A Pure X-Wing Collection.

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

Postby JPF » Wed Dec 12, 2007 1:13 pm

Pat wrote:here's a nice example --
Code: Select all
 . 9 . | . . . | . 6 .
 5 . . | . 2 . | . . 4
 . . 1 | 7 . 4 | 9 . .
-------+-------+------
 9 . . | . 5 . | . . 3
 . 5 . | 4 . 2 | . 9 .
 4 . . | . 1 . | . . 8
-------+-------+------
 . . 6 | 2 . 5 | 3 . .
 3 . . | . 9 . | . . 6
 . 7 . | . . . | . 5 .


Well, this puzzle is not really minimal...
Ocean wrote:... 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).


May I propose this one :
Code: Select all
 . 1 . | . . . | . 2 .
 3 . . | . 4 . | . . 5
 . . 6 | 7 . 5 | 8 . .
-------+-------+-------
 8 . . | . 9 . | . . 1
 . 3 . | 5 . 4 | . 6 .
 2 . . | . 6 . | . . 3
-------+-------+-------
 . . 2 | 4 . 9 | 1 . .
 1 . . | . 7 . | . . 2
 . 8 . | . . . | . 9 .


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Postby TTHsieh » Thu Dec 13, 2007 2:45 am

  • How about this one ?
Code: Select all
 . 1 . | . . . | . 2 .
 3 . . | . 4 . | . . 5
 . . 4 | 6 . 5 | 7 . .
 - - - + - - - + - - -
 7 . . | . 8 . | . . 1
 . 6 . | 5 . 1 | . 7 .
 5 . . | . 9 . | . . 3
 - - - + - - - + - - -
 . . 2 | 9 . 8 | 1 . .
 1 . . | . 6 . | . . 2
 . 3 . | . . . | . 9 . 

  • and this one ?
Code: Select all
 . 1 . | . . . | . 2 .
 3 . . | . 4 . | . . 5
 . . 6 | 1 . 5 | 7 . .
 - - - + - - - + - - -
 8 . . | . 9 . | . . 1
 . 7 . | 5 . 4 | . 8 .
 2 . . | . 6 . | . . 3
 - - - + - - - + - - -
 . . 2 | 4 . 8 | 1 . .
 1 . . | . 7 . | . . 2
 . 3 . | . . . | . 9 . 


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Postby ronk » Thu Dec 13, 2007 2:55 am

JPF wrote:
Ocean wrote:For the esthetics, the puzzles are minimal (absolute minimal), and have full symmetry (rotation and reflection)

May I propose this one :
Code: Select all
 . 1 . | . . . | . 2 .
 3 . . | . 4 . | . . 5
 . . 6 | 7 . 5 | 8 . .
-------+-------+-------
 8 . . | . 9 . | . . 1
 . 3 . | 5 . 4 | . 6 .
 2 . . | . 6 . | . . 3
-------+-------+-------
 . . 2 | 4 . 9 | 1 . .
 1 . . | . 7 . | . . 2
 . 8 . | . . . | . 9 .


JPF

Doesn't "full symmetry (rotation and reflection)" include 90-degree rotational symmetry:?:
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Postby JPF » Thu Dec 13, 2007 9:32 am

ronk wrote:Doesn't "full symmetry (rotation and reflection)" include 90-degree rotational symmetry:?:

Right,
Gould's pattern has a symmetry type III (horizontal and vertical reflection) but not a 90-degree symmetry.

So the pattern doesn't qualify as a full dihedral symmetric as requested.
Same remark for gsf's, TTHsieh's puzzles and mine's.

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Postby TTHsieh » Thu Dec 13, 2007 1:49 pm

