The New Sudoku Players' Forum

[DonM]

Welcome to Suggest A Play, the little brother of the occasional/sporadic 'Suggest A Move' (SAM) series. Like the latter, this consists of of a puzzle at a point where there are some interesting patterns. However, here, manual solvers are invited to come up with any interesting patterns/chains they discover and/or solve the puzzle (SAM puzzles ordinarily emphasize coming up with moves before the puzzle is opened up for full solving). Suggest A Play puzzles are also selected to be both of interest to experienced solvers and to be perfectly accessible by newer solvers.

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 bypasses basic patterns solvers may find in most puzzles in this Puzzles Section, the puzzle at this starting point is not particularly difficult though it is a step up in difficulty.

Code: Select all

*-----------*
 |2..|.1.|..6|
 |...|..2|..7|
 |..8|...|42.|
 |---+---+---|
 |.12|.5.|3..|
 |...|4.1|...|
 |..5|.8.|97.|
 |---+---+---|
 |.84|...|59.|
 |6..|5..|...|
 |5..|.3.|...|
 *-----------*


Code: Select all

SAP #1 Post SSTS (Simple Sudoku Technique Set)  ER=7.7
 *--------------------------------------------------------------------*
 | 2      34579  379    | 379    1      4579   | 8      35     6      |
 | 39     3459   6      | 8      49     2      | 1      35     7      |
 | 1      357    8      | 367    67     567    | 4      2      9      |
 |----------------------+----------------------+----------------------|
 | 789    1      2      | 679    5      679    | 3      468    48     |
 | 3789   379    379    | 4      679    1      | 2      68     5      |
 | 4      6      5      | 2      8      3      | 9      7      1      |
 |----------------------+----------------------+----------------------|
 | 37     8      4      | 1      267    67     | 5      9      23     |
 | 6      239    139    | 5      249    489    | 7      148    2348   |
 | 5      279    179    | 79     3      4789   | 6      148    248    |
 *--------------------------------------------------------------------*

[Leren]

Forcing Chain from -4 r1c2 solves that cell (but not the puzzle).

Code: Select all

- 4 r1c2 = r2c2 - (4=9) r2c5                                         - 9 r5c5;
                          ||
                           -  (9=3)  r2c1 - r3c2 = (3-6) r3c4 = r4c4 - 6 r5c5;
                                      ||
                                       - (3=7) r7c1 - r4c1 = r4c46   - 7 r5c5; => r1c2 = 4

Leren

[JC Van Hay]

While doing the "basics", it is observed that there is no N(>1)-Fish for the digits 7 and 9, the only digits where one could find one.
However, the potential FinnedXWings on 7s and 9s in the columns 1 and 5 cannot be both true otherwise r5c2=r5c3=3! IOW, 7r3c5=9r8c5.

Code: Select all

+----------------------+------------------+--------------+
| 2       34579  379   | 379  1      4579 | 8  35   6    |
| 3(9)    3459   6     | 8    4(9)   2    | 1  35   7    |
| 1       357    8     | 367  6(7)   567  | 4  2    9    |
+----------------------+------------------+--------------+
| 8(79)   1      2     | 679  5      679  | 3  468  48   |
| 38(79)  (379)  (379) | 4    6(79)  1    | 2  68   5    |
| 4       6      5     | 2    8      3    | 9  7    1    |
+----------------------+------------------+--------------+
| 3(7)    8      4     | 1    26(7)  67   | 5  9    23   |
| 6       239    139   | 5    24(9)  489  | 7  148  2348 |
| 5       279    179   | 79   3      4789 | 6  148  248  |
+----------------------+------------------+--------------+

Almost FinnedXWing(7) : 7r3c5=FinnedXWing(7r57c5,r574c1)-7r5c23
Almost FinnedXWing(9) : 9r8c5=FinnedXWing(9r25c5,r254c1)-9r5c23
:=> 7r3c5=9r8c5

This suggests the following path :

Code: Select all

+----------------------+-------------------+--------------+
| 2       34579  379   | 379   1      4579 | 8  35   6    |
| 3(9)    3459   6     | 8     4(9)   2    | 1  35   7    |
| 1       357    8     | 367   67     567  | 4  2    9    |
+----------------------+-------------------+--------------+
| 8(79)   1      2     | 679   5      679  | 3  468  48   |
| 38(79)  (379)  (379) | 4     67(9)  1    | 2  68   5    |
| 4       6      5     | 2     8      3    | 9  7    1    |
+----------------------+-------------------+--------------+
| 3(7)    8      4     | 1     26-7   6-7  | 5  9    23   |
| 6       239    139   | 5     24(9)  489  | 7  148  2348 |
| 5       29-7   19-7  | (79)  3      4789 | 6  148  248  |
+----------------------+-------------------+--------------+

(7=9)r9c4-9r8c5=FinnedXWing(9r25c5,r254c1)-(9=37)r5c23-7r45c1=7r7c1 :=> -7r9c23,r7c56; 4 Singles
After that : LC(7r4c46)-7r5c5=7r3c5, Singles to end.

