The New Sudoku Players' Forum

[ncantoral]

I have been clicking on random fiendish puzzles from sudokupuzz.com and this one came up today. I don't know how in the world its even part of the collection. the site obviously has a large range of difficulty

Code: Select all

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

Code: Select all

| 1      568    28    | 289    4      58    | 7      3      69    |
| 56     3456   235   | 1      259    7     | 8      269    469   |
| 9      48     7     | 238    238    6     | 5      12     14    |
----------------------+---------------------+---------------------
| 568    5678   1     | 789    689    4     | 2      589    3     |
| 4      38     9     | 5      138    2     | 6      18     7     |
| 2      3567   358   | 3789   13689  18    | 4      1589   159   |
----------------------+---------------------+---------------------
| 3      2      6     | 4      15     15    | 9      7      8     |
| 7      9      4     | 28     28     3     | 1      56     56    |
| 58     1      58    | 6      7      9     | 3      4      2     |

[submacrolize]

Just go here.

Click on the gray squares that you want to see. Right click to view the whole solution

[Draco]

That's a tough one alright. It took my solver 7 forcing chains/nets interspersed with SSTS to crack it.

Others may have insights into shorter paths to a solution.

Cheers...

- drac

[daj95376]

If you can survive my notation, I believe that two chains (nets?) do the job.

Code: Select all

 SSTS, XYZ-Wing, UR Type 2, finned Swordfish ...

 +-----------------------------------------------------------------------+
 |  1      568    28     |  289    4      58     |  7      3      69     |
 |  56     3456   235    |  1      259    7      |  8      269    469    |
 |  9      48     7      |  238    238    6      |  5      12     14     |
 |-----------------------+-----------------------+-----------------------|
 |  568    5678   1      |  789    689    4      |  2      589    3      |
 |  4      38     9      |  5      138    2      |  6      18     7      |
 |  2      3567   358    |  3789   13689  18     |  4      1589   159    |
 |-----------------------+-----------------------+-----------------------|
 |  3      2      6      |  4      15     15     |  9      7      8      |
 |  7      9      4      |  28     28     3      |  1      56     56     |
 |  58     1      58     |  6      7      9      |  3      4      2      |
 +-----------------------------------------------------------------------+

  1r6c5 6r4c5 6r2c1 6r1c9 9r1c4 9r46c5        => [r6c5]<>1
  1r7c5 1r6c6 8r1c6 8r3c2 4r3c9 1r6c9  1r5c5  => [r7c5]<>1


[hobiwan]

If you can survive my notation

Help!

The jump from r4c5 to r2c1 is a bit large for me...
I can see
r6c5=1=>r4c5=6=>r6c2=6=>r1c9=6=>r1c4=9=>r46c5=9
which is definitly a chain and not a net (as is the second one).

[daj95376]

If you can survive my notation

Help!

The jump from r4c5 to r2c1 is a bit large for me...
I can see
r6c5=1=>r4c5=6=>r6c2=6=>r1c9=6=>r1c4=9=>r46c5=9
which is definitly a chain and not a net (as is the second one).

Okay, we'll see how my NL notation holds up. I'm not sure if the first is a chain, but I'm fairly sure the second is a chain. But, my track record isn't very good.

Code: Select all

1=[r6c5]=6=[r4c5]-6-[r4c1]=6=[r2c1]-6-[r2c89]=6=[r1c9]=9=[r1c4]-9-[r2c5]=9=[r4|6c5]       => [r6c5]<>1
[r7c5]-1-[r7c6]-1-[r6c6]=8=[r1c6]-8-[r1c23]=8=[r3c2]=4=[r3c9]=1=[r6c9]-1-[r6c56]=1=[r5c5] => [r7c5]<>1
_______________________________________________________________________________________________________


[hobiwan]

Code: Select all

1=[r6c5]=6=[r4c5]-6-[r4c1]=6=[r2c1]-6-[r2c89]=6=[r1c9]=9=[r1c4]-9-[r2c5]=9=[r4|6c5]       => [r6c5]<>1

Oops
I was so fixed on the grouped link r4c12 that I missed the simple connection over r4c1.

As for chain versus net - definitely a chain (with grouped nodes) in my book: every step depends only on the step immediately before it.

