Double x-wing's

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Double x-wing's

Postby MCC » Wed Oct 26, 2005 4:34 pm

The following is a pappocom v.hard.

After 16 placements I found two x-wings ( a SuperSizeMe x-wing and a Mini-Me x-wing ) in the same number, following eliminations a placement can be made, then it's downhill from there.

Both x-wings seem to be needed to progress.

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


It's the alignment of the two x-wings to each other and the grid that I find pleasing.
MCC
 
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Postby emm » Wed Oct 26, 2005 6:30 pm

Nice layout, MCC, very neat - though I hate to contradict you but you only need the Super-Size. Mini-Me is superfluous to requirements!
emm
 
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Joined: 02 July 2005

Postby r.e.s. » Wed Oct 26, 2005 9:22 pm

Just to show that Sherlocking would also work ...
Candidate grid at the stage of interest:
Code: Select all
  17    5     2     | 8     3     6     | 9     4     17   
  79    6     39    | 5     1     4     | 27    8     237   
  4     8     13    | 2     7     9     | 16    136   5     
  ------------------+-------------------+----------------
  8     12    6     | 4     9     3     | 5     7     12   
  5     9     4     | 1     2     7     | 68    36    368   
  3     12    7     | 6     8     5     | 4     12    9     
  ------------------+-------------------+----------------
  1269  7     19    | 3     5     28    | 1268  126   4     
  26    3     8     | 9     4     1     | 267   5     267   
  12    4     5     | 7     6     28    | 3     9     128   

The allowable permutations of candidates for col 1 & col 9:
Code: Select all
 col 1        col 9
-------    -----------
1 7 7 7    1 1 7 7 7 7
7 9 9 9    3 7 2 3 3 3
. . . .    . . . . . .
. . . .    2 2 1 1 1 2
. . . .    6 3 3 6 8 8
. . . .    . . . . . .
9 1 2 6    . . . . . .
6 6 6 2    7 6 6 2 6 6
2 2 1 1    8 8 8 8 2 1
-------    -----------
x                x
  x        x
    x      x
      x    x
      x      x

Two x's in a row mark a compatible pair of column permutations.

All the compatible pairs have r9c9=8; therefore, r9c9=8.
r.e.s.
 
Posts: 337
Joined: 31 August 2005

Postby MCC » Thu Oct 27, 2005 11:18 am

em wrote:... though I hate to contradict you but you only need the Super-Size. Mini-Me is superfluous to requirements!


You're probably right em, I saw Super-Size and whilst doing the eliminations I spotted Mini-Me and did further eliminations so there may have been a placement or elimination I missed.

It's just that I took a more scenic pathway:D
MCC
 
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Postby emm » Thu Oct 27, 2005 11:38 am

Talking about scenic pathways and perhaps I shouldn’t say this – but what the heck - I find the Sherlock technique mind-numbingly tedious and the enthusiasm for it quite mystifying. All credit to its inventor and the notable people who wax lyrical about it, but as a technique for puzzle solving, I have to say it strikes me as the least scenically-appealing method of all time and I was relieved to read that it only got so far with the Hardest Known Sudoku. Phew! For a terrible moment I thought I might have to learn it! Speaking as a common-garden puzzle solver, I doubt that this technique would tempt me even if I was alone on a desert island, suicidally-bored and desperate for any kind of diversion! I have learnt to never say never but I think this once might be the exception that proves the rule.
emm
 
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Postby CathyW » Thu Oct 27, 2005 11:53 am

em wrote:... I find the Sherlock technique mind-numbingly tedious and the enthusiasm for it quite mystifying. ... I have to say it strikes me as the least scenically-appealing method of all time ... Phew! For a terrible moment I thought I might have to learn it!


I have to agree with you Em - I really don't think I could be bothered to write down all the permutations and I (probably!) spend too much time on Sudoku in various forms as it is. It's good to learn about new techniques but I prefer those that help to solve some of the puzzles a bit quicker and are more elegant.

Equally I can't see the fascination with the maths and minimum number of clues though they are clearly very popular threads in this forum. Each to their own:)
CathyW
 
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Postby r.e.s. » Thu Oct 27, 2005 10:12 pm

em, and CathyW ...

I mostly agree with your reservations about Sherlocking, and am not particularly enthusiastic about it -- in the present case I only did it on a whim. It would be nice to find a puzzle (if there are any) where Sherlocking actually has a clear advantage over more-standard methods.
r.e.s.
 
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Joined: 31 August 2005


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