A Pure X-Wing Collection.

Everything about Sudoku that doesn't fit in one of the other sections

A Pure X-Wing Collection.

Postby Ocean » Fri Apr 28, 2006 7:54 pm

Here is a collection of puzzles that "NEED" X-wing to solve, and also can be solved ONLY with X-wing (besides naked/hidden singles). For the esthetics, the puzzles are minimal (absolute minimal), and have full symmetry (rotation and reflection).

Code: Select all
1. (XW @52)
 *-----------*
 |...|1.6|...|
 |..4|...|3..|
 |.9.|8.2|.5.|
 |---+---+---|
 |2.5|...|7.9|
 |...|...|...|
 |3.8|...|1.6|
 |---+---+---|
 |.1.|4.5|.2.|
 |..2|...|5..|
 |...|6.8|...|
 *-----------*

2. (XW @50)
 *-----------*
 |..8|...|2..|
 |...|537|...|
 |5..|...|..1|
 |---+---+---|
 |.1.|.4.|.7.|
 |.9.|2.3|.1.|
 |.2.|.6.|.4.|
 |---+---+---|
 |1..|...|..6|
 |...|428|...|
 |..9|...|4..|
 *-----------*

3. (XW @40)
 *-----------*
 |5..|.8.|..3|
 |.7.|9.6|.8.|
 |..4|...|7..|
 |---+---+---|
 |.2.|...|.1.|
 |8..|...|..5|
 |.5.|...|.3.|
 |---+---+---|
 |..2|...|9..|
 |.6.|7.5|.2.|
 |4..|.3.|..7|
 *-----------*

4. (XW @40)
 *-----------*
 |...|8.4|...|
 |.3.|.1.|.6.|
 |..7|...|9..|
 |---+---+---|
 |7..|.3.|..4|
 |.9.|7.2|.1.|
 |4..|.9.|..2|
 |---+---+---|
 |..5|...|6..|
 |.1.|.5.|.7.|
 |...|9.3|...|
 *-----------*
 
5. (XW @38)
 *-----------*
 |..8|9.5|2..|
 |...|.4.|...|
 |1..|...|..9|
 |---+---+---|
 |4..|.7.|..1|
 |.7.|6.1|.9.|
 |9..|.2.|..3|
 |---+---+---|
 |7..|...|..5|
 |...|.1.|...|
 |..6|4.8|9..|
 *-----------*

6. (XW @34)
 *-----------*
 |...|...|...|
 |.62|...|18.|
 |.9.|5.1|.3.|
 |---+---+---|
 |..7|3.8|2..|
 |...|...|...|
 |..6|4.7|5..|
 |---+---+---|
 |.5.|7.4|.9.|
 |.23|...|86.|
 |...|...|...|
 *-----------*

7. (XW @32)
 *-----------*
 |...|.6.|...|
 |..9|.7.|8..|
 |.4.|2.8|.5.|
 |---+---+---|
 |..7|...|5..|
 |96.|...|.12|
 |..2|...|9..|
 |---+---+---|
 |.3.|9.1|.4.|
 |..8|.5.|3..|
 |...|.8.|...|
 *-----------*


:idea: Definitions (for this post/thread):
1. A puzzle that "NEEDS" X-wing to solve: A puzzle that can not be solved with naked/hidden pairs/triples/quads, or locked candidates alone. Some other method is needed. X-wing is a method that can be applied, and helps solving the puzzle.
2. A puzzle that can be solved with ONLY X-wing: If elimination of candidates by X-wing is applied, then there is no need to use any other method besides "naked/hidden singles".
Last edited by Ocean on Sat Apr 29, 2006 5:46 pm, edited 1 time in total.
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Postby ronk » Fri Apr 28, 2006 8:41 pm

Hi Ocean,
Thanks for the very nice collection.
Ron
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Re: A Pure X-Wing Collection.

Postby gsf » Fri Apr 28, 2006 10:10 pm

Ocean wrote:Here is a collection of puzzles that "NEED" X-wing to solve, and also can be solved ONLY with X-wing (besides naked/hidden singles).

thanks
for taxonomy purposes here are the pencimark grids at the moment the xwings are required

I also preceded the comments with # -- easier to snarf and parse

Code: Select all
# 1. (XW @52)

 578  35   37  |  1   34    6  | 489  79    2 
 168   2    4  |  5    9    7  |  3   16   18 
 167   9  1367 |  8   34    2  | 46    5   147
---------------+---------------+---------------
  2    4    5  |  3    6    1  |  7    8    9 
 19    6   19  |  7    8    4  |  2    3    5 
  3    7    8  |  2    5    9  |  1    4    6 
---------------+---------------+---------------
 69    1   369 |  4    7    5  | 689   2   38 
 467   8    2  |  9    1    3  |  5   67   47 
4579  35   379 |  6    2    8  | 49   179 1347