[ttt]

Other path. Sorry... I present my way by other notation
1) (9)r1c4=(9)r2c5 – (9)r4c5*={(6)r6c2=(6)r6c5 – (6=8)*r4c5 – (8)r6c6=(8-5)r1c6=(5)r1c2} – (6)r1c2=(6)r1c9 => r1c9<>9
Above chain meat : if r4c5<>9 => r1c2<>6 – used Kraken cell at r4c5
2) (8=2)r3c4 – (2=1)r3c8 – (1)r3c9=(1)r6c9 – (1=8)r6c6 => r1c6<>8

[ronk]

Okay, we'll see how my NL notation holds up. I'm not sure if the first is a chain, but I'm fairly sure the second is a chain. But, my track record isn't very good.

Code: Select all

1=[r6c5]=6=[r4c5]-6-[r4c1]=6=[r2c1]-6-[r2c89]=6=[r1c9]=9=[r1c4]-9-[r2c5]=9=[r4|6c5]       => [r6c5]<>1
[r7c5]-1-[r7c6]-1-[r6c6]=8=[r1c6]-8-[r1c23]=8=[r3c2]=4=[r3c9]=1=[r6c9]-1-[r6c56]=1=[r5c5] => [r7c5]<>1
_______________________________________________________________________________________________________


You're using an almost-hidden-set (AHS) in the first which actually yields two more elims ... although they don't seem to be helpful. Via the nice loop, either r6c5=6 or r46c5=69. Therefore r46c5=69.

[r6c5]=6=[r4c5]-6-[r4c1]=6=[r2c1]-6-[r2c89]=6=[r1c9]=9=[r1c4]-9-AHS:([r2c5]=9|69=[r46c5]) => [r6c5]=69

Your second chain "collides" at r6c6 ... so r7c5 and r7c6 aren't necessary.

[Carcul]

Code: Select all

 *----------------------------------------------------------*
 | 1      568    258 | 289    4      58 | 7      3      69  |
 | 56     3456   235 | 1      259    7  | 8      269    469 |
 | 9      48     7   | 238    238    6  | 5      12     14  |
 |-------------------+------------------+-------------------|
 | 568    5678   1   | 789    689    4  | 2      589    3   |
 | 4      38     9   | 5      138    2  | 6      18     7   |
 | 2      35678  358 | 3789   13689  18 | 4      1589   159 |
 |-------------------+------------------+-------------------|
 | 3      2      6   | 4      15     15 | 9      7      8   |
 | 7      9      4   | 28     28     3  | 1      56     56  |
 | 58     1      58  | 6      7      9  | 3      4      2   |
 *----------------------------------------------------------*


1) [r46c45]-8-[r6c6]=8=[r1c6]-8-[r3c45]=8=[r3c2]-8-[r5c2]-3-
-[r5c5|r6c6]-8-[r46c45], => r4c4, r4c5, r6c4, r6c5 <> 8.

2) [r6c5]=6=[r6c2]-6-[r4c1]=6=[r2c1]-6-[r1c2]=6=[r1c9]=9=[r1c4]-9-
-[r4c4|r5c5|r6c46]-1,3-[r6c5], => r6c5<>1,3.

3) [r4c1]=8|4=[r2c2]-4-[r2c9]-9-[r6c9]-1-[r6c6]-8-[r6c3]=8=[r4c1], => r4c1=8.

4) BUG: r6c8=1 , and the puzzle is solved.

[daj95376]

1) [r46c45]-8-[r6c6]

Welcome back Carcul. The start of this chain has me confused because it appears that you are skipping the fact that [r5c5] contains an 8.

[Glyn]

daj95376 wrote:

Carcul wrote:
1) [r46c45]-8-[r6c6]

Welcome back Carcul. The start of this chain has me confused because it appears that you are skipping the fact that [r5c5] contains an 8.

Not really acquainted with Nice loops but the first part of the chain is a weak inference so only a maximum of one end can be true, and although r5c5 might well be the 8 that is not needed in the construct.

The discontinuity -8-[r46c45]-8- => r46c45<>8.

As an implication stream leading to a contradiction:
If 8 is contained in r46c45 => r6c6<>8 => r1c6=8 => r3c45<>8 => r3c2=8 => r5c3=3 => r5c5|r6c6 <>3 => r5c5|r6c6=1&8 => r46c45<>8.

I'll have to mug up on these at it seems to be a distinction between Nice Loops and AIC, with which I am more familiar.

[daj95376]

My Mistake

I'm groggy from staring at a bug in my solver and mistakenly read Carcul's first link as a strong link instead of a weak link.

Sorry