The New Sudoku Players' Forum

[Sudtyro]

Need hint to advance beyond the following:

Code: Select all

569  156   2    | 156  569  8    | 3   7   4
3589 1358  589  | 4    7    1359 | 58  2   6 
4    35678 578  | 2    356  356  | 58  1   9 
----------------+----------------+-----------
2    3578  4    | 5678 3568 356  | 1   9   58
1    58    6    | 58   29   29   | 4   3   7 
358  9     578  | 1578 4    135  | 2   6   58
----------------+----------------+-----------
5689 2     1    | 568  568  7    | 69  4   3
7    568   589  | 3    1    4    | 69  58  2
568  4     3    | 9    2568 256  | 7   58  1


All suggestions welcome!

[tarek]

Looking at the PMs, I couldn't see anything obvious........

could u supply the original puzzle?

tarek

[Sudtyro]

Sure...here's the original:

Code: Select all

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


[tarek]

No....

I couldn't spot anything easy......no even an almost locked sets rules...

It looks like some complex chains are needed.........

tarek

[Sudtyro]

Right, I saw that "almost" UR, too, and used the link between (9)r2c3 and (7)r3c3 as a bridge in some 3D coloring, but couldn't make any headway there either.

Is there a non-T&E method that will also advance this puzzle?

[Sudtyro]

Sorry...I somehow killed the post that preceded mine. It referred to the 58 "almost" UR.

[daj95376]

Sorry...I somehow killed the post that preceded mine. It referred to the 58 "almost" UR.

You didn't kill my post. I withdrew it while you were (apparently) preparing a reply. I checked the contradiction chain for [r2c3]=9 and it was a nightmare. So, it didn't make my suggestion/post feasible. I'm sorry!

[Sudtyro]

So, does this mean that only T&E will advance this puzzle?

[Pat]

Code: Select all

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



Need hint to advance beyond the following:

Code: Select all

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



Code: Select all

569  156   2    | 156  569  8    | 3   7   4
3589 1358  589  | 4    7    1359 | 58  2   6 
4    35678 578  | 2    356  356  | 58  1   9 
----------------+----------------+-----------
2    3578  4    | 5678 3568 356  | 1   9   58
1    58    6    | 58   29   29   | 4   3   7 
358  9     578  | 1578 4    135  | 2   6   58
----------------+----------------+-----------
5689 2     1    | 568  568  7    | 69  4   3
7    568   589  | 3    1    4    | 69  58  2
568  4     3    | 9    2568 256  | 7   58  1 



hey Sudtyro, looks like you found a real tough one

so i thought i'd check out Sudoku Explainer
-- this is what i got:
Multiple Forcing Chains to exclude the 6 at r1c4:
• b1 6 in r1 immediately excludes the 6 at r1c4
• b1 6 in r3c2 puts the r3 7 in c3, the r6 7 in c4, the c4 1 in r1
Forcing Chain to exclude the 5 at r2c2

etc etc
too tough for me

[Sudtyro]

too tough for me

I'm shocked! And coming from someone who can spot a "finned mutant swordfish" to boot!

[Pat]

but now Carcul is back

perhaps we'll see some action here --

[udosuk]

Before Carcul terrifies us with his amazing chains, here is my effort to solve this one...
(I'm no chain notation expert though, so the notation police please feel free to correct me...)

After basic techniques (SSTS):

Code: Select all

 *--------------------------------------------------------------------*
 |*569   *156    2      |*156    569    8      | 3      7      4      |
 |*3589   1358  *589    | 4      7      1359   |#58     2      6      |
 | 4     -73568 *578    | 2      356    356    |#58     1      9      |
 |----------------------+----------------------+----------------------|
 | 2     @3578   4      |@5678   3568   356    | 1      9      58     |
 | 1      58     6      | 58     29     29     | 4      3      7      |
 | 358    9      578    | 1578   4      135    | 2      6      58     |
 |----------------------+----------------------+----------------------|
 |*5689   2      1      |*568    568    7      |*69     4      3      |
 | 7      568    589    | 3      1      4      | 69     58     2      |
 | 568    4      3      | 9      2568   256    | 7      58     1      |
 *--------------------------------------------------------------------*

There is a potential UR {58} in r23c37 => r23c3 must have 7|9
[r3c2](-7-[r4c2]=7=[r4c4])-7|9=[r23c3]-9-[r12c1]=9=[r7c1]-9-[r7c7]-6-[r7c4]=6=[r1c4]-6-[r1c12]=6=[r3c2]
Therefore r3c2<>7

After a few more singles/locked candidates:

