The New Sudoku Players' Forum

[DonM]

Welcome to the occasional/sporadic 'Suggest A Move' (SAM) series (returning after a brief pause of 3 years ), consisting of of a puzzle at a point where there are some interesting patterns and whereby people are invited to come up with any interesting patterns/chains they discover. There is no hidden surprise or backdoor (at least not that I know of) or some other trick awaiting and I haven't made any exhaustive search for all possible interesting patterns. It is simply an interesting puzzle.

Note: SSTS means Simple Sudoku Techniques Set. Post-SSTS means that the original puzzle was solved by Simple Sudoku to the point where there is 'No Hint Available'. ER means Explainer Rating whereby Sudoku Explainer assigns a general difficulty value to the puzzle.

Even though the SSTS position eliminates a number of basic patterns that some solvers may be used to finding in more recent puzzles in this Puzzles Section, this is not an extremely difficult puzzle. Also note that the primary objective is more finding interesting patterns or chains rather than necessarily solving the puzzle.

Code: Select all

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

SAM#3: ER=7.1 at the SSTS position:

Code: Select all

 *-----------------------------------------------------------*
 | 1357  35    4     | 23    9     27    | 135   6     8     |
 | 135   8     69    | 36    56    4     | 1359  7     2     |
 | 357   29    269   | 8     567   1     | 359   359   4     |
 |-------------------+-------------------+-------------------|
 | 8     3459  359   | 7     12    29    | 346   134   136   |
 | 6     1     7     | 5     4     3     | 2     8     9     |
 | 2     349   39    | 169   16    8     | 7     134   5     |
 |-------------------+-------------------+-------------------|
 | 9     23    8     | 4     127   267   | 356   135   1367  |
 | 345   6     135   | 19    8     579   | 49    2     137   |
 | 45    7     125   | 129   3     2569  | 8     49    16    |
 *-----------------------------------------------------------*


[daj95376]

Additional level of difficulty! You are not allowed to use the following Skyscraper in any solution you propose.

Skyscraper: (2) r1c4 = r9c4 - r9c3 = r3c3

[SudoQ]

Additional level of difficulty! You are not allowed to use the following Skyscraper in any solution you propose.

Skyscraper: (2) r1c4 = r9c4 - r9c3 = r3c3

Code: Select all

|-------------------|-----------------|-----------------|
| 1357  235   4     |(2)3  9    (27)  | 135   6    8    |
| 135   8     13569 | 36   56    4    | 1359  7    2    |
| 357   2359  23569 | 8    2567  1    | 359   359  4    |
|-------------------|-----------------|-----------------|
| 8     3459  359   | 7    12    29   | 346   134  136  |
| 6     1     7     | 5    4     3    | 2     8    9    |
| 2     349   39    | 169  16    8    | 7     134  5    |
|-------------------|-----------------|-----------------|
| 9    (23)   8     | 4    127   267  | 356   135  1367 |
|1(3)45 6     1(3)5 | 19    8   5(7)9 | 49    2    1(37)|
| 145   7     15-2  |1(2)9  3    2569 | 8     49   16   |
|-------------------|-----------------|-----------------|


/SudoQ

[ArkieTech]

Code: Select all

 *--------------------------------------------------------------------*
 | 1357   235    4      |a23     9      27     | 135    6      8      |
 | 135    8     c13569  |b36     56     4      | 1359   7      2      |
 | 357    2359   23569  | 8      2567   1      | 359    359    4      |
 |----------------------+----------------------+----------------------|
 | 8      3459  c359    | 7      12     29     | 346    134    136    |
 | 6      1      7      | 5      4      3      | 2      8      9      |
 | 2      349   c39     | 169    16     8      | 7      134    5      |
 |----------------------+----------------------+----------------------|
 | 9      23     8      | 4      127    267    | 356    135    1367   |
 | 1345   6     c135    | 19     8      579    | 49     2      137    |
 | 145    7     c125    | 19-2   3      2569   | 8      49     16     |
 *--------------------------------------------------------------------*
als xy-wing
(2=3)r1c4-(3=6)r2c4-(6r2c3=2r9c3)r24689c3 => -2r9c4; lclste

[DonM]

Additional level of difficulty! You are not allowed to use the following Skyscraper in any solution you propose.

