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2006-01-02 Really Deserving of the Sobriquet 'Nightmare' ?

 
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lac
Hooked
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Joined: 02 Jan 2006
Posts: 43
Location: Göteborg, Sweden

PostPosted: Mon Jan 02, 2006 12:30 pm    Post subject: 2006-01-02 Really Deserving of the Sobriquet 'Nightmare' ? Reply with quote

Ruud,

I think you are slipping. Wink At any rate, while hard, I wouldn't consider this one a nightmare. I think that this means that I know something your program doesn't, (yet) and I think I know what it is, too.

Allow me to pull up the soapbox:

So: first you do the obvious stuff and get to here:

Code:

129     6       5       |4       19      8       |7       3       129
4       92      132     |2369    7       12369   |8       29      5
12397   279     8       |239     5       1239    |4       6       129
----------------------------------------------------------------------
6       8       132     |57      139     57      |23      4       293     
57      57      9       |2       6       4       |1       2398    2398
123     4       123     |8       139     1239    |6       5       7
----------------------------------------------------------------------
2589    1       6       |3579    4       39      |235     2789    238
259     259     7       |35679   8       369     |253     1       4
85      3       4       |1       2       57      |9       78      6



The only tricky bit is seeing that the 57 pair are forced in row 4,
columns 4 and 6, which forces the 4 for column 7. State
shown after placing the 4s.

Then after solving for a bit ... you get to ...

Code:

19      6       5       |4      19      8       |7      3       2
4       2       13      |36     7       137     |8      9       5
397     97      8       |39     5       2       |4      6       1
----------------------------------------------------------------------

6       8       13      |5      13      7       |2      4       9
57      57      9       |2      6       4       |1      8       3
123     4       123     |8      139     139     |6      5       7
----------------------------------------------------------------------
59      1       6       |7      4       39      |53     2       8
259     259     7       |369    8       369     |53     1       4
8       3       4       |1      2       5       |9      7       6



And this is where something very interesting is revealed. 1,3 are the candidates for row 2 column 3, row 4 column 3, and row 4 column 5. This means that either _both_ 2,3 and 4,5 are 1, or both 2,3 and 4,5 are 3. But they cannot be 1s, because then row 1 column 1 and row 1 column 5 would both force to 9s. Thus they are 3s.

Then this all falls out nicely.

So what did your program have to do to solve this? Something
harder I would bet. Smile

Thank you very much for the Daily Sudoku Nightmare, and this
forum to discuss things like this. I hope I did not make any
transcription errors writing this posting. If I did, let me know
and I will fix them.

Thanks very much again,

Laura Creighton


Last edited by lac on Mon Jan 02, 2006 11:19 pm; edited 2 times in total
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Ruud
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Joined: 30 Dec 2005
Posts: 601

PostPosted: Mon Jan 02, 2006 10:26 pm    Post subject: Reply with quote

Hi Laura,

You obviously followed a different path in solving this 'nightmare'. My attempt led me to almost the same candidate situation as in your first diagram, but at that point, you can either use the naked pair, or work through a series of 4 line=box interactions (locked candidates) to reach this point:

Code:
.------------.------------.------------.
| 19  6   5  | 4   19  8  | 7   3   2  |
| 4   2   13 | 36  7   136| 8   9   5  |
| 379 79  8  | 39  5   2  | 4   6   1  |
:------------+------------+------------:
| 6   8   13 | 5   13  7  | 2   4   9  |
| 57  57  9  | 2   6   4  | 1   8   3  |
| 13  4   2  | 8   139 19 | 6   5   7  |
:------------+------------+------------:
| 59  1   6  | 7   4   39 | 35  2   8  |
| 2   59  7  | 369 8   369| 35  1   4  |
| 8   3   4  | 1   2   5  | 9   7   6  |
'------------'------------'------------'


Here, Sudo Cue found a Swordfish in the 9-s, immediately followed by a colouring check in the 1-s. This bottleneck allowed this Sudoku to become a nightmare.

I've encountered other players who, through experience, are able to see the shortcuts that always exist in these puzzles.

New human solving techniques will soon be implemented in Sudo Cue, so it may be able to find these shortcuts.

Thanks for your input.

Ruud.
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