The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |8.3|94.|...|
 |.4.|...|...|
 |.69|5..|7..|
 |---+---+---|
 |1.8|..7|9..|
 |...|.8.|...|
 |..4|6..|8.1|
 |---+---+---|
 |..2|..9|18.|
 |...|...|.7.|
 |...|.56|2.9|
 *-----------*

Play/Print this puzzle online

[SteveG48]

Code: Select all

 *--------------------------------------------------------------------*
 | 8      7      3      | 9      4      12     | 56     1256   256    |
 | 5      4      1      | 7      6      28     | 3      9      28     |
 | 2      6      9      | 5      13     138    | 7      14     48     |
 *----------------------+----------------------+----------------------|
 | 1      235    8      |c234   c23     7      | 9      23456 b23456  |
 | 36     9      56     | 1234   8      1345   | 45     2345   7      |
 | 7      235    4      | 6      9      35     | 8      235    1      |
 *----------------------+----------------------+----------------------|
 |e346   e35     2      |d34     7      9      | 1      8     a3456   |
 | 9      18     56     | 12348  123    134    | 456    7     a3456   |
 |f34     18     7      | 18     5      6      | 2      4-3    9      |
 *--------------------------------------------------------------------*


3r78c9 = r4c9 - (3=24)r4c45 - (4=3)r7c4 - r7c12 = 3r9c1 => -3 r9c8 ; stte

[pjb]

Code: Select all

 8       7       3      | 9      4      12     | 56     1256   256   
 5       4       1      | 7      6      28     | 3      9      28     
 2       6       9      | 5      13     138    | 7      14     48     
------------------------+----------------------+---------------------
 1      b235     8      | 234    23     7      | 9      23456  23456 
 36      9      a56     | 123-4  8     f134-5  |g45     23-45  7     
 7      b235     4      | 6      9      35     | 8      235    1     
------------------------+----------------------+---------------------
 46-3   c35      2      |d34     7      9      | 1      8      456-3   
 9       18      56     | 1238-4 123   e134    | 456    7      3456   
 34      18      7      | 18     5      6      | 2      34     9     


Good one Steve, couldn't find an alternative single chain. I've gone off Kraken 3-in-one solutions except where there is seriously no alternative.
Continuous loop: (5)r5c3=r46c2-(5=3)r7c2 - (3=4)r7c4 - r8c6 = r5c6 - (4=5)r5c7 - loop => -3 r7c19, -4 r8c4, r5c48, -5 r5c68; lclste
Phil

[Cenoman]

Code: Select all

 +-------------------+-----------------------+------------------------+
 |  8     7     3    |  9       4     12     |  56    1256    256     |
 |  5     4     1    |  7       6     28     |  3     9       28      |
 |  2     6     9    |  5       13    138    |  7     14      48      |
 +-------------------+-----------------------+------------------------+
 |  1     235   8    |  234     23    7      |  9     23456   23456   |
 |  36    9     56   |  1234    8     1345   |  45    2345    7       |
 |  7     235   4    |  6       9     35     |  8     235     1       |
 +-------------------+-----------------------+------------------------+
 |  346   35    2    |  34      7     9      |  1     8       3456    |
 |  9     18    56   |  12348   123   134    |  456   7       3456    |
 |  34    18    7    |  18      5     6      |  2     34      9       |
 +-------------------+-----------------------+------------------------+

Doubly linked ALS-XZ rule (with 4, 5 as restricted commons):
(345)r7c24 -45- (2345)r4c245 => -23r4c89, -3r7c19, -4r58c4, -5r6c2; stte

Note: efficient eliminations for stte finish are -3r47c9

Cenoman

[wmild2017]