    The Patterns Game's pattern posted in here.
  • It is a fully symmetrical pattern.
  • Can generate a lot of X-Wing puzzles including many pure X-Wing.
20 pure X-Wing puzzles wrote:000000000001020300045030610000206000076000840000701000038090270009010500000000000
000000000001020300045030610000206000076000480000701000038090270009010500000000000
000000000001020300045030610000206000076000580000701000059040230003010800000000000
000000000001020300045030620000407000068000540000801000026010430009070800000000000
000000000001020300045030620000407000068000540000801000029010460006070800000000000
000000000001020300045030620000407000068000540000801000026010490003070800000000000
000000000001020300045030620000407000089000540000901000026010480008070900000000000
000000000001020300045030260000407000058000640000501000062010590003070800000000000
000000000001020300045030260000701000067000540000408000039010670006080100000000000
000000000001020300045060710000204000054000890000608000089030170003010600000000000
000000000001020300045060710000208000018000970000607000073050190009030600000000000
000000000001020300045060270000408000039000740000901000074010620003080900000000000
000000000001020300045060120000601000078000490000409000097030560003010700000000000
000000000001020300045060270000703000038000150000509000084070620002090400000000000
000000000001020300045060270000703000038000150000509000084070630002090400000000000
000000000001020300045060720000803000078000450000701000092010670004030800000000000
000000000001020300045060720000809000078000450000701000032010670004090800000000000
000000000001020300045060170000806000084000950000205000057030610009070800000000000
000000000001020300045060170000806000084000950000205000057030640009070800000000000
000000000001020300045060270000801000078000540000409000036010780007090100000000000


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Postby tarek » Thu Dec 13, 2007 8:07 pm

here are 2 20-clue fully symmetric & minimal puzzles (which are -1+1 apart) and require only singles & x-wing:
Code: Select all
 . . . | . 2 . | . . . 
 . . . | 3 4 6 | . . . 
 . . 8 | . . . | 5 . . 
-------+-------+------
 . 2 . | . . . | . 3 . 
 3 1 . | . . . | . 2 7 
 . 9 . | . . . | . 6 . 
-------+-------+------
 . . 6 | . . . | 1 . . 
 . . . | 8 7 4 | . . . 
 . . . | . 3 . | . . . 

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

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Postby TTHsieh » Fri Dec 14, 2007 2:12 am

tarek wrote:here are 2 20-clue fully symmetric & minimal puzzles (which are -1+1 apart) and require only singles & x-wing
    here are another 2:
Code: Select all
 . . . | . 1 . | . . .
 . 2 . | . . . | . 1 .
 . . . | 3 4 5 | . . .
 - - - + - - - + - - -
 . . 6 | . . . | 3 . .
 5 . 7 | . . . | 6 . 8
 . . 9 | . . . | 5 . .
 - - - + - - - + - - -
 . . . | 4 8 2 | . . .
 . 3 . | . . . | . 9 .
 . . . | . 5 . | . . . 

Code: Select all
 . . . | . 1 . | . . .
 . 2 . | . . . | . 3 .
 . . . | 4 5 6 | . . .
 - - - + - - - + - - -
 . . 7 | . . . | 4 . .
 6 . 8 | . . . | 1 . 9
 . . 3 | . . . | 6 . .
 - - - + - - - + - - -
 . . . | 5 8 2 | . . .
 . 4 . | . . . | . 8 .
 . . . | . 6 . | . . . 


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Postby Pat » Sun Dec 16, 2007 10:04 am

TTHsieh wrote:
Code: Select all
 . . . | . 1 . | . . .
 . 2 . | . . . | . 3 .
 . . . | 4 5 6 | . . .
 - - - + - - - + - - -
 . . 7 | . . . | 4 . .
 6 . 8 | . . . | 1 . 9
 . . 3 | . . . | 6 . .
 - - - + - - - + - - -
 . . . | 5 8 2 | . . .
 . 4 . | . . . | . 8 .
 . . . | . 6 . | . . . 



thanks but this last puzzle can be solved by subsets (without X-wing),
thus fails Ocean's basic requirement --
Ocean wrote: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".

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Postby Pat » Sun Dec 16, 2007 10:10 am

TTHsieh wrote:
  • and this one ?
Code: Select all
 . 1 . | . . . | . 2 .
 3 . . | . 4 . | . . 5
 . . 6 | 1 . 5 | 7 . .
 - - - + - - - + - - -
 8 . . | . 9 . | . . 1
 . 7 . | 5 . 4 | . 8 .
 2 . . | . 6 . | . . 3
 - - - + - - - + - - -
 . . 2 | 4 . 8 | 1 . .
 1 . . | . 7 . | . . 2
 . 3 . | . . . | . 9 . 



sorry, this puzzle cannot be solved by X-wing (with "singles").
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Postby daj95376 » Sun Dec 16, 2007 10:25 am

So, using a hierarchy of ...

