The New Sudoku Players' Forum

[JeffInCA]

First of all let me say that I'm not looking for the "solution" to this puzzle. My question is more about methodology

I have a puzzle that I have gotten to the following state:

Code: Select all

 *--------------------------------------------------------------------*
 | 2      8      3      | 46     5      46     | 1      9      7      |
 | 7      6      5      | 89     189    19     | 2      4      3      |
 | 14     14     9      | 7      2      3      | 58     58     6      |
 |----------------------+----------------------+----------------------|
 | 56     35     4      | 1      68     7      | 9      358    2      |
 | 156    12359  12     | 2389   4      29     | 568    7      58     |
 | 8      239    7      | 239    69     5      | 46     13     14     |
 |----------------------+----------------------+----------------------|
 | 9      124    12     | 5      7      8      | 3      6      14     |
 | 3      7      6      | 29     19     1249   | 458    158    58     |
 | 145    145    8      | 46     3      146    | 7      2      9      |
 *--------------------------------------------------------------------*


At this point I've exhuasted all the basic techniques as well as the advanced ones with which I am well-versed - X-wing, swordfish, XY-wing, coloring.

My question is... once you've got past this stage, what do you look for next? Is there some sort of methodology? If forcing chains are the only real technique short of trial and error, what's the best way to seek them out in a puzzle such as this one?

As I say, I'm not looking specifically for the answer as much as the thought process that gets you from this state to the elimination which unlocks the puzzle.

Thanks,

Jeff

P.S. As I'm reviewing this post I just noticed that the square defined by r56c24 has an interesting pattern in that all four cells contain 239. Is this some form of the "Almost Unique Rectangle" family? This is another technique which I haven't quite absorbed yet.

[smoof]

I plugged your puzzle into this solver
http://www.stolaf.edu/people/hansonr/sudoku/index.htm

and enabled the almost-locked-sets option. It shows that if you solve just one ALS, the rest of the puzzle becomes trivial. ALS appears to be a very powerful technique but I'm struggling to learn it myself.

[sweetbix]

Uniqueness is most obvious r1c46 and r9c46 that gives r9c6=1

Code: Select all

 *--------------------------------------------------------------------*
 | 2      8      3      | 46*     5      46*    | 1      9      7      |
 | 7      6      5      | 89     189    19     | 2      4      3      |
 | 14     14     9      | 7      2      3      | 58     58     6      |
 |----------------------+----------------------+----------------------|
 | 56     35     4      | 1      68     7      | 9      358    2      |
 | 156    12359  12     | 2389   4      29     | 568    7      58     |
 | 8      239    7      | 239    69     5      | 46     13     14     |
 |----------------------+----------------------+----------------------|
 | 9      124    12     | 5      7      8      | 3      6      14     |
 | 3      7      6      | 29     19     1249   | 458    158    58     |
 | 145    145    8      | 46*    3      146*   | 7      2      9      |
 *--------------------------------------------------------------------*


Also quite a long chain.
r4c1=5 => r4c2=3
r4c1=6 => r4c5=8 => r6c5=6 =>r6c7=4 => r6c9=1 => r6c8=3 => r4c8=5 => r4c2=3

My 'thought process' is to try any other tactic I can think of. I 'guess' to find the starting cell for longer chains which I think is considered 'inelegant' in this forum but there are threads here on using bilocation/bivalue plots eg http://forum.enjoysudoku.com/viewtopic.php?p=10012#p10012

[MCC]

Once you've used the uniqueness rectangle that sweetbix pointed out, this places a 1 in r9c6, leaving a naked pair in r9c12, from there it's singles all the way.

MCC

[tarek]

Uniqueness should be enough Jeff,

There is also for fun an xyz wing

Code: Select all

*-----------------------------------------------------------------*
| 2      8      3     | 46     5      46    | 1      9      7     |
| 7      6      5     | 89     189    19    | 2      4      3     |
| 14     14     9     | 7      2      3     | 58     58     6     |
|---------------------+---------------------+---------------------|
| 56     35     4     | 1      68     7     | 9      358    2     |
| 156    12359  12    | 2389   4      29    | 568    7      58    |
| 8      239    7     | 239    69     5     | 46     13     14    |
|---------------------+---------------------+---------------------|
| 9      124    12    | 5      7      8     | 3      6      14    |
| 3      7      6     | 29     19     1249  | 458    158    58    |
| 145    145    8     | 46     3      146   | 7      2      9     |
*-----------------------------------------------------------------*
Eliminating 1 From r9c2 (2 & 4 & 1 in r7c2 form an XYZ wing with r7c3 & r3c2)

Tarek

[JeffInCA]

Ah, uniqueness... good catch. this is a technique with several variations of which I think I should be more familiar.

Funny thing is the particular pattern sweetbix found is the one which I can spot (I just didn't in this case).

Can anyone tell me if the cells at r56c24 form some kind of "almost unique rectangle" from which any deductions can be made?

Also, tarek, good call on the xyz-wing. I missed that one too

Jeff

[Myth Jellies]

Can anyone tell me if the cells at r56c24 form some kind of "almost unique rectangle" from which any deductions can be made?

Not much you can do with that one, however there is another uniqueness pattern which can lead to a reduction.

Code: Select all

*-----------------------------------------------------------------*
| 2      8      3     | 46     5      46    | 1      9      7     |
| 7      6      5     | 89     189    19    | 2      4      3     |
| 14     14     9     | 7      2      3     |*58    *58     6     |
|---------------------+---------------------+---------------------|
| 56     35     4     | 1      68     7     | 9      358    2     |
| 156    12359  12    | 2389   4      29    |*58+6   7     *58    |
| 8      239    7     | 239    69     5     | 46     13     14    |
|---------------------+---------------------+---------------------|
| 9      124    12    | 5      7      8     | 3      6      14    |
| 3      7      6     | 29     19     1249  | 458   *58+1  *58    |
| 145    145    8     | 46     3      146   | 7      2      9     |
*-----------------------------------------------------------------*


The starred cells represent a uniqueness or BUG-lite+2 pattern which must be avoided. From here it is pretty easy to show that both r5c7 = 6 and/or r8c8 = 1 implies r8c7 <> 4. That will solve a lot of fours.

The quantum (16) node idea can be used for xy-wings as well as for locked sets.

The little xy-wing-like nice loop looks like
r8c7 - 4 - r6c7 - 6|AUR|1 - r7c9 - 4 - r8c7 => r8c7 <> 4, & where AUR refers to the starred cells

Or the way I "see" it
[4 = 6] - [6 =AUR= 1] - [1 = 4] chain eliminates all 4's in cells that see both endpoints in r6c7 and r7c9. Thus 4's in r8c7 and r6c9 are eliminated.

This looks like a grid where Carcul made a similar observation.

[ronk]

Can anyone tell me if the cells at r56c24 form some kind of "almost unique rectangle" from which any deductions can be made?

I illustrated that 'rectangle' in the context of a discussion on the Help with particular puzzles forum. In retrospect, the topic is more appropriate for this forum. Sorry.

Ron