Code: Select all

 +-------------------+-----------------------+------------------------+
 |  8     7     3    |  9       4     12     |  56    1256    256     |
 |  5     4     1    |  7       6     28     |  3     9       28      |
 |  2     6     9    |  5       13    138    |  7     14      48      |
 +-------------------+-----------------------+------------------------+
 |  1     235   8    |  234     23    7      |  9     23456   23456   |
 |  36    9     56   |  1234    8     1345   |  45    2345    7       |
 |  7     235   4    |  6       9     35     |  8     235     1       |
 +-------------------+-----------------------+------------------------+
 |  346   35    2    |  34      7     9      |  1     8       3456    |
 |  9     18    56   |  12348   123   134    |  456   7       3456    |
 |  34    18    7    |  18      5     6      |  2     34      9       |
 +-------------------+-----------------------+------------------------+

Doubly linked ALS-XZ rule (with 4, 5 as restricted commons):
(345)r7c24 -45- (2345)r4c245 => -23r4c89, -3r7c19, -4r58c4, -5r6c2; stte

Note: efficient eliminations for stte finish are -3r47c9

Cenoman

Hi,Cenoman,Is this allowed to use chains only here?no xwing、ur、sdc and so on. I'm new here.

[Cenoman]

Hi,Cenoman,Is this allowed to use chains only here?no xwing、ur、sdc and so on. I'm new here.

Hi, wmild2017,
welcome on this forum. If you look at my inscription date, you see that I am also a recent member...
The conventions between participants are as follows:
- the puzzle is first processed with "basics", i.e. locked candidates, locked sets, without explicit minutes of these techniques. X-wing XY-wings, ..., are not expected at this step
- then one displays a solution in one step only, using any advanced technique ( AIC's, fish strategies, UR or deadly patterns including BUG+n, ALS chains and so many others whose name is unknown to me...)
- the end of the solution after the above elimination(s) is obtained with singles (naked and/or hidden) only, called here "stte" (singles to the end)
- this is presented with a diagram showing the grid after basics, with tags for each node in one's advanced step, written in Eureka notation (afap) with r-c location of candidates.
- every one tries to present a solution different from the previously issued.

Puzzles proposed by dan (most often) are not so hard as to need more than one step. It is a challenge nevertheless to find a different solution (sometimes the difference is rather slight...). I take the opportunity to say "Many thanks, dan ! for issuing every day a puzzle with these constraints.

So, wmild2017, feel free to use any advanced technique you know, between a first "basics" start and a "singles to the end" finish.

Cenoman

[wmild2017]

Hi,Cenoman,Is this allowed to use chains only here?no xwing、ur、sdc and so on. I'm new here.

Hi, wmild2017,
welcome on this forum. If you look at my inscription date, you see that I am also a recent member...
The conventions between participants are as follows:
- the puzzle is first processed with "basics", i.e. locked candidates, locked sets, without explicit minutes of these techniques. X-wing XY-wings, ..., are not expected at this step
- then one displays a solution in one step only, using any advanced technique ( AIC's, fish strategies, UR or deadly patterns including BUG+n, ALS chains and so many others whose name is unknown to me...)
- the end of the solution after the above elimination(s) is obtained with singles (naked and/or hidden) only, called here "stte" (singles to the end)
- this is presented with a diagram showing the grid after basics, with tags for each node in one's advanced step, written in Eureka notation (afap) with r-c location of candidates.
- every one tries to present a solution different from the previously issued.

Puzzles proposed by dan (most often) are not so hard as to need more than one step. It is a challenge nevertheless to find a different solution (sometimes the difference is rather slight...). I take the opportunity to say "Many thanks, dan ! for issuing every day a puzzle with these constraints.

So, wmild2017, feel free to use any advanced technique you know, between a first "basics" start and a "singles to the end" finish.

Cenoman

I'm very glad to see your reply，and I see now .Thank you very much for your kind  and detailed description.I've  been in Sudoku for only a few months  ,  but I really like this kind of  digital logic reasoning game.For English is not my native language .Forgive my English  expression ability.In the end,You are a good one,Cenoman. Thank you again.
wmild2017

[Sudtyro2]

Code: Select all

*-----------------------------------------------------------*
| 8    7    3    |  9      4    12    |  56    1256   256   |
| 5    4    1    |  7      6    28    |  3     9      28    |
| 2    6    9    |  5      13   138   |  7     14     48    |
|----------------+--------------------+---------------------|
| 1    235  8    |  234    23   7     |  9     23456  23456 |
| 36   9    56   | c1234   8   d135-4 | B45d  b2345   7     |
| 7    235  4    |  6      9    35    |  8   Aa235a   1     |
|----------------+--------------------+---------------------|
| 346  35   2    |  34     7    9     |  1     8      3456  |
| 9    18   56   |  12348  123  134   |  456c  7      3456  |
| 34   18   7    |  18     5    6     |  2     34b    9     |
*-----------------------------------------------------------*

Kraken cell (235)r6c8.