# 2. (XW @50)

  9   37    8  |  6    1    4  |  2   35   357
  2    6    1  |  5    3    7  | 89   89    4 
  5   37    4  | 89   89    2  | 37    6    1 
---------------+---------------+---------------
 368   1   356 | 89    4   59  | 35    7    2 
  4    9    7  |  2   58    3  |  6    1   58 
 38    2   35  |  7    6    1  | 359   4  3589
---------------+---------------+---------------
  1    4    2  |  3   579  59  | 578  58    6 
 367   5   36  |  4    2    8  |  1   39   379
 37    8    9  |  1   57    6  |  4    2   357

# 3. (XW @40)

  5     19   169  |  12    8     7   | 126    4     3   
 123    7     13  |  9     4     6   |  5     8     12 
 126    8     4   | 1235  125   123  |  7     9    126 
------------------+------------------+------------------
 369    2    3679 |34568  5679  3489 | 468    1    689 
  8     4    1369 | 1236  1269  1239 |  26    7     5   
 169    5    1679 |12468 12679 12489 | 2468   3    2689
------------------+------------------+------------------
  7     3     2   | 1468   16   148  |  9     5     18 
  19    6     8   |  7     19    5   |  3     2     4   
  4     19    5   | 128    3    1289 |  18    6     7   

# 4. (XW @40)

12569  256   269  |  8     7     4   | 1235  235   135 
  58    3     48  |  2     1     9   | 458    6     7   
 128   248    7   |  3     6     5   |  9    248    18 
------------------+------------------+------------------
  7    2568  1268 |  56    3     18  |  58    9     4   
 358    9     38  |  7     4     2   | 358    1     6   
  4    568   1368 |  56    9     18  |  7    358    2   
------------------+------------------+------------------
 2389  248    5   |  1     28    7   |  6    2348  389 
 2389   1    2389 |  4     5     6   | 238    7    389 
 268    7    2468 |  9     28    3   |12458  2458  158 

# 5. (XW @38)

  36    4     8   |  9     36    5   |  2     1     7   
 2356  2359 23579 |  1     4    237  | 3568  3568   68 
  1    235   2357 | 2378  368   237  | 3456  3456   9   
------------------+------------------+------------------
  4    3568   35  | 358    7     9   | 568    2     1   
 2358   7    235  |  6    358    1   | 458    9     48 
  9    568    1   |  58    2     4   |  7    568    3   
------------------+------------------+------------------
  7    238   234  |  23    9    236  |  1    3468   5   
 2358 23589 23459 | 2357   1    2367 | 3468  3468  468 
  35    1     6   |  4     35    8   |  9     7     2   

# 6. (XW @34)

134578  3478   1458  |  268   24678   26   | 4679    25   245679
  457     6      2   |   9     47      3   |   1      8     457 
  478     9     48   |   5    24678    1   |  467     3    2467 
---------------------+---------------------+---------------------
  59      1      7   |   3     569     8   |   2      4     69   
234589   348   4589  |  26      1     59   |  69      7     38   
  29     38      6   |   4     29      7   |   5      1     38   
---------------------+---------------------+---------------------
  168     5     18   |   7     268     4   |   3      9     12   
  47      2      3   |   1     59     59   |   8      6     47   
146789   478   1489  |  268     3     26   |  47     25     125 

# 7. (XW @32)

123578  12578   135  | 1345     6      9   | 1247    237   1347 
 12356   125     9   | 1345     7     345  |   8     236   1346 
 1367     4     136  |   2     13      8   |  167     5      9   
---------------------+---------------------+---------------------
 1348    18      7   |  136     9      2   |   5     368    346 
   9      6     345  |   8     34     357  |  47      1      2   
 13458   158     2   | 13567   134   3567  |   9    3678   3467 
---------------------+---------------------+---------------------
  567     3     56   |   9      2      1   |  67      4      8   
 12467  1279     8   |  467     5     467  |   3    2679    167 
 12467  1279    146  | 3467     8    3467  | 1267   2679     5   

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Postby Ocean » Fri Apr 28, 2006 11:17 pm

Glad you liked them, Ron. And thanks for the pencilmark grids, gsf. Makes it easier to find and study the effect of the xwings directly on screen.
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Postby gsf » Sat Apr 29, 2006 1:58 am

Ocean wrote:Glad you liked them, Ron. And thanks for the pencilmark grids, gsf. Makes it easier to find and study the effect of the xwings directly on screen.