1) Naked/Hidden Singles
2) Naked/Hidden Pairs/Triples/Quads
3) Locked Candidate (1/2)
4) X-Wing

could be used provided: steps (2) & (3) never appear in the solution, steps (1) & (4) do appear in the solution, and symmetry constraints are met.
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Postby tarek » Sun Dec 16, 2007 10:28 am

daj95376 wrote:So, using a hierarchy of ...

1) Naked/Hidden Singles
2) Naked/Hidden Pairs/Triples/Quads
3) Locked Candidate (1/2)
4) X-Wing

could be used provided: steps (2) & (3) never appear in the solution, steps (1) & (4) do appear in the solution, and symmetry constraints are met.


No,

provided: if steps (2) OR/AND (3) are missing then it is still solvable
if step (4) is missing then it is not solvable with (1)+(2)+(3)

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Postby Pat » Sun Dec 16, 2007 3:44 pm

using gsf's software,
i need to combine 2 separate tests --
  • -qNFW2-G ==> valid
  • -qNFBHT-G ==> invalid
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Postby Pat » Sun Dec 16, 2007 4:40 pm

when Ocean launched this Topic on "pure X-wing" puzzles,
he apparently found there is a plentiful supply of such puzzles --
    this would explain his decision to add an "esthetic" filter
when i reviewed his 7 puzzles,
i was sorry he chose this filter --
    each of his puzzles is a pure 1 X-wing puzzle,
    it only needs 1 X-wing
when i did encounter some pure 2 X-wing puzzles,
i was very happy to post them
( ignoring the "esthetic" filter )


as for the recent contributions by JPF + TTHsieh + tarek,
i've only reviewed about half of them
and those all need just 1 X-wing --
    the other half may still provide some examples needing more than 1
    ( but i'm not too hopeful )


  1. puzzle number 1-36 ( but 12 and 36 don't belong here )
  2. the puzzle
  3. number of clues
  4. number of X-wings needed -- underscore for those not yet known
  5. puzzle source
Code: Select all
01,...1.6.....4...3...9.8.2.5.2.5...7.9.........3.8...1.6.1.4.5.2...2...5.....6.8...,24,1,Ocean
02,..8...2.....537...5.......1.1..4..7..9.2.3.1..2..6..4.1.......6...428.....9...4..,24,1,Ocean
03,5...8...3.7.9.6.8...4...7...2.....1.8.......5.5.....3...2...9...6.7.5.2.4...3...7,24,1,Ocean
04,...8.4....3..1..6...7...9..7...3...4.9.7.2.1.4...9...2..5...6...1..5..7....9.3...,24,1,Ocean
05,..89.52......4....1.......94...7...1.7.6.1.9.9...2...37.......5....1......64.89..,24,1,Ocean
06,..........62...18..9.5.1.3...73.82.............64.75...5.7.4.9..23...86..........,24,1,Ocean
07,....6......9.7.8...4.2.8.5...7...5..96.....12..2...9...3.9.1.4...8.5.3......8....,24,1,Ocean

08,.473..8......1..5..132.8......1....5..15.26..7....3......4.516..9..6......4..127.,28,2,gsf
09,.9.....6.5...2...4..17.49..9...5...3.5.4.2.9.4...1...8..62.53..3...9...6.7.....5.,28,2,Wayne Gould

10,.1.....2.3...4...5..67.58..8...9...1.3.5.4.6.2...6...3..24.91..1...7...2.8.....9.,28,_,JPF

11,.1.....2.3...4...5..46.57..7...8...1.6.5.1.7.5...9...3..29.81..1...6...2.3.....9.,28,1,TTHsieh
12,.1.....2.3...4...5..61.57..8...9...1.7.5.4.8.2...6...3..24.81..1...7...2.3.....9.,28,*,TTHsieh