Code: Select all

2r6c8 - r5c8 = (2-1)r5c4 = 1r5c6 - 4r5c6;
3r6c8 - (3=4)r9c8 - r8c7 = r5c7  - 4r5c6;
5r6c8 - (5=4)r5c7                - 4r5c6; stte

Note added for wmild2017:
Starting from the "basics" grid, the above approach is considered "single-step" and uses a kraken cell (exactly one candidate must be true). So, if each cell candidate, treated as true, leads to a common "stte" elimination, then you've got a valid solution. You can use Andrew Stewart's online solver (like I do) to check if a potential elimination candidate is stte. As Cenoman pointed out, it's also helpful to include some sort of alphabetic labeling for each chain. Hope this helps.

SteveC

[wmild2017]

Code: Select all

*-----------------------------------------------------------*
| 8    7    3    |  9      4    12    |  56    1256   256   |
| 5    4    1    |  7      6    28    |  3     9      28    |
| 2    6    9    |  5      13   138   |  7     14     48    |
|----------------+--------------------+---------------------|
| 1    235  8    |  234    23   7     |  9     23456  23456 |
| 36   9    56   | c1234   8   d135-4 | B45d  b2345   7     |
| 7    235  4    |  6      9    35    |  8   Aa235a   1     |
|----------------+--------------------+---------------------|
| 346  35   2    |  34     7    9     |  1     8      3456  |
| 9    18   56   |  12348  123  134   |  456c  7      3456  |
| 34   18   7    |  18     5    6     |  2     34b    9     |
*-----------------------------------------------------------*

Kraken cell (235)r6c8.

Code: Select all

2r6c8 - r5c8 = (2-1)r5c4 = 1r5c6 - 4r5c6;
3r6c8 - (3=4)r9c8 - r8c7 = r5c7  - 4r5c6;
5r6c8 - (5=4)r5c7                - 4r5c6; stte

Note added for wmild2017:
Starting from the "basics" grid, the above approach is considered "single-step" and uses a kraken cell (exactly one candidate must be true). So, if each cell candidate, treated as true, leads to a common "stte" elimination, then you've got a valid solution. You can use Andrew Stewart's online solver (like I do) to check if a potential elimination candidate is stte. As Cenoman pointed out, it's also helpful to include some sort of alphabetic labeling for each chain. Hope this helps.

SteveC

Of course.It does!Thanks.

wmild2017

[nedBlake]

Solution of this puzzle beyond the basics that included an XYZwing and an Xwing, is accomplished by 3 chains, all made up of strong links.

The first one I drew had both endpoints in the same cell at R7C9:

June 22 A.png (29.54 KiB) Viewed 559 times

Since the end points 5 and 6 are different colors and strongly linked, the other candidates in that cell are eliminated.

I could then draw the second one, since I eliminated the 3 in R7C9:

June 22 B.png (33.62 KiB) Viewed 559 times

We could then eliminate candidate 3 in R4C4 which sees both ends of this chain.
This created a line-block intersection in block 8, where the line C4 forced the solution to be in the intersection, thus eliminating the other 3's in the block.

The third chain is then drawn, and this interesting one essentially solved the puzzle:

June 22 C.png (32.31 KiB) Viewed 559 times

The endpoints are different candidates and are of the same color.
This normally wouldn't be too useful, but in this case, assuming the color green indicated a solution, the 2 and 3 in R4C5 would disappear leaving an empty cell.
We can't have that, so all green candidates can be eliminated. And after that its all singles to the end.