The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |..9|...|..4|
 |...|...|.9.|
 |.2.|.8.|6.1|
 |---+---+---|
 |3..|1.2|...|
 |.6.|...|.5.|
 |...|9.3|..2|
 |---+---+---|
 |4.5|.2.|.3.|
 |.1.|...|...|
 |8..|...|5..|
 *-----------*


Play/Print this puzzle online

[SteveG48]

Code: Select all

.-------------------.----------------------.-------------------.
| 167  378    9     | 23567   137    1567  | 238    f28   4    |
| 167  3478   13478 | 23467   1347   1467  | 238    9     5    |
| 5    2      34    | 34      8      9     | 6      7     1    |
:-------------------+----------------------+-------------------:
| 3    45789  478   | 1       56     2     | 4789   g468  6789 |
| a29  6      12    | 478     47     478   | b19    5     3    |
| 17   4578   1478  | 9       56     3     | 1478  cg1468 2    |
:-------------------+----------------------+-------------------:
| 4    79     5     | 678     2      1678  | 1789   3     6789 |
| d29  1      2367  | 345678  3479   45678 | 24789  g2468 6789 |
| 8    379    2367  | 3467    13479  1467  | 5      e1246 679  |
'-------------------'----------------------'-------------------'


Suppose r5c1=9
Then 1-r5c7 => r6c8 <>1
And 2-r8c1-2-r9c8-8-r1c8 => r468c8 <> 2/8
But this leaves a 4/6 pair in r468c8; contradiction removing 9 from r5c1; stte

[Leren]

Code: Select all

*-----------------------------------------------------------------------*
| 167    378    9       | 23567  137    1567    | 238    28     4       |
| 167    3478   13478   | 23467  1347   1467    | 238    9      5       |
| 5      2      34      | 34     8      9       | 6      7      1       |
|-----------------------+-----------------------+-----------------------|
| 3      45789  478     | 1      56     2       | 4789   468    6789    |
| 29     6     e1-2     | 478    47     478     |d19     5      3       |
| 17     4578   1478    | 9      56     3       | 1478  c1468   2       |
|-----------------------+-----------------------+-----------------------|
| 4      79     5       | 678    2      1678    | 1789   3      6789    |
| 29     1      2367    | 345678 3479   45678   | 24789  2468   6789    |
| 8      379   a2367    | 3467   13479  1467    | 5     b1246   679     |
*-----------------------------------------------------------------------*

L2 Wing: (2) r9c3 = (2-1) r9c8 = r6c8 - r5c7 = r5c3 => - 2 r5c3; stte

Leren

[Leren]

SteveG48 Wrote: Suppose r5c1=9
Then 1-r5c7 => r6c8 <>1
And 2-r8c1-2-r9c8-8-r1c8 => r468c8 <> 2/8
But this leaves a 4/6 pair in r468c8; contradiction removing 9 from r5c1; stte

More formally you can write this as a discontinuous Nice loop with an ALS as one of the nodes:

- 2 r5c1 = r8c1 - r8c78 = r9c8 - (2=1468) r1468c8 - (1=9) r5c7 - (9=2) r5c1 => r5c1 = 2

Leren

[SteveG48]

More formally you can write this as a discontinuous Nice loop with an ALS as one of the nodes:

- 2 r5c1 = r8c1 - r8c78 = r9c8 - (2=1468) r2468c8 - (1=9) r5c7 - (9=2) r5c1 => r5c1 = 2

Leren

Thanks, Leren. I'm going to try to figure that out.

Steve

OK, I'm back. The r2468c8 should be r1468c8?

I like the way this works. I wrote it as a parallel chain. You ran the first leg of my chain backwards, bringing the contradiction back to r5c1. Neat.

[Leren]

SteveG48 wrote: The r2468c8 should be r1468c8?

Quite right - edited my post to correct typo.

Leren

[7b53]

L2 Wing: (2) r9c3 = (2-1) r9c8 = r6c8 - r5c7 = r5c3 => - 2 r5c3; stte

trying to find different approach for the same elimination...

