The New Sudoku Players' Forum

[bruceka9]

I would like someone to step-by-step explain how my color logic needs correcting.
I started with this Simple Sudoku puzzle

Code: Select all

 *-----------*
 |..3|.65|...|
 |...|4..|69.|
 |6..|...|4.2|
 |---+---+---|
 |...|.84|..9|
 |.3.|679|.8.|
 |4..|12.|...|
 |---+---+---|
 |8.5|...|..1|
 |.19|..6|...|
 |...|91.|7..|
 *-----------*

After working the puzzle for awhile, I could use colors to eliminate a 2.

I am focusing only on number 2, setup this way.

Code: Select all

 *--------------------------------------------------*
 | .    .    .    | .    .    .    | .    .    .    |
 | 2    .    2    | .    .    .    | .    .    .    |
 | .    .    .    | .    .    .    | .    .    .    |
 |----------------+----------------+----------------|
 | .    2    .    | .    .    .    | .    2    .    |
 | .    .    2    | .    .    .    | 2    .    .    |
 | .    .    .    | .    .    .    | .    .    .    |
 |----------------+----------------+----------------|
 | .    2    .    | .    .    2    | .    2    .    |
 | 2    .    .    | .    .    .    | 2    .    .    |
 | .    2    .    | .    .    2    | .    .    .    |
 *--------------------------------------------------*

Let's start at r2c1 coded "+" and the conjugate pairing at r2c3 coded "-"
Following the conjugate pairing,
r5c3 is "+" & r4c2 is "-"
r4c8 is "+" & r5c7 is "-"
r8c7 is "+" & c7r8 is "-"
r7c6 is "+" & r9c6 is "-"
r9c2 is "+" & r8c1 is "-" giving this

Code: Select all

 *--------------------------------------------------*
 | .    .    .    | .    .    .    | .    .    .    |
 | 2+   .    2-   | .    .    .    | .    .    .    |
 | .    .    .    | .    .    .    | .    .    .    |
 |----------------+----------------+----------------|
 | .    2-   .    | .    .    .    | .    2+   .    |
 | .    .    2+   | .    .    .    | 2-   .    .    |
 | .    .    .    | .    .    .    | .    .    .    |
 |----------------+----------------+----------------|
 | .    2    .    | .    .    2+   | .    2-   .    |
 | 2-   .    .    | .    .    .    | 2+   .    .    |
 | .    2+   .    | .    .    2-   | .    .    .    |
 *--------------------------------------------------*


Finally cell r7c2 can see "+" from r4c2 and it can see a "-" from r7c6.
So I thought I could eliminate 2 from r7c2, but that is an error per Simple Sudoku.

What is wrong with my understanding of Colors?

[tso]

You've colored two separate groups that will require FOUR colors. Below shows the extent that you can label PLUS and MINUS. There are three more cells that can be labled with two more colors, POUND and ASTERISK. But no cell in one group is a conjugate with any cell in the other.

Code: Select all

 *--------------------------------------------------*
 | .    .    .    | .    .    .    | .    .    .    |
 |+2    .   -2    | .    .    .    | .    .    .    |
 | .    .    .    | .    .    .    | .    .    .    |
 |----------------+----------------+----------------|
 | .   -2    .    | .    .    .    | .   +2    .    |
 | .    .   +2    | .    .    .    |-2    .    .    |
 | .    .    .    | .    .    .    | .    .    .    |
 |----------------+----------------+----------------|
 | .    2    .    | .    .   #2    | .   -2    .    |
 |-2    .    .    | .    .    .    |+2    .    .    |
 | .   #2    .    | .    .   *2    | .    .    .    |
 *--------------------------------------------------*

In then end, we know that either:

MINUS is true, POUND is false

OR

MINUS is false, POUND is true

OR

MINUS is false, POUND is false


Because of the third possibility, the candidate 2 cannot be excluded from r7c2.

[TKiel]

Bruceka9,

Even though colouring on the 2's didn't lead to an exclusion, if my candidate list is the same as yours at this stage of the puzzle, you can do it with 7's and it only involves one chain.

