7
   r3c9 => 2
   r4c1 => 2
   r4c2 => 9
   r4c3 => 7
   r4c9 => 5
   r5c4 => 8
   r5c5 => 9

_________________
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Humble Programmer
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www.humble-programmer.com

arkietech

Joined: 09 Mar 2007

Posts: 22

Items

Posted: Wed Apr 23, 2008 6:24 pm Post subject:

wapati said:

Quote:

I'd like to see that, I have tried with three solvers to get past this point and two (SE and SQ) find an APE while the other quits here.

Oops I have done it again. I went back and walked through the process again and you are correct you need the aligned pair or your new bent thingy. I got on this thing of looking for shortcuts and took one to many.

Thanks for putting my feet back on the ground. Looks like you are on tosomething.

dan

hobiwan

Joined: 11 Feb 2008

Posts: 83

Items

Posted: Wed Apr 23, 2008 8:00 pm Post subject: Re: What is this almost xy thing?

wapati wrote:

Code:

I seem to have a problem with your notation. I read it as "2378" can be eliminated from r4c8, but according to my solver, r4c8=8.

wapati wrote:

Code:

.------------------.------------------.-------------------.
| 4 19 25 | 19 3 6 | 8 *25 7 |
| 28 17 6 | 178 5 128 | 9 4 3 |
| 289 3579 357 | 789 289 4 | 6 1 25 |
:------------------+------------------+-------------------:
| 29 479 247 | 348 6 23 | 1 *23578 *258 |
| 5 6 237 | 1389 89 128 | 3-7 *2378 4 |
| 1 34 8 | 24 7 5 |*23 6 9 |
:------------------+------------------+-------------------:
| 7 2 9 | 6 4 38 | 5 38 1 |
| 6 45 1 | 35 28 9 | 347 3-7 28 |
| 3 8 45 | 25 1 7 | 24 9 6 |
'------------------'------------------'-------------------'

Same here: r5c7=7, r8c8=7.

wapati

Joined: 12 Jun 2007

Posts: 622

Location: Canada

Items

Posted: Thu Apr 24, 2008 3:03 am Post subject: Re: What is this almost xy thing?

hobiwan wrote:

SNIP...
I seem to have a problem with your notation. I read it as "2378" can be eliminated from r4c8, but according to my solver, r4c8=8. ...SNIP

Thanks hobiwan, this idea needs more work.

Embarassed

wapati

Joined: 12 Jun 2007

Posts: 622

Location: Canada

Items

Posted: Thu Apr 24, 2008 6:24 am Post subject:

arkietech wrote:

Thanks for putting my feet back on the ground. Looks like you are on tosomething.

dan

I am

also, much of my assumptions are wrong. <sigh>

Keep smiling! Smile

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