Skyscraper: (2) r1c4 = r9c4 - r9c3 = r3c3

Code: Select all

|-------------------|-----------------|-----------------|
| 1357  235   4     |(2)3  9    (27)  | 135   6    8    |
| 135   8     13569 | 36   56    4    | 1359  7    2    |
| 357   2359  23569 | 8    2567  1    | 359   359  4    |
|-------------------|-----------------|-----------------|
| 8     3459  359   | 7    12    29   | 346   134  136  |
| 6     1     7     | 5    4     3    | 2     8    9    |
| 2     349   39    | 169  16    8    | 7     134  5    |
|-------------------|-----------------|-----------------|
| 9    (23)   8     | 4    127   267  | 356   135  1367 |
|1(3)45 6     1(3)5 | 19    8   5(7)9 | 49    2    1(37)|
| 145   7     15-2  |1(2)9  3    2569 | 8     49   16   |
|-------------------|-----------------|-----------------|


/SudoQ

Hey SudoQ- that's a pretty good chain, but more people will be able to appreciate it if you notate it:
(2=3)r7c2-grp(3)r7c13=(3-7)r8c9=r8c6-(7=2)r1c6-r1c4=(2)r9c4 => r9c3<>2 => r7c2=2

[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
| 1357    235     4        |a23      9      A27       | 135     6       8        |
| 135     8       13569    | 36      56      4        | 1359    7       2        |
| 357     2359   d23569    | 8      e56-27B  1        | 359     359     4        |
|--------------------------+--------------------------+--------------------------|
| 8       3459    359      | 7       12      29       | 346     134     136      |
| 6       1       7        | 5       4       3        | 2       8       9        |
| 2       349     39       | 169     16      8        | 7       134     5        |
|--------------------------+--------------------------+--------------------------|
| 9       23      8        | 4       127     267      | 356     135     1367     |
| 1345    6       135      | 19      8       579      | 49      2       137      |
| 145     7      c125      |b129     3       2569     | 8       49      16       |
*--------------------------------------------------------------------------------*

L2 Wing with bivalue extension cell:

(2) r1c4 = r9c4 - r9c3 = (2-6) r3c3 = r3c5; 2 r1c4 - (2=7) r1c6 - r3c5: => r3c5<> 2, 7 ; 1c1ste

Leren

[SudoQ]

Hey SudoQ- that's a pretty good chain, but more people will be able to appreciate it if you notate it...

Sorry, I can only do it like this:

Code: Select all

r2c4=6 -> r3c3=6 -> r9c3=2
    =3 -> r1c4=2           => r9c4<>2


/SudoQ

[eleven]

Skyscraper: (2) r1c4 = r9c4 - r9c3 = r3c3

Here is one without using any of the 2 strong links (or calling it an ALS):

Code: Select all

+-------------------+-------------------+-------------------+
| 1357  35    4     | 23    9    *27    | 135   6     8     |
| 135   8     69    | 36    56    4     | 1359  7     2     |
|c357  a29    269   | 8     567   1     |b359  b359   4     |
+-------------------+-------------------+-------------------+
| 8     3459  359   | 7    #12   #29    | 346   134   136   |
| 6     1     7     | 5     4     3     | 2     8     9     |
| 2     349   39    | 169   16    8     | 7     134   5     |
+-------------------+-------------------+-------------------+
| 9    @23    8     | 4    #127  #267   | 356   135   1367  |
| 345   6     135   | 19    8     579   | 49    2     137   |
| 45    7     125   | 129   3     2569  | 8     49    16    |
+-------------------+-------------------+-------------------+

Almost x-wing for 2 in r47c56
If its an x-wing, then r1c6=7
if not, then r7c2=2->r3c2=9->r3c78=35->r3c1=7->r1c6=7

(7=2)r1c6-(xwing 2r47c56)=2r7c2-(2=9)r3c2-(9=35)r3c78-(35=7)r3c1; r1c1<>7


HNY, eleven

[storm_norm22]

als xz rule chain

[DonM]

als xz rule chain

Hi Norm. That's what I call pure pattern solving and with a pretty picture too.

[storm_norm22]

als xz rule chain

Hi Norm. That's what I call pure pattern solving and with a pretty picture too.

so just a question then.

how is that chain in the picture denoted in AIC? the reason I ask is because that chain can be extended to include a lot more cells so as to not included the ALS structure.

[DonM]

als xz rule chain

Hi Norm. That's what I call pure pattern solving and with a pretty picture too.

so just a question then.

how is that chain in the picture denoted in AIC? the reason I ask is because that chain can be extended to include a lot more cells so as to not included the ALS structure.

als(2=19)r89c4-als(9=126)r4c5/r6c45 => r7c5<>2

Norm, I'm not sure what potential limitations (if that is the right word) are implied by the part after 'the reason I ask...'

[ronk]

how is that chain in the picture denoted in AIC? the reason I ask is because that chain can be extended to include a lot more cells so as to not included the ALS structure.

als xy-wing: (2=9)r89c4 - (9=1)r6c45 - (1=2)r4c5 ==> r7c5<>2

[Luke]

I see all als-xz patterns as just two weakly linked almost locked sets. (adding: pretty much what Don posted)

(2=169)als:r4c5,r6c45-(9=12)als:r89c4 ==>r7c5<>2