Code: Select all

    *-----------------------------------------------------------------------*
    | 167    378    9       | 23567  137    1567    | 238    28     4       |
    | 167    3478   13478   | 23467  1347   1467    | 238    9      5       |
    | 5      2      34      | 34     8      9       | 6      7      1       |
    |-----------------------+-----------------------+-----------------------|
    | 3      45789  478     | 1      56     2       | 4789   468    6789    |
    | 2(9)    6      12     | 478    47     478     | 19     5      3       |
    | 17     4578   1478    | 9      56     3       | 1478   1468   2       |
    |-----------------------+-----------------------+-----------------------|
    | 4      79     5       | 678    2      1678    | 1789   3      6789    |
    | 29     1      2367    | 345678 3479   45678   | 24789  2468   6789    |
    | 8      379    2367    | 3467   13479  1467    | 5      1(2)4  679     |
    *-----------------------------------------------------------------------*

(9)r5c1 and (2)r9c8 cannot both be true. otherwise there will be two 1s in box 6.
so either r5c1=2 or at row 9,r9c3=2...which gives us (2)r5c1 = (2)r9c3 => r8c1, r5c3 <> 2
now, I notice there's always a chain that will do the same...[(2=9)r5c1 - (9=1)r5c7 - r6c8 = (1-2)r8c9 = (2)r9c3] -or- [Leren's L2 Wing]

another example;

Suppose r5c1=9
Then 1-r5c7 => r6c8 <>1
And 2-r8c1-2-r9c8-8-r1c8 => r468c8 <> 2/8
But this leaves a 4/6 pair in r468c8; contradiction removing 9 from r5c1; stte

(2)r8c1 and (1)r5c7 cannot both be true, because r9c8 cannot hold two digits (12)
so, (9)r8c1 = (9)r5c7 => r5c1, r8c7 <> 9
again, this chain will do the same... (9=2)r8c1 - r8c78 = (2-1)r9c8 = r6c8 - (1=9)r5c7 => r5c1. r8c7 <> 9

like to hear you guys comment..
7b53

[JC Van Hay]

like to hear you guys comment..

I too ...

[Leren]

7b53 wrote:
1. (9)r5c1 and (2)r9c8 cannot both be true. otherwise there will be two 1s in box 6. and
2. (2)r8c1 and (1)r5c7 cannot both be true, because r9c8 cannot hold two digits (12)

JC Van Hay Wrote: I too ...

Back by popular demand ? I'm sweatin' here - gotta say something - let's see now ... hmmm ... Ahhh - think I've got it !

1. and 2. both sound like pattern based recognition of underlying Nice loops - both include contradiction statements - that would indicate discontinuous Nice loops wouldn't it ?

For 1 how about: (1-9) r5c7 = (9-2) r5c1 = r8c1 - r8c78 = (2-1) r9c8 = r6c8 - r5c7 => r5c7 <> 1 [ This discontinuous loop has r5c1 = 9 and r9c8 = 2 and comes up with a contradiction on 1 in Box 6]

Now for 2: 2 r8c1 - (2=9) r5c1 - (9=1) r5c7 - r6c8 = (1-2) r9c8 = r8c78 - r8c1 => r8c1 <> 2 [ This discontinuous loop has r8c1 = 2 and r5c7 = 1 and includes 1 & 2 in r9c8 although admittedly not both true]

You should be able to find a host of information on Nice loops in the Collection of Solving Techniques pages here http://forum.enjoysudoku.com/collection-of-solving-techniques-t3315.html

How was that ?

Leren

[ArkieTech]

Code: Select all

 *-----------------------------------------------------------------------------*
 | 167     378     9       | 23567   137     1567    | 238     28      4       |
 | 167     3478    13478   | 23467   1347    1467    | 238     9       5       |
 | 5       2       34      | 34      8       9       | 6       7       1       |
 |-------------------------+-------------------------+-------------------------|
 | 3       45789   478     | 1       56      2       | 4789    468     6789    |
 | 29      6      a12      | 478     47      478     | 9-1     5       3       |
 | 7-1     4578    478-1   | 9       56      3       | 1478   d1468    2       |
 |-------------------------+-------------------------+-------------------------|
 | 4       79      5       | 678     2       1678    | 1789    3       6789    |
 | 29      1       2367    | 345678  3479    45678   | 24789   2468    6789    |
 | 8       379    b2367    | 3467    13479   1467    | 5      c1246    679     |
 *-----------------------------------------------------------------------------*
(1=2)r5c3-r9c3=(2-1)r9c8=1r6c8 => -1r6c13,r5c7; ste