[ArkieTech]

Code: Select all

 *--------------------------------------------------------------------*
 | 2      34579  379    | 379    1      4579   | 8      35     6      |
 | 39     3459   6      | 8      49     2      | 1      35     7      |
 | 1      357    8      | 367   b67     567    | 4      2      9      |
 |----------------------+----------------------+----------------------|
 | 89-7   1      2      | 679    5      679    | 3      468    48     |
 | 389-7 c379   c379    | 4     b679    1      | 2      68     5      |
 | 4      6      5      | 2      8      3      | 9      7      1      |
 |----------------------+----------------------+----------------------|
 |a37     8      4      | 1     b267    67     | 5      9     a23     |
 | 6      239    139    | 5      249    489    | 7      148    2348   |
 | 5      279    179    | 79     3      4789   | 6      148    248    |
 *--------------------------------------------------------------------*
(7=2)r7c19-(2=9)r357c5-(9=37)r5c23 => -7r45c1; lclste

[eleven]

Hm, hope it is correct now ...

Code: Select all

     *--------------------------------------------------------------------*
     | 2      34579  379    | 379    1      4579   | 8      35     6      |
     | 39     3459   6      | 8      49     2      | 1      35     7      |
     | 1      357    8      | 367   e67     567    | 4      2      9      |
     |----------------------+----------------------+----------------------|
     | 789    1      2      |d679    5     d679    | 3    c#48+6  #48     |
     | 3789   379    379    | 4     e679    1      | 2     b6*8    5      |
     | 4      6      5      | 2      8      3      | 9      7      1      |
     |----------------------+----------------------+----------------------|
     | 37     8      4      | 1     e267    67     | 5      9     *23     |
     | 6      239    139    | 5     a2*49  #48+9   | 7     #148   #248+3  |
     | 5      279    179    | 79     3     #48+79  | 6     #148   #248    |
     *--------------------------------------------------------------------*

MUG 1248 with external SIS 4r8c5;8r5c8;2r7c9
I had missed 2r7c9 first, but we can exclude it, because 2r7c9-(2=3)r8c9 directly leads to a MUG 148 with external SIS 4r8c5;8r5c8 too:
So we have the link 4r8c5=8r5c8
2r7c5=(2-4)r8c5=(8-6)r5c8=6r4c8-r4c46=267r357c5 => r7c5=2

[ronk]

Code: Select all

     *--------------------------------------------------------------------*
     | 2      34579  379    | 379    1      4579   | 8      35     6      |
     | 39     3459   6      | 8      49     2      | 1      35     7      |
     | 1      357    8      | 367   e67     567    | 4      2      9      |
     |----------------------+----------------------+----------------------|
     | 789    1      2      |d679    5     d679    | 3    c#48+6  #48     |
     | 3789   379    379    | 4     e679    1      | 2     b6*8    5      |
     | 4      6      5      | 2      8      3      | 9      7      1      |
     |----------------------+----------------------+----------------------|
     | 37     8      4      | 1     e267    67     | 5      9     *23     |
     | 6      239    139    | 5     a2*49  #48+9   | 7     #148   #248+3  |
     | 5      279    179    | 79     3     #48+79  | 6     #148   #248    |
     *--------------------------------------------------------------------*

MUG 1248 with external SIS 4r8c5;8r5c8;2r7c9

Nice find, you guys are really into uniqueness patterns lately. However, in this case digits <1> and <2> cannot be part of the MUG. Why? I think because there are 4 digits but only 3 pattern cells in rows 8 and 9. [edit: As eleven proves below, his MUG is indeed a MUG.]

