The New Sudoku Players' Forum

[Del]

This appeared recently in a French national newspaper:

2XX XX4 XXX
91X 8XX XXX
XX8 3XX 641

XXX XXX 7XX
XXX 4XX XXX
X7X XX3 X98

XX3 XXX XXX
XXX X5X 4X2
8X5 XXX 9XX

I arrived at the following before needing to fill in the possible candidates:

236 XX4 XX9
914 8XX XXX
758 3XX 641

3XX XXX 7X4
5XX 4XX XXX
47X XX3 X98

X23 X4X XXX
X97 X58 432
845 X3X 9XX

Colouring then enabled me to remove a 5 from G2; i.e. r2c7.

What could be done next?

[udosuk]

Simple Sudoku is stuck at here:

Code: Select all

 *--------------------------------------------------------------------*
 | 2      3      6      | 157    17     4      | 58     578    9      |
 | 9      1      4      | 8      67     567    | 23     257    357    |
 | 7      5      8      | 3      29     29     | 6      4      1      |
 |----------------------+----------------------+----------------------|
 | 3      68     129    | 1259   1289   1259   | 7      1256   4      |
 | 5      68     129    | 4      12789  1279   | 123    126    36     |
 | 4      7      12     | 1256   126    3      | 125    9      8      |
 |----------------------+----------------------+----------------------|
 | 16     2      3      | 1679   4      1679   | 158    15678  567    |
 | 16     9      7      | 16     5      8      | 4      3      2      |
 | 8      4      5      | 1267   3      1267   | 9      167    67     |
 *--------------------------------------------------------------------*

There is a UR type 1 in r78c14, but not much helpful...

Hopefully someone could find a UVWXYZ-wing or ALS...

[emm]

Code: Select all

 *--------------------------------------------------------------------*
 | 2      3      6      | 157    17     4      | 58     578    9      |
 | 9      1      4      | 8      67     567    | 23     257    357    |
 | 7      5      8      | 3      29     29     | 6      4      1      |
 |----------------------+----------------------+----------------------|
 | 3      68     129    | 1259   1289   1259   | 7      1256   4      |
 | 5      68     129    | 4      12789  1279   | 123    126    36     |
 | 4      7      12     | 1256   126    3      | 125    9      8      |
 |----------------------+----------------------+----------------------|
 | 16     2      3      | 1679   4      1679   | 158    15678  567    |
 | 16     9      7      | 16     5      8      | 4      3      2      |
 | 8      4      5      | 1267   3      1267   | 9      167    67     |
 *--------------------------------------------------------------------*

r2c5=7 -> r1c5=1
r2c5=6 -> r6c4=6 -> r8c4=1 -> r1c5=1

Code: Select all

 *--------------------------------------------------------------------*
 | 2      3      6      | 57     1      4      | 58     578    9      |
 | 9      1      4      | 8      67     567    | 23     257    357    |
 | 7      5      8      | 3      29     29     | 6      4      1      |
 |----------------------+----------------------+----------------------|
 | 3      68     129    | 1259   289    1259   | 7      1256   4      |
 | 5      68     129    | 4      2789   1279   | 123    126    36     |
 | 4      7      12     | 1256   26     3      | 125    9      8      |
 |----------------------+----------------------+----------------------|
 | 16     2      3      | 1679   4      1679   | 158    15678  567    |
 | 16     9      7      | 16     5      8      | 4      3      2      |
 | 8      4      5      | 1267   3      1267   | 9      167    67     |
 *--------------------------------------------------------------------*

If r6c4=5 -> r6c5=6 -> r2c5=7 -> r1c4=5 => r6c4<>5 => r6c7=5

From here the puzzle unravels

[daj95376]

It's strange that a newspaper would publish a non-symmetrical puzzle of this complexity.

Code: Select all

 *-----------*
 |2..|..4|...|
 |91.|8..|...|
 |..8|3..|641|
 |---+---+---|
 |...|...|7..|
 |...|4..|...|
 |.7.|..3|.98|
 |---+---+---|
 |..3|...|...|
 |...|.5.|4.2|
 |8.5|...|9..|
 *-----------*

# after Singles, Naked Pair, Locked Candidate (2)
 *--------------------------------------------------------------------*
 | 2      3      6      | 157    17     4      | 58     578    9      |
 | 9      1      4      | 8      67     567    | 235    257    357    |
 | 7      5      8      | 3      29     29     | 6      4      1      |
 |----------------------+----------------------+----------------------|
 | 3      68     129    | 1259   1289   1259   | 7      1256   4      |
 | 5      68     129    | 4      12789  1279   | 123    126    36     |
 | 4      7      12     | 1256   126    3      | 125    9      8      |
 |----------------------+----------------------+----------------------|
 | 16     2      3      | 1679   4      1679   | 158    15678  567    |
 | 16     9      7      | 16     5      8      | 4      3      2      |
 | 8      4      5      | 1267   3      1267   | 9      167    67     |
 *--------------------------------------------------------------------*

r1c7    =  8     [r1c7]=5,[r2c6]=5,[r2c5]=6 => [r6]=INVALID


[Edited] Removed extraneous information.

[TKiel]

There is a UR Type 6 (I think that is the designation, it's the kind of UR that's also an X-wing) in r17c78 that makes a couple of exclusions that create an X-wing that eventually allows the placement of 5 in r7c9. Simple Sudoku gets stuck again after that. There also seems to be large potential for UR's in box 1 & 2 invoving (2,9), but time doesn't allow a close examination right now. Maybe later.

