The New Sudoku Players' Forum

[jphamel]

I'm trying to figure ou why, when using color to find conjugate pair. I can never remove the one that would logically, to me anyway be the one to remove.

Code: Select all

 *-----------*
 |..5|2.9|8..|
 |6..|...|...|
 |.8.|3..|..5|
 |---+---+---|
 |..9|.7.|.2.|
 |87.|...|.63|
 |.6.|.3.|1..|
 |---+---+---|
 |2..|..8|.4.|
 |...|...|..2|
 |..8|6.1|3..|
 *-----------*


 *-----------*
 |..5|2.9|8..|
 |6..|...|...|
 |.8.|3..|..5|
 |---+---+---|
 |..9|.76|.2.|
 |87.|...|.63|
 |.6.|.3.|1..|
 |---+---+---|
 |2..|..8|.4.|
 |...|..3|..2|
 |..8|621|3..|
 *-----------*

 
 *--------------------------------------------------------------------*
 | 1347   134    5      | 2      146+   9      | 8      137    1467-  |
 | 6      12349  12347  | 14578  1458   457    | 2479   1379   1479   |
 | 1479   8      1247   | 3      146-   47     | 24679+ 179    5      |
 |----------------------+----------------------+----------------------|
 | 1345   1345   9      | 1458   7      6      | 45     2      48     |
 | 8      7      124    | 1459   1459   245    | 459    6      3      |
 | 45     6      24     | 89     3      245    | 1      789    789    |
 |----------------------+----------------------+----------------------|
 | 2      1359   1367-  | 579    59     8      | 679    4      1679+  |
 | 14579  1459   1467+  | 4579   459    3      | 679-   15789  2      |
 | 4579   459    8      | 6      2      1      | 3      579    79     |
 *--------------------------------------------------------------------*


Conjugate pairs:

I have marked the conjugate pairs with +s an -s

This is for candidates 6s, so if my logic is correct, the 6 I should remove is r7c7, but when I try to exclude this 6, Simple Sudoku tells me it is an invalid move, please tell me what I dont understand if you could explain me why!. I'm playing at extreme level because the others are to easy.

It would be easier to visualize with an image, but when I try to paste an image it does no work.

Thank you.



jphamel

Edited to dislplay the image

[ihope127]

You can upload a picture to a hosting service like http://tinypic.com/.

[jphamel]

Thanks ihope127

[sweetbix]

If you are doing simple colouring you have labelled too many 6s. r7c3, r8c7 have three 6s in their group but conjugates should have only two.

You have two separate chains here. The one in r7c3, r8c3, r8c7 is separate from the other one. I don’t think that you can use multiple colouring either but I have only just been learning about it so I hope I’ve got this right but in this case the two chains don’t seem to overlap.

[tso]

No exclusions can be made from coloring 6s here.

Code: Select all

 .  .  . | . +6  . | .  . -6
 .  .  . | .  .  . | .  .  .
 .  .  . | . -6  . |+6  .  .
---------+---------+---------
 .  .  . | .  .  . | .  .  .
 .  .  . | .  .  . | .  .  .
 .  .  . | .  .  . | .  .  .
---------+---------+---------
 .  . x6 | .  .  . |o6  . +6
 .  . o6 | .  .  . |x6  .  .
 .  .  . | .  .  . | .  .  .


You can see that there are three equally valid placements for the last four 6s -- and each possible placement occurs at least once:

Code: Select all

 .  .  . | .  .  . | .  .  6
 .  .  . | .  .  . | .  .  .
 .  .  . | .  6  . | .  .  .
---------+---------+---------
 .  .  . | .  .  . | .  .  .
 .  .  . | .  .  . | .  .  .
 .  .  . | .  .  . | .  .  .
---------+---------+---------
 .  .  6 | .  .  . | .  .  .
 .  .  . | .  .  . | 6  .  .
 .  .  . | .  .  . | .  .  .


 .  .  . | .  .  . | .  .  6
 .  .  . | .  .  . | .  .  .
 .  .  . | .  6  . | .  .  .
---------+---------+---------
 .  .  . | .  .  . | .  .  .
 .  .  . | .  .  . | .  .  .
 .  .  . | .  .  . | .  .  .
---------+---------+---------
 .  .  . | .  .  . | 6  .  .
 .  .  6 | .  .  . | .  .  .
 .  .  . | .  .  . | .  .  .


 .  .  . | .  6  . | .  .  .
 .  .  . | .  .  . | .  .  .
 .  .  . | .  .  . | 6  .  .
---------+---------+---------
 .  .  . | .  .  . | .  .  .
 .  .  . | .  .  . | .  .  .
 .  .  . | .  .  . | .  .  .
---------+---------+---------
 .  .  . | .  .  . | .  .  6
 .  .  6 | .  .  . | .  .  .
 .  .  . | .  .  . | .  .  .

