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What is this almost xy thing?

 
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wapati

Joined: 12 Jun 2007
Posts: 622
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Location: Canada

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PostPosted: Wed Apr 23, 2008 4:26 pm    Post subject: What is this almost xy thing? Reply with quote

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
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wapati

Joined: 12 Jun 2007
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PostPosted: Wed Apr 23, 2008 5:43 pm    Post subject: Reply with quote

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.
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humble_programmer

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Posts: 69
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PostPosted: Wed Apr 23, 2008 6:18 pm    Post subject: Reply with quote

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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arkietech

Joined: 09 Mar 2007
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PostPosted: Wed Apr 23, 2008 6:24 pm    Post subject: Reply with quote

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.


Embarassed 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
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hobiwan

Joined: 11 Feb 2008
Posts: 83
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PostPosted: Wed Apr 23, 2008 8:00 pm    Post subject: Re: What is this almost xy thing? Reply with quote

wapati wrote:
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    |
'------------------'------------------'---------------------'

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.
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wapati

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PostPosted: Thu Apr 24, 2008 3:03 am    Post subject: Re: What is this almost xy thing? Reply with quote

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
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wapati

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PostPosted: Thu Apr 24, 2008 6:24 am    Post subject: Reply with quote

arkietech wrote:

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

dan


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

Keep smiling! Smile
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