Code: Select all

 *-----------------------------------------------------------*
 | 56   *56    2     | 1     9     8     | 3     7     4     |
 | 89    1     89    | 4     7     3     | 5     2     6     |
 | 4     3     7     | 2     56    56    | 8     1     9     |
 |-------------------+-------------------+-------------------|
 | 2     7     4     | 568   3     56    | 1     9     58    |
 | 1    *58    6     |*58    2     9     | 4     3     7     |
 | 3     9     58    | 7     4     1     | 2     6     58    |
 |-------------------+-------------------+-------------------|
 | 5689  2     1     |*56    568   7     |*69    4     3     |
 | 7    -658   589   | 3     1     4     |*69    58    2     |
 | 568   4     3     | 9     568   2     | 7     58    1     |
 *-----------------------------------------------------------*

There is a relatively short xy-chain:

[r8c2]-6-[r8c7]=6=[r7c7]-6-[r7c4]-5-[r5c4]=5=[r5c2]-5-[r1c2]-6-[r8c2]
Therefore r8c2<>6, and the puzzle is solved.

Or alternatively, we can do an ALS-xyz:

Code: Select all

 *-----------------------------------------------------------*
 | 56   *56    2     | 1     9     8     | 3     7     4     |
 | 89    1    @89    | 4     7     3     | 5     2     6     |
 | 4     3     7     | 2     56    56    | 8     1     9     |
 |-------------------+-------------------+-------------------|
 | 2     7     4     | 568   3     56    | 1     9     58    |
 | 1    -58    6     |*58    2     9     | 4     3     7     |
 | 3     9    @58    | 7     4     1     | 2     6     58    |
 |-------------------+-------------------+-------------------|
 | 5689  2     1     |*56    568   7     | 69    4     3     |
 | 7    #568  #589   | 3     1     4     | 69   #58    2     |
 | 568   4     3     | 9     568   2     | 7     58    1     |
 *-----------------------------------------------------------*

A=r1c2={56}
B=r26c3={589}
C=r8c238={5689}
x (common to A,B)=5
y (restricted common to A,C)=6
z (restricted common to B,C)=9

Therefore r5c2<>5, and the puzzle is solved.

Solution:

562198374
918473526
437265819
274836195
186529437
395741268
821657943
759314682
643982751

[Carcul]

Need hint to advance beyond the following:

Code: Select all

 *-----------------------------------------------------------*
 | 569    156    2   | 156    569    8    | 3      7      4  |
 | 3589   1358   589 | 4      7      1359 | 58     2      6  |
 | 4      35678  578 | 2      356    356  | 58     1      9  |
 |-------------------+--------------------+------------------|
 | 2      3578   4   | 5678   3568   356  | 1      9      58 |
 | 1      58     6   | 58     29     29   | 4      3      7  |
 | 358    9      578 | 1578   4      135  | 2      6      58 |
 |-------------------+--------------------+------------------|
 | 5689   2      1   | 568    568    7    | 69     4      3  |
 | 7      568    589 | 3      1      4    | 69     58     2  |
 | 568    4      3   | 9      2568   256  | 7      58     1  |
 *-----------------------------------------------------------*


[r8c3]=9=[r7c1](-9-[r7c7]-6-[r7c45])-9-[r1c1]=9=[r1c5]-9-[r2c6]=9=
=[r5c6]=2=[r9c6]=6=[r9c5]-6-[r9c1]=6=[r8c2](-6-[r1c2])-6-[r3c2]=6=
=[r3c56]-6-[r1c4]=6=[r4c4]=7=[r4c2]-7-[r3c2]=7=[r3c3],

but this cannot be, because now we have an incompatible pattern of “5s” in cells {r1c24|r3c25|r5c24|r7c45}.

So, r8c3 must be “9” and the puzzle is solved.

here is my effort to solve this one...

Nice solution. Here is still another alternative for your last step:

[r8c3]=9=[r2c3]=8=[r2c1]-8-[r79c1]=8=[r8c23]-8-[r8c8]-5-[r8c3], => r8c3<>5.

Carcul

[udosuk]

...but this cannot be, because now we have an incompatible pattern of “5s” in cells {r1c24|r3c256|r4c56|r5c24|r7c45}.

Thanks for the compliments on my solutions, but as always I'm puzzled by yours... I simply cannot see the incompatible pattern of 5s...

After I run through your steps, I get the 5s in r1c24|r5c24|r7c45 but the 5 on r3 can be in r3c2567 and on r4 it can be in r4c569... So I'm not sure where you eliminated the 5s from r3c7 and r4c9...

[Carcul]

I simply cannot see the incompatible pattern of 5s...

That's because I have written too many cells. Thanks, I have edited the post.

Carcul