[QBasicMac]

This is for candidates 6s

Well, as re the 6's, starting with your original puzzle, I got to here

Code: Select all

+-----------------+-----------------+------------------+
| 1347  134   5   | 2     14    9   | 8     137   6    |
| 6     2     137 | 15    8     57  | 479   1379  479  |
| 9     8     147 | 3     6     47  | 2     17    5    |
+-----------------+-----------------+------------------+
| 1345  1345  9   | 1458  7     6   | 45    2     48   |
| 8     7     124 | 1459  1459  245 | 459   6     3    |
| 45    6     24  | 4589  3     245 | 1     579   4789 |
+-----------------+-----------------+------------------+
| 2     359   367 | 579   59    8   | 5679  4     1    |
| 157   159   167 | 4579  459   3   | 5679  8     2    |
| 457   459   8   | 6     2     1   | 3     579   79   |
+-----------------+-----------------+------------------+


via
Hidden single 2 in col 2
Hidden single 8 in col 5
Hidden single 9 in box 1
Hidden single 2 in row 3
Hidden single 6 in row 4
Hidden single 3 in col 6
Hidden single 8 in row 8
Hidden single 2 in row 9
Hidden single 6 in box 3
Hidden single 6 in row 3
Hidden single 1 in box 9
Locked candidate 4 in box 3
Locked candidate 4 in box 8
Locked candidate 7 in box 8

So I didn't see a problem with 6. But I got stuck here and had to use T&E to prove there is only one solution.

Maybe your coloring stuff will work starting at that point.

Mac

[Crazy Girl]

Well, as re the 6's, starting with your original puzzle, I got to here

Code: Select all

+-----------------+-----------------+--------------------+
| 1347  134   5   | 2     14    9   | 8       137   6    |
| 6     2     137 | 15    8     57  | 479     1379  479  |
| 9     8     147 | 3     6     47  | 2       17    5    |
+-----------------+-----------------+--------------------+
| 1345  1345  9   | 1458  7     6   | 45      2     48   |
| 8     7     124 | 1459  1459  245 | 459     6     3    |
| 45    6     24  | 89    3     245 | 1       79    789  |
+-----------------+-----------------+--------------------+
| 2     359   367 | 579   59    8   | (5)679  4     1    |
| 157   159   167 | 4579  459   3   | (5)679  8     2    |
| 457   459   8   | 6     2     1   | 3       579   79   |
+-----------------+-----------------+--------------------+


via
Hidden single 2 in col 2
Hidden single 8 in col 5
Hidden single 9 in box 1
Hidden single 2 in row 3
Hidden single 6 in row 4
Hidden single 3 in col 6
Hidden single 8 in row 8
Hidden single 2 in row 9
Hidden single 6 in box 3
Hidden single 6 in row 3
Hidden single 1 in box 9
Locked candidate 4 in box 3
Locked candidate 4 in box 8
Locked candidate 7 in box 8

So I didn't see a problem with 6. But I got stuck here and had to use T&E to prove there is only one solution.

Maybe your coloring stuff will work starting at that point.

Mac

There's a Naked {2, 4, 5} triple in Row 6, so i've eliminated some more pencilmarks for you.

This leaves 5 in Box 6 in Column 7 enabling one to place 5 in Box 9

This allows you to get abit further, but not solve the puzzle completely

[Carcul]

Hi Jphamel, and welcome to this forum.

After the naked triple pointed out by Crazy Girl (and the respective simplifications) you have a Swordfish and next a Turbot Fish, from which emerges a naked pair. After that, there are only singles.

Regards, Carcul

[jphamel]

Tanks everyone for all the replys, I`ve been able to solve the puzzle finally.

But I should have been more clear, it`s just the thing with coloring or conjugate pairs I have a hard time understanding, sometimes I can remove some numbers sometimes I`m wrong eventhough I think I correctly link those pairs.

Anyway thanks for the help, and I enjoy really enjoy this board, we learn a lot here.

JPHamel

[rubylips]

I appreciate that the OP asked specifically about the possibility of elimination of 6s and didn't request a solution but here's a solution anyway. It elegantly removes some candidate 7s in a manner not explicitly discussed elsewhere. I've presented the solution in more detail than usual because the original candidate grid suggests that the original poster isn't familiar with locked candidates or disjoint subsets (my name for pairs/triples etc.). BTW, I fully agree that it's not possible to eliminate 6s.

My solution starts from the OP with hidden singles added.