Tracy

[keith]

Tracy is correct:

Code: Select all

+-------------------+-------------------+-------------------+
| 2     3     6     | 157   17    4     | 58    578   9     |
| 9     1     4     | 8     67    567   | 235   257   357   |
| 7     5     8     | 3     29    29    | 6     4     1     |
+-------------------+-------------------+-------------------+
| 3     68    129   | 1259  1289  1259  | 7     1256  4     |
| 5     68    129   | 4     12789 1279  | 123   126   36    |
| 4     7     12    | 1256  126   3     | 125   9     8     |
+-------------------+-------------------+-------------------+
| 16    2     3     | 79    4     1679  | 158   15678 567   |
| 16    9     7     | 16    5     8     | 4     3     2     |
| 8     4     5     | 1267  3     1267  | 9     167   67    |
+-------------------+-------------------+-------------------+

The UR on <58> in R17C78 is also an X-wing on <8>. R7C8 cannot be <5>, for that forces a deadly solution.

Not much help, so far as I can see.

Keith

[Del]

Many thanks to you all for your replies. They have opened my eyes to a wider range of possibilities of Forcing Chains.
To daj95376: The paper publishes a puzzle labelled "Expert" in their weekend magazine; it is generally asymmetrical. This one was the hardest so far.

[udosuk]

To cap it off, here is a simple ALS to resolve that position:

Code: Select all

 *--------------------------------------------------------------------*
 | 2      3      6      |A157   A17     4      |-58     578    9      |
 | 9      1      4      | 8     A67     567    | 23     257    357    |
 | 7      5      8      | 3      29     29     | 6      4      1      |
 |----------------------+----------------------+----------------------|
 | 3      68     129    | 1259   1289   1259   | 7      1256   4      |
 | 5      68     129    | 4      12789  1279   | 123    126    36     |
 | 4      7     B12     |-1256  B126    3      |B125    9      8      |
 |----------------------+----------------------+----------------------|
 | 16     2      3      | 1679   4      1679   | 158    15678  567    |
 | 16     9      7      | 16     5      8      | 4      3      2      |
 | 8      4      5      | 1267   3      1267   | 9      167    67     |
 *--------------------------------------------------------------------*

ALS-xz:
A: r1c45 + r2c5 = {1567}
B: r6c357 = {1256}
x = 6 (restricted common)
z = 5 (other common)

If r1c7=5 or r6c4=5 then A={167} and B={126} and we're forced to have two 6s on c5 (r26c5).

Hence r1c7<>5 and r6c4<>5, r1c7=8, r6c7=5 and the rest are all singles...

[daj95376]

udosuk, I must admit that I turn and run when I see an ALS explanation -- even when the word simple preceeds it. In this case, I stopped and took a close look at your explanation and found it interesting. So then I took a look around and asked myself if [r6c4]<>5 qualifies as well with the ALS you presented. For sure, it works ... and ... it eliminates the turbot fish and only leaves singles to complete the puzzle. (No, I'm not converted to an ALS fan.)

[udosuk]

Thanks! My mistake for missing the obvious dual eliminations... Edited the explanation now...

[Del]

To udosuk:
I can follow the logic of your solution, i.e. if r1c7=5 then r6c4=5 and vice versa but if both cells contain 5 then this results in two 6's in col.5. Therefore there cannot be a 5 in both r1c7 and r6c4.
Finding this solution by searching through all the available candidates would seem to be a formidable task and is presumably made easier with the ALS technique; which is new territory for me. I found a discourse on the subject by a contributor with the pseudonym "benny" and managed to retain a vague understanding of it for about ten seconds. Are you able to help me further by defining what is an Almost Locked Set so that I may be able to recognise one in the future?

[udosuk]

Take a look at this post:
http://forum.enjoysudoku.com/viewtopic.php?t=3315&start=3

Look up the 3 links under "Almost Locked Sets (ALS)"...

From my own understanding, a Locked Set is a set of n cells (all in the same row/column/box) collectively holding n different candidates. We often call them in other basic names: naked single (n=1), naked pair (n=2), naked triple (n=3), naked quad (n=4)...

An Almost Locked Set is a set of n cells (all in the same row/column/box) collectively holding (n+1) different candidates... And manipulations of the extra candidates on 2 or more of such sets would often lead us to useful eliminations...

[Mike Barker]

I just wrote up a description in the preceding post "a bunch of naked triples" here.

[daj95376]

I am far from versed on Locked Sets and Almost Locked Sets, but I'd like to make an observation on Del's puzzle and what bothers me about using ALS to solve it.

From what I can tell, there are two Quads/N-Tuples/Locked Sets: <1567> in [b2], and <1256> in [r6]. Now, to create the ALS, cell [r2c6] was dropped from one Quad and cell [r6c4] was dropped from the other Quad. This left two over-determined sets of three cells from which conclusions were drawn via the ALS technique. This may be acceptable, but it doesn't seem right.

To me, what exists in this puzzle are two Quads that overlay in such a way that they both can't be <6> in [c5]. It just turns out that placing <5> in two key cells forces this condition and results in the elimination of those <5>s.

Is there another technique that'd work with the Quads intact??? How about a Double Implication Chain on <6> in [c5]???

[ronk]

Is there another technique that'd work with the Quads intact??? How about a Double Implication Chain on <6> in [c5]???

With the quads intact? ... I don't think so. But the nice loop -- with double implication chains -- using the ALSs is ...

[r1c7,r6c4]-5-{ALS A:r1c45=5|6=r2c5}-6-{ALS B:r6c35=6|5=r6c7}-5-[r1c7,r6c4]
... which implies r1c7<>5, r6c4<>5

Read left-to-right, either premise r1c7=5 or r6c4=5 excludes the 5 from set A. With the 5 excluded, set A must contain a 6 excluding the 6 from set B, which means set B must contain a 5, excluding the 5 from r1c7 and r6c4. This contradicts the premises ... meaning both premises must be false.