I'll post an update to my solver in a week or so
I produced those with one command
there's a few other additions related to the inferior/superior/symmetric threads too
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Re: A Pure X-Wing Collection.

Postby tso » Sat Apr 29, 2006 5:26 pm

Ocean wrote:Here is a collection of puzzles that "NEED" X-wing to solve, and also can be solved ONLY with X-wing (besides naked/hidden singles).


This is nitpicking, but the claim that a particular puzzle requires a particular tactic is dependant on some abritrary agreed upon heirarchy of solving techniques. For example, your third puzzle can be solved with a single simple xy-type forcing chain and a locked candidate.

Conversely, you can find x-wings (and most other specific tactics) in most puzzles, regardless of how "easy" or "hard" they are labled. We've all found naked pairs or triples without realizing there were still singles to be found.
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Re: A Pure X-Wing Collection.

Postby fermat » Sat Apr 29, 2006 5:51 pm

tso wrote:
Ocean wrote:Here is a collection of puzzles that "NEED" X-wing to solve, and also can be solved ONLY with X-wing (besides naked/hidden singles).


This is nitpicking, but the claim that a particular puzzle requires a particular tactic is dependant on some abritrary agreed upon heirarchy of solving techniques. For example, your third puzzle can be solved with a single simple xy-type forcing chain and a locked candidate.
.


If someone finds a method, however tedious (brute force comes to mind), that solves all puzzles where lies your complaint? All puzzles are the same to brute force, except number of steps.

If 17 is the minimum puzzle the easiest to solve would be 64 steps.
Well, the first step could be arbitrary, any method, advanced, trivial, who knows. If it was uniqueness a fair few would call it invalid. Needs batfish, no one gets it. <I get it, batfish is a joke, so far!>
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Re: A Pure X-Wing Collection.

Postby tso » Sat Apr 29, 2006 8:21 pm

fermat wrote:
tso wrote:
Ocean wrote:Here is a collection of puzzles that "NEED" X-wing to solve, and also can be solved ONLY with X-wing (besides naked/hidden singles).


This is nitpicking, but the claim that a particular puzzle requires a particular tactic is dependant on some abritrary agreed upon heirarchy of solving techniques. For example, your third puzzle can be solved with a single simple xy-type forcing chain and a locked candidate.
.


If someone finds a method, however tedious (brute force comes to mind), that solves all puzzles where lies your complaint? All puzzles are the same to brute force, except number of steps.


Though I wouldn't charactorize my post as a "complaint" -- my point is simple. It is impossible to create a sudoku that requires any specific tactic without first agreeing upon what that means. What seems to be implied is that there is a specific list of tactics that must be applied in a specific order of increasing something -- difficulty, complexity, rarity, etc. But in specific case, this fails, as individuals often disagree in a particular instance. If a particular solver is adept in finding simple xy-type forcing chains, it is *very* likely that that solver will find one *before* s/he will find an x-wing, as x-wings are often easier to find after filtering -- something that is difficult when solving on paper -- whereas forcing chains do not need nor are they simplified by filtering. I'm *sure* I've found forcing chains when there were simpler -- however you choose to define that -- tactics available.

Now, if you were to say "If one applies the ONLY the following X tactics, applying tactic N if and only if all tactics N-Y are unavailable, then the following puzzles will require tactic Z to be solved.", and then gave a list of the X tactics you will allow, then I would have no "complaint".
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Re: A Pure X-Wing Collection.

Postby Ocean » Sun Apr 30, 2006 12:13 am

gsf wrote:I'll post an update to my solver in a week or so.
I produced those with one command
there's a few other additions related to the inferior/superior/symmetric threads too

Interesting that these threads gave ideas and inspiration for programs also!

Was curious about the pencilmark grids (which techniques were applied for eliminations, when are the grids printed, etc), so I checked a few details. First: seems that you have a way of specifying "print the pm-grids before an x-wing is applied", or "every crucial step", or "every step", which is a nice option. Second, for choice of elimination techniques, I checked especially #6: Here are six possible eliminations by naked pairs (@34), but these are not sufficient (and not necessary). The x-wing can be applied directly, the np-eleminations are not needed. If we compare:

Code: Select all
#6.  (XW @34) - but NOT applying the six(!) successive NP-elimiations (not needed).
 *-------------------------------------------------------------------------*
 | 134578  3478    1458   | 268    -24678   26     | 4679   25    -245679  |
 | 457     6       2      | 9       47      3      | 1      8      457     |
 | 478     9       48     | 5      *24678   1      | 467    3     *2467    |
 |------------------------+------------------------+-----------------------|
 | 59      1       7      | 3       569     8      | 2      4      69      |
 | 234589  348     4589   | 26      1       2569   | 69     7      3689    |
 | 2389    38      6      | 4      -29      7      | 5      1      389     |
 |------------------------+------------------------+-----------------------|
 | 168     5       18     | 7      *268     4      | 3      9     *12      |
 | 479     2       3      | 1       59      59     | 8      6      457     |
 | 146789  478     1489   | 268     3       2569   | 47     25    -12457   |
 *-------------------------------------------------------------------------*