In any case, they are really not needed. Using your style (mostly):

Code: Select all

     *--------------------------------------------------------------------*
     | 2      34579  379    | 379    1      4579   | 8      35     6      |
     | 39     3459   6      | 8      49     2      | 1      35     7      |
     | 1      357    8      | 367   e67     567    | 4      2      9      |
     |----------------------+----------------------+----------------------|
     | 789    1      2      | 679    5      679    | 3     #48+6  #48     |
     | 3789   379    379    | 4     d679    1      | 2     c6*8    5      |
     | 4      6      5      | 2      8      3      | 9      7      1      |
     |----------------------+----------------------+----------------------|
     | 37     8      4      | 1    ae267    67     | 5      9      23     |
     | 6      239    139    | 5     b2*49  #48+9   | 7     #48+1  #48+23  |
     | 5      279    179    | 79     3     #48+79  | 6     #48+1  #48+2   |
     *--------------------------------------------------------------------*

MUG(48)r489c689 with external SIS 4r8c5;8r5c8
2r7c5=(2-4)r8c5=MUG=(8-6)r5c8=6r4c8-(6=72)r37c5 => r7c5=2

[eleven]

Thanks Ron,

i knew that somehow i was complicating things, but could not see the wood for the trees.
After having seen Luke's MUG i was fixed to that and missed the BUG Lite.

However i still believe that

Code: Select all

.  |  .   .  .
12 | 123 124 .
12 | 123 124 .
--------------
.  | 12   12 .

is a MUG.
(Setting 1 or 2 outside gives 0 solutions, as well as 3 or 4 in c2 or c3 resp., or 34 in rows 2 or 3, while a 3r2/4r3 or 4r2/3r3 leave a deadly 12 pattern.)

[Added]
I saw now, that if it was not a MUG, Myth might have burst into tears

Code: Select all

-------------------+-------------------+-------------------
 .     .     .     | .     .     .     | .     .     .     
 .     .     abcd  | abcd  abcd  .     | .     .     .     
 .     .     abcd  | abcd  abcd  .     | .     .     .     
-------------------+-------------------+-------------------
 .     .     .     | abcd  abcd  .     | .     c     d
 .     .     c     | .     .     .     | .     .     .     
 .     .     d     | .     .     .     | .     .     .     
-------------------+-------------------+-------------------
                      d     c


[ronk]

However i still believe that

Code: Select all

.  |  .   .  .
12 | 123 124 .
12 | 123 124 .
--------------
.  | 12   12 .

is a MUG.
(Setting 1 or 2 outside gives 0 solutions, as well as 3 or 4 in c2 or c3 resp., or 34 in rows 2 or 3, while a 3r2/4r3 or 4r2/3r3 leave a deadly 12 pattern.)

Agreed , and I like the "deadly 12" argument the best ... by far. MJ won't have to cry on my account.

[Luke]

Very excellent stuff, eleven. The DP proves to be a cold and efficient killer.

Wow, I was about to post that exact "burst into tears" MUG prototype when I saw your addendum.

You know, I've always said, "If a DP has only bivalues, then it's a BUG-Lite; if it has even one cell with three or more values, it's a MUG." I may have to rethink that in the light of Ronk's MUG reduction. Even so, I still want to call it a BUG-Lite.

I see Ron's approach as the composite of these two BUG-Lites:

Code: Select all

----------+-----------+-----------
 .  .  .  |  .  .  .  |  .  .  .       
 .  .  .  |  .  .  .  |  .  .  .     
 .  .  .  |  .  .  .  |  .  .  .       
----------+-----------+-----------
 .  .  .  |  .  .  .  |  . 48  48       
 .  .  .  |  .  .  .  |  .  .  .     
 .  .  .  |  .  .  .  |  .  .  .       
----------+-----------+-----------
 .  .  .  |  .  .  .  |  .  .  .       
 .  .  .  |  .  . 48  |  . 48  .     
 .  .  .  |  .  . 48  |  .  .  48     
----------+-----------+-----------

Code: Select all

----------+-----------+-----------
 .  .  .  |  .  .  .  |  .  .  .       
 .  .  .  |  .  .  .  |  .  .  .     
 .  .  .  |  .  .  .  |  .  .  .       
----------+-----------+-----------
 .  .  .  |  .  .  .  |  . 48  48       
 .  .  .  |  .  .  .  |  .  .  .     
 .  .  .  |  .  .  .  |  .  .  .       
----------+-----------+-----------
 .  .  .  |  .  .  .  |  .  .  .       
 .  .  .  |  .  . 48  |  .  .  48     
 .  .  .  |  .  . 48  |  . 48  .     
----------+-----------+-----------

[eleven]

Cross posted, Luke
Dealing with deadly patterns has many pitfalls (i already visited). What i learned:

I remember 2 different ways to show that BUG lites or MUGs are deadly.

The 48 BUG Lite above (not sure, but i guess that BUG lites are a subset of MUGs) is a combination of 2 BUG lites

Code: Select all

12| 12 12 .       12| 12 .  .    12| .  12 .
12| 12 12 .       12| .  12 .    12| 12 .  .
-----------       -----------    -----------
    12 12             12 12          12 12

Both have 2 solutions, independant of the rest of the grid.
So to prove, that it is deadly in a unique puzzle, you show that it must fall into one of them to enable a solution, therefore it cannot be unique.