Code: Select all

 *--------------------------------------------------*
 | 9    4    3    | 2    6    5    | 18   17   78   |
 | 127  8    127  | 4    3    17   | 6    9    5    |
 | 6    5    17   | 78   9    178  | 4    3    2    |
 |----------------+----------------+----------------|
 | 17   27   6    | 5    8    4    | 3    12   9    |
 | 5    3    12   | 6    7    9    | 12   8    4    |
 | 4    9    8    | 1    2    3    | 5    67   67   |
 |----------------+----------------+----------------|
 | 8    267  5    | 3    4    27   | 9    26   1    |
 | 27   1    9    | 78   5    6    | 28   4    3    |
 | 3    26   4    | 9    1    28   | 7    5    68   |
 *--------------------------------------------------*


I didn't mark the conjugates in the grid above because you seem to know enough to be able to do that on your own. I merely posted it to see if my candidate list is the same as yours. Plus you didn't really ask for help in solving the puzzle and you may have already done that using some other method.

Tracy

[tso]

But there is a box/line exclusion: r23c3 must hold a 7, therefore r2c2<>7 ... so he probably doesn't have the same grid as you.

[TKiel]

tso,

You're right. It's the same cell. I was thinking about colouring and never saw the box-line exclusion.

Tracy

[bruceka9]

TSO

Thanks, I didn't know about a multi-color option. Your last statement, e.g. pound & minus could not be true makes sense.

Where can I read about Multi-Coloring?

[TKiel]

Bruceka9,

In order to use two seperate conjugate chains to make an exclusion, one marker (plus, minus, pound, asterisk) of each chain must be linked (share a row, column or box). Since both of those markers can't be true (they share a group) one or both of the other marker in each chain must be true. Any cell that sees both of those markers can be excluded.

There is a discussion on using two chains on this thread http://forum.enjoysudoku.com/viewtopic.php?t=3272. There is also discussion of colouring using three chains at this linkwww.sudoku.com/boards/viewtopic.php?t=3201.

Tracy

[Cec]

iHi bruceka9,

This thread and the above responses have been interesting but I would appreciate clarification on the following two items. Firstly, in your post you say:

"...Let's start at r2c1 coded "+" and the conjugate pairing at r2c3 coded "-"
Following the conjugate pairing,
r5c3 is "+" & r4c2 is "-"
r4c8 is "+" & r5c7 is "-"
r8c7 is "+" & c7r8 is "-"
r7c6 is "+" & r9c6 is "-"
r9c2 is "+" & r8c1 is "-" giving this..."

In the third notation above you say c7r8 is "-" . Is this correct or did you mean r7c8 ?

Secondly, I notice Tracy's above grid only has candidates [17] in cell r4c1 whereas the SS solver shows candidates [127] in this same cell with no further hint to proceed other than Swordfish which presumably requires the colouring technique as discussed above. I would also appreciate help to explain this.
Cec

[bruceka9]

Sorry, CEC

This is a typo, I mean r7c8

[emm]

Hi Cec

Hope you haven't read this post cos I'm editing it - the swordfish (not the same thing as colouring) eliminates the 2s at r4c1 and r9c1 - the upshot of the dialogue above was that colouring was not useful in this puzzle.

It looks like Tracy has already found the swordfish.

[TKiel]

Since it is a 2-2-2 swordfish, colouring actually does work to make the exclusion of 2 in r4c1 and r9c1, which is how I did it since I didn't actually see the swordfish, until em pointed it out. Just like I missed the box-line exclusion that tso pointed out. I'm beginning to notice a pattern here.

Tracy

[Cec]

Thanks bruceka9, em and Tracy for your above comments in clearing things up for me.
Cec

[AndyT]

Please let me chip in and also ask for help with colours (just 2 to start with). This is an image from a hint using AngusJ's excellent little program. Now I get the concept (I think) but I don't get the detail. My problem is that it seems to me crucial where you start the thread and the sequence you follow.



In this image, if you went right from the blue at R4C6 that would put a green at R4C8. If you go right from R2C6 and put a blue at R2C8, the conflict then appears to be at R2C9!

Equally why did the program not head down to R8C4 and colour there?

The technique appears very selective. Almost as if you need to know the result before you start.

Thanks, Andy

[angusj]

In this image, if you went right from the blue at R4C6 that would put a green at R4C8.

No, you can only colour "conjugate" cells. Since there are more than 2 cells with candidate '3' in that row, you can't colour across that row (ie you can't colour R4C8).

Equally why did the program not head down to R8C4 and colour there?

For the same reason. R8C4 isn't a "conjugate" cell since that column contains more than 2 cells with candidate '3'.

[AndyT]

CONJUGATE: adj, joined together as a pair

So what do you mean by conjugate?

Again, this appears selective. You then arbitrarily choose which to reject.