# 6. (XW @34) - [after the six NP-eleminiations]

134578  3478   1458  |  268   24678   26   | 4679    25   245679
  457     6      2   |   9     47      3   |   1      8     457 
  478     9     48   |   5    24678    1   |  467     3    2467 
---------------------+---------------------+---------------------
  59      1      7   |   3     569     8   |   2      4     69   
234589   348   4589  |  26      1     59   |  69      7     38   
  29     38      6   |   4     29      7   |   5      1     38   
---------------------+---------------------+---------------------
  168     5     18   |   7     268     4   |   3      9     12   
  47      2      3   |   1     59     59   |   8      6     47   
146789   478   1489  |  268     3     26   |  47     25     125 


I don't know which is the 'most correct' pencilmark grid (if any). As mentioned, the x-wing can be applied directly to the first, (and after application of x-wing the np-reductions are superfluous). If insisting on always doing the 'easier techniques' first, whether useful or not, we reach the second grid.

[Edit: Split a long post into two separate answers.]
Last edited by Ocean on Sun Apr 30, 2006 12:33 am, edited 1 time in total.
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Re: A Pure X-Wing Collection.

Postby fermat » Sun Apr 30, 2006 12:36 am

tso"][quote="fermat"][quote="tso wrote:[

Now, if you were to say "If one applies the ONLY the following X tactics, applying tactic N if and only if all tactics N-Y are unavailable, then the following puzzles will require tactic Z to be solved.", and then gave a list of the X tactics you will allow, then I would have no "complaint".


Kinda my point.

Who defines that? If it is the poster...status quo.

I don't see how to agree on the others. Brute force steps (whose brute force?) is arbitrary. 3 x-wings are (may be) easier than 1 uniqueness.

Which was harder? What if it was only 1 x-wing?
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Re: A Pure X-Wing Collection.

Postby Ocean » Sun Apr 30, 2006 4:01 am

tso wrote:... the claim that a particular puzzle requires a particular tactic is dependant on some abritrary agreed upon heirarchy of solving techniques. For example, your third puzzle can be solved with a single simple xy-type forcing chain and a locked candidate.

Thanks for your comment. The original post is now edited, and hopefully a bit clearer. I agree with you that a solver can choose any method during the solution process, and that there is no strict hierarchy deciding which method to use first. The preferred methods will vary from person to person, and also whether you solve on paper or use a support tool that helps with pencilmarks, filtering, hints, etc.

About xy-chain in #3: Interesting to compare alternative methods that solve the puzzles.
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Re: A Pure X-Wing Collection.

Postby Havard » Sun Apr 30, 2006 9:23 pm

Ocean wrote:About xy-chain in #3: Interesting to compare alternative methods that solve the puzzles.

Here is my contribution to "interesting...":)

Code: Select all
5      19#c    169   | 12      8       7       | 126#a#e   4     3
123#c  7       13#c  | 9       4       6       | 5         8     12#d
126#c  8       4     | 1235    125     123     | 7         9     126#d
---------------------+-------------------------+------------------------
369    2       3679  | 34568   5679    3489    | 468#a#e   1     689
8      4       1369  | 1236    1269    1239    | 26#a#e    7     5
169    5       1679  | 12468   12679   12489   | 2468#a#e  3     2689-2
---------------------+-------------------------+------------------------
7      3       2     | 1468    16      148     | 9         5     18
19     6       8     | 7       19      5       | 3         2     4
4      19#b    5     | 128-1   3       1289-1  | 18#b      6     7

"Continuous" Almost Locked Sets XY


Havard
Last edited by Havard on Sun Apr 30, 2006 6:04 pm, edited 1 time in total.
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Postby ronk » Sun Apr 30, 2006 9:44 pm

Havard, candidate grids are really hard to read when lines wrap. Would you please trim some white space out of that last post?

Thx, Ron
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Postby Havard » Sun Apr 30, 2006 9:57 pm

ronk wrote:Havard, candidate grids are really hard to read when lines wrap. Would you please trim some white space out of that last post?

Thx, Ron


That's strange, mine does not wrap... I'll try and fix it now!:)

Havard
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Postby Ruud » Sun Apr 30, 2006 10:12 pm

Havard,

you must be aware of the fact that Ron has a very small screen.:D

Ruud.
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