13,...........1.2.3...45.3.61....2.6....76...84....7.1....38.9.27...9.1.5...........,24,_,TTHsieh
14,...........1.2.3...45.3.61....2.6....76...48....7.1....38.9.27...9.1.5...........,24,_,TTHsieh
15,...........1.2.3...45.3.61....2.6....76...58....7.1....59.4.23...3.1.8...........,24,1,TTHsieh
16,...........1.2.3...45.3.62....4.7....68...54....8.1....26.1.43...9.7.8...........,24,1,TTHsieh
17,...........1.2.3...45.3.62....4.7....68...54....8.1....29.1.46...6.7.8...........,24,_,TTHsieh
18,...........1.2.3...45.3.62....4.7....68...54....8.1....26.1.49...3.7.8...........,24,1,TTHsieh
19,...........1.2.3...45.3.62....4.7....89...54....9.1....26.1.48...8.7.9...........,24,1,TTHsieh
20,...........1.2.3...45.3.26....4.7....58...64....5.1....62.1.59...3.7.8...........,24,_,TTHsieh
21,...........1.2.3...45.3.26....7.1....67...54....4.8....39.1.67...6.8.1...........,24,_,TTHsieh
22,...........1.2.3...45.6.71....2.4....54...89....6.8....89.3.17...3.1.6...........,24,_,TTHsieh
23,...........1.2.3...45.6.71....2.8....18...97....6.7....73.5.19...9.3.6...........,24,_,TTHsieh
24,...........1.2.3...45.6.27....4.8....39...74....9.1....74.1.62...3.8.9...........,24,_,TTHsieh
25,...........1.2.3...45.6.12....6.1....78...49....4.9....97.3.56...3.1.7...........,24,_,TTHsieh
26,...........1.2.3...45.6.27....7.3....38...15....5.9....84.7.62...2.9.4...........,24,1,TTHsieh
27,...........1.2.3...45.6.27....7.3....38...15....5.9....84.7.63...2.9.4...........,24,_,TTHsieh
28,...........1.2.3...45.6.72....8.3....78...45....7.1....92.1.67...4.3.8...........,24,1,TTHsieh
29,...........1.2.3...45.6.72....8.9....78...45....7.1....32.1.67...4.9.8...........,24,_,TTHsieh
30,...........1.2.3...45.6.17....8.6....84...95....2.5....57.3.61...9.7.8...........,24,1,TTHsieh
31,...........1.2.3...45.6.17....8.6....84...95....2.5....57.3.64...9.7.8...........,24,1,TTHsieh
32,...........1.2.3...45.6.27....8.1....78...54....4.9....36.1.78...7.9.1...........,24,_,TTHsieh

33,....2.......346.....8...5...2.....3.31.....27.9.....6...6...1.....874.......3....,20,1,tarek
34,....6.....1.....3....952.....4...9..2.7...6.8..6...2.....581....9.....4.....2....,20,1,tarek

35,....1.....2.....1....345.....6...3..5.7...6.8..9...5.....482....3.....9.....5....,20,1,TTHsieh
36,....1.....2.....3....456.....7...4..6.8...1.9..3...6.....582....4.....8.....6....,20,*,TTHsieh

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Postby tarek » Mon Dec 17, 2007 6:27 pm

With what you mentioned somewhere else Pat regarding Red Herrings.....

As x-wings are usually used after subset search has been exhausted (or even up to hidden triples).... this provides so many red herrings:D

I am thinking of something similar but with (swordfishes) if anyone is interested !!!???

the set however should be extended to include (finned xwing, sashimi x-wings, simple coulouring & uniqueness)


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puzzles 10 and 23 do need more than 1 X-wing

Postby Pat » Tue Dec 18, 2007 4:26 pm

      status report
    in addition to puzzles 8-9,
    i'm glad to report that puzzles 10 and 23
    do need more than 1 X-wing

    ( this is based on gsf's counting of "steps"
    which provides a lower bound on the number of needed X-wings.
    sorry i had neglected to run this earlier.
    )

10
JPF wrote:
Code: Select all
 . 1 . | . . . | . 2 .
 3 . . | . 4 . | . . 5
 . . 6 | 7 . 5 | 8 . .
-------+-------+------
 8 . . | . 9 . | . . 1
 . 3 . | 5 . 4 | . 6 .
 2 . . | . 6 . | . . 3
-------+-------+------
 . . 2 | 4 . 9 | 1 . .
 1 . . | . 7 . | . . 2
 . 8 . | . . . | . 9 .



23
TTHsieh wrote:
Code: Select all
 . . . | . . . | . . .
 . . 1 | . 2 . | 3 . .
 . 4 5 | . 6 . | 7 1 .
-------+-------+------
 . . . | 2 . 8 | . . .
 . 1 8 | . . . | 9 7 .
 . . . | 6 . 7 | . . .
-------+-------+------
 . 7 3 | . 5 . | 1 9 .
 . . 9 | . 3 . | 6 . .
 . . . | . . . | . . .

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