This is different to Myth's main method to show, that MUG's are deadly.
Here he shows that whatever MUG digits are in the rest of the grid, there will be always a (proved) MUG left in the pattern [edit] or no solution [of course].

[Luke]

This is supposed to be fun, but now it's getting downright educational

Thanks for the Resurrection of SAM, Don. Wait, it's SAP now? Let's just call it "Son of SAM," then.

You're gonna have to make the next one harder to avoid the overriding inclination of this crew to one-step everything...

Here's another way to soften this one up a bit:

Code: Select all

 *--------------------------------------------------------------------*
 | 2      34579  379    | 379    1      4579   | 8      35     6      |
 | 39     3459   6      | 8     *49     2      | 1      35     7      |
 | 1      357    8      | 367    67     567    | 4      2      9      |
 |----------------------+----------------------+----------------------|
 |*78-9   1      2      |*679    5     *679    | 3      468    48     |
 |*3789   379    379    | 4     *679    1      | 2      68     5      |
 | 4      6      5      | 2      8      3      | 9      7      1      |
 |----------------------+----------------------+----------------------|
 |*37     8      4      | 1     *267   *67     | 5      9      23     |
 | 6      239    139    | 5     *249    489    | 7      148    2348   |
 | 5      279    179    | 79     3      4789   | 6      148    248    |
 *--------------------------------------------------------------------*

hp(78)r45c1=(7)r7c1-(7=62)r7c56-(2=49)r28c5-(9)r5c5=(9)r4c46==>r4c1<>9

[DonM]

This is supposed to be fun, but now it's getting downright educational

Thanks for the Resurrection of SAM, Don. Wait, it's SAP now? Let's just call it "Son of SAM," then.

You're gonna have to make the next one harder to avoid the overriding inclination of this crew to one-step everything...

hp(78)r45c1=(7)r7c1-(7=62)r7c56-(2=49)r28c5-(9)r5c5=(9)r4c46==>r4c1<>9

Hi Luke!

Yes, it turns out that this is very close to a one-stepper- rather unusual for an ER=7.7 puzzle. But it is an interesting little critter. There are some puzzles like this that will be easier for the overall solving group here -and open to full solving- but a step up from the 'usual' one-steppers, hence the Suggest A Play (SAP) category. On the other hand, SAM puzzles will not be one-steppers! (I wish I'd thought of 'Son of Sam'- that gave me a good laugh. )

Anyway, your chain, after a little different start, headed in the same direction as mine:

(9-3)r2c1-r7c1=(3-2)r7c9=r7c5-als(2=49)r28c5-(9)r5c5=grp(9)r4c46 => r4c1<>9
=> one locked candidate (9)r5c5 leads to a NP(67) in c5 and the puzzle falls apart.

[Leren]

OK - No more Mr Nice Guy ! Forcing Net contradiction on 9 in Column 5 does solve the puzzle.

Code: Select all

3 r7c1 - (3=9) r2c1                   - 9 r2c5;
3 r7c1 - (3=9) r2c1 - r4c1 = r4c46    - 9 r5c5;
3 r7c1 - 7 r7c1 = r9c23 - (7=9) r9c4  - 9 r8c5; => - 3 r7c1; lclste

Leren

[DonM]

OK - No more Mr Nice Guy ! Forcing Net contradiction on 9 in Column 5 does solve the puzzle.

There's no doubt that the puzzle is left bleeding and spread all over the field after that move. I think there's just one minor typo (the 4 was left out):

3 r7c1 - (3=9) r2c1 - 9 r2c5;
3 r7c1 - (3=9) r2c1 - r4c1 = r4c46 - 9 r5c5;
3 r7c1 - 7 r7c1 = r9c23 - (7=9) r9c4 - 9 r8c5; => - 3 r7c1; lclste
[/quote]

BTW: This move is seen more commonly as an AAIC/column (or Kraken column) notated:

9r2c5 - (9=3)r2c1
II
9r5c5 - r4c46 = r4c1 - (9=3)r2c1
II
9r8c5 - (9=7)r9c4 - r9c23 = 7r7c1

=> -3r7c1; lclste

Either way, it's a nice pattern.

[Leren]

DonM wrote: This move is seen more commonly as an AAIC/column (or Kraken column)

Thanks for spotting the Typo and the notation tip. From the responses of the other solvers I felt that the use of WME's (that's Weapons of Mass Elimination) was warranted .

Leren