Code: Select all

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

  1347   134     5 |     2    14    9 |     8   137     6
     6     2  1347 |  1457     8  457 |   479  1379   479
     9     8   147 |     3     6   47 |     2    17     5
-------------------+------------------+------------------
  1345  1345     9 |  1458     7    6 |    45     2    48
     8     7   124 |  1459  1459  245 |   459     6     3
    45     6    24 |  4589     3  245 |     1   579  4789
-------------------+------------------+------------------
     2   359   367 |   579    59    8 |  5679     4     1
  1457  1459  1467 |  4579   459    3 |  5679     8     2
   457   459     8 |     6     2    1 |     3   579    79

The value 4 in Box 7 must lie in Row 9.
- The moves r8c1:=4, r8c2:=4 and r8c3:=4 have been eliminated.
The value 4 in Row 2 must lie in Box 3.
- The moves r2c3:=4, r2c4:=4 and r2c6:=4 have been eliminated.
The value 7 in Box 2 must lie in Column 6.
- The move r2c4:=7 has been eliminated.
The values 7, 8 and 9 occupy the cells r6c4, r6c8 and r6c9 in some order.
- The moves r6c4:=4, r6c4:=5, r6c8:=5 and r6c9:=4 have been eliminated.
The cell r9c8 is the only candidate for the value 5 in Column 8.

  1347   134    5 |     2    14    9 |    8   137    6
     6     2  137 |    15     8   57 |  479  1379  479
     9     8  147 |     3     6   47 |    2    17    5
------------------+------------------+----------------
  1345  1345    9 |  1458     7    6 |   45     2   48
     8     7  124 |  1459  1459  245 |  459     6    3
    45     6   24 |    89     3  245 |    1    79  789
------------------+------------------+----------------
     2   359  367 |   579    59    8 |  679     4    1
   157   159  167 |  4579   459    3 |  679     8    2
    47    49    8 |     6     2    1 |    3     5   79

1. Consider the chain r1c8-7-r1c1~7~r9c1-7-r9c9~7~r6c9-7-r6c8.
The cell r6c8 must contain the value 7 if the cell r1c8 doesn't.
Therefore, these two cells are the only candidates for the value 7 in Column 8.
- The moves r2c8:=7 and r3c8:=7 have been eliminated.
The value 1 is the only candidate for the cell r3c8.
2. Consider the chain r5c3~1~r2c3-1-r2c4-1-r1c5-1-r5c5.
When the cell r5c3 contains the value 1, so does the cell r5c5 - a contradiction.
Therefore, the cell r5c3 cannot contain the value 1.
- The move r5c3:=1 has been eliminated.
The value 1 in Box 5 must lie in Row 5.
- The move r4c4:=1 has been eliminated.
The values 1 and 3 occupy the cells r4c1 and r4c2 in some order.
- The moves r4c1:=4, r4c1:=5, r4c2:=4 and r4c2:=5 have been eliminated.
The cell r6c1 is the only candidate for the value 5 in Box 4.
3. The value 4 in Column 3 must lie in Box 4.
- The move r3c3:=4 has been eliminated.
The value 7 is the only candidate for the cell r3c3.


[Lardarse]

That is bizarre... Three solvers taking three completely different routes through the puzzle. If MadOverlord is still reading these forums, then me might want to take a look at this. I'll start my list of highlights from the position that rubylips starts from...

Sudoku Susser:
Some hidden singles and locked candidates
Hidden triple (789) in row 6
Swordfish (7) in rows 1,6,9 affecting columns 1,8,9
Forcing chain removing 8 from r6c9
Nishio (!!!) removing 1 from r4c4

Simple Sudoku:
Some hidden singles and locked candidates
Naked triple (245) in row 6
Swordfish (7) in rows 1,6,9 affecting columns 1,8,9
Colouring on candidate 1s: r2c3 blue, r2c4 red, r1c5 blue, r5c5 red, r5c3 can't be either colour, therefore r5c3 can't be a 1

Both solvers finish easily from there...

[rubylips]

Essentially I agree with Simple Sudoku - however, we describe each of the three major eliminations using different terminology!

[Lardarse]

Care to explain your arcane syntax for the chains? (and while we're on the subject, how so you get this output from your program?)

[rubylips]

I use the notation introduced to this forum by, I believe, Wolfgang, i.e. '-' for a strong link (exactly two candidates in a sector) and '~' for a weak link (more than two candidates in a sector).

I post my puzzles from a development version on my PC, which would explain differences between what I post and what users who use my software might see.

[Shazbot]

jphamel

Getting back to your original question, your colouring in the top 4 cells are correct. But that's almost as far as you can go. A 6 in r3c7 means the 6s can be excluded from r7c7 and r8c7, so must go in r7c9. So that's correct. But a 6 in r1c9 does not lead you to a potential placement in the bottom cells - you know it has to go in c7, but you don't know which row. If there were only 2 cells in box 9 with candidate 6 it'd be a different matter.