I too

[tlanglet]

Code: Select all

 *-----------------------------------------------------------------------------*
 | 167     378     9       | 23567   137     1567    | 238     28      4       |
 | 167     3478    13478   | 23467   1347    1467    | 238     9       5       |
 | 5       2       34      | 34      8       9       | 6       7       1       |
 |-------------------------+-------------------------+-------------------------|
 | 3      c45789   478     | 1       56      2       | 4789    468     6789    |
 |d29      6       12      | 478     47      478     |e19      5       3       |
 | 17      4578    1478    | 9       56      3       | 1478   f1468    2       |
 |-------------------------+-------------------------+-------------------------|
 | 4      b79      5       | 678     2       1678    | 1789    3       6789    |
 |a9-2     1       2367    | 345678  3479    45678   |h24789  h2468    6789    |
 | 8      b379     2367    | 3467    13479   1467    | 5      g1246    679     |
 *-----------------------------------------------------------------------------*


9r8c1=9r79c2-r4c2=r5c1-(9=1)r5c7-r6c8=(1-2)r9c8=2r8c78 => r8c1<>2

Ted

[daj95376]

Comment:

This puzzle has numerous ways to create simple chains that will crack the puzzle. I look for solutions that aren't produced by my solvers or that reflect some unusal combination of logic/interactions. Solutions like Leren's, Dan's, and Ted's seldom leave room for comment because they are well-formed chains with obvious outcomes. Since I seldom try to solve puzzles manually, I don't recognize that they saw something that I would/wouldn't have seen while working the puzzle.

I pause to examine uniqueness solutions when they are outside the methods used by my solver. So, I often pay close attention to Luke's and Ted's uniqueness solutions.

JC relies heavily on network patterns and embedded structures. I'll pull up Simple Sudoku to mark his secondary eliminations and to isolate his structures while trying to recreate his logic. I tend not to discuss networks unless questions occur. However, I will sometimes comment if a network can also be represented as a Kraken Unit.

When it comes to solutions like those by SteveG48 and 7b53, I only take a cursory look because their logic descriptions often seem incomplete/fragmented ... and I seldom try to fill in the holes. I catch the final elimination(s) and cross-check them against my solver's solutions to see if common cells/values are present.

Bottom Line: I look for solutions with logic that I might want to add to my solver.



Addendum: I also check to see if anyone posts long chains like these discontinuous loops.

Code: Select all

(9)r4c2=r5c1-(9=1)r5c7-r7c7=(1-2)r9c8=r9c3-(2=9)r8c1-r79c2=(9)r4c2

(2)r9c3=r8c13-r8c7=r12c7-(2=8)r1c8-(8=379)r179c2-(9)r4c2=r5c1-(9=1)r5c7-r7c7=(1-2)r9c8=(2)r9c3


[Marty R.]

Code: Select all

+-----------------+--------------------+-----------------+
| 167 378   9     | 23567  137   1567  | 238   28   4    |
| 167 3478  13478 | 23467  1347  1467  | 238   9    5    |
| 5   2     34    | 34     8     9     | 6     7    1    |
+-----------------+--------------------+-----------------+
| 3   45789 478   | 1      56    2     | 4789  468  6789 |
| 29  6     12    | 478    47    478   | 19    5    3    |
| 17  4578  1478  | 9      56    3     | 1478  1468 2    |
+-----------------+--------------------+-----------------+
| 4   79    5     | 678    2     1678  | 1789  3    6789 |
| 29  1     2367  | 345678 3479  45678 | 24789 2468 6789 |
| 8   379   2367  | 3467   13479 1467  | 5     1246 679  |
+-----------------+--------------------+-----------------+


Play this puzzle online at the Daily Sudoku site

2r9c3=(2-1)r9c8=r6c8-(1=9)r5c7-(9=2)r5c1=>r5c3,r8c1<>2