The New Sudoku Players' Forum

[FEARDIZ]

the hit say's colors, but I don't understand what or how it works...
I know it's with the 5's and 9's but can't see it.. is it more of a fill it in and see how it works out?

thanks

Code: Select all


 *-----------*
 |5..|..2|6..|
 |...|.65|.31|
 |.1.|..3|.75|
 |---+---+---|
 |...|..1|.2.|
 |8..|3.7|..6|
 |.3.|4..|...|
 |---+---+---|
 |36.|7..|.8.|
 |28.|53.|...|
 |..4|2..|..7|
 *-----------*


 *-----------*
 |543|172|698|
 |728|965|431|
 |916|843|275|
 |---+---+---|
 |47.|6.1|823|
 |8..|3.7|.46|
 |63.|4.8|7.9|
 |---+---+---|
 |36.|714|.82|
 |287|53.|..4|
 |1.4|28.|3.7|
 *-----------*

 
 *--------------------------------------------------*
 | 5    4    3    | 1    7    2    | 6    9    8    |
 | 7    2    8    | 9    6    5    | 4    3    1    |
 | 9    1    6    | 8    4    3    | 2    7    5    |
 |----------------+----------------+----------------|
 | 4    7    59   | 6    59   1    | 8    2    3    |
 | 8    59   12   | 3    259  7    | 15   4    6    |
 | 6    3    12   | 4    25   8    | 7    15   9    |
 |----------------+----------------+----------------|
 | 3    6    59   | 7    1    4    | 59   8    2    |
 | 2    8    7    | 5    3    69   | 19   16   4    |
 | 1    59   4    | 2    8    69   | 3    56   7    |
 *--------------------------------------------------*


[Ruud]

Coloring the 5's is sufficient.

Start in any row/column/box that has 2 candidates. Color one green and the other blue.

Next check whether these 2 candidates also belong to a pair in another row/column/box. When you find these, color the counterpart with the opposite color. Make sure you always have 2 different colors in each row/column/box.

Keep coloring them this way until you notice the same color in a single row/column/box. That color is the wrong one, because it leads to a contradiction. Eliminate all candidates of that color.

That should do it.

Ruud.

[TKiel]

FEARDIZ,

Colouring works only with conjugate cells. Cells are conjugate if only two cells in any type of group (row, box ,column) contain a certain candidate. If one cells contains the value, the other must not. But it is also true if one of the cells does not contain the value, the other must. Colouring the cells doesn't assume anything about whether a certain color is true or false, it merely highlights the relationship between the cells. In this puzzle there is only one conjugate chain, when colouring on 5's, so all cells in the chain are either blue or green. All greens are true and blues are false, or else all blues are true and greens are false. Since there ends up being two cells of the same colour in column 5, that color must be false and the other color must be true.

Tracy

[Cec]

Hi FEARDIZ,
Following on from Ruud's and Tracy's above explanations, a glance back through previous forum posts will show many other members, including myself, have been troubled to understand the coloring technique. Where an individual candidate, in this case digit 5, occupies only two cells in a group (row, column or box) to form a conjugate pair with another candidate in that group then the following alternative coloring on the 5's would occur in the grid below. I've assigned a '+' for green color and a '-' for the blue color.

Code: Select all

 *--------------------------------------------------*
 | 5    4    3    |  1    7    2   |  6    9    8   |
 | 7    2    8    |  9    6    5   |  4    3    1   |
 | 9    1    6    |  8    4    3   |  2    7    5   |
 |----------------+----------------+----------------|
 | 4    7   +59   |  6   -59   1   |  8    2    3   |
 | 8   -59   12   |  3    259  7   | -15   4    6   |
 | 6    3    12   |  4   -25   8   |  7   +15   9   |
 |----------------+----------------+----------------|
 | 3    6   -59   |  7    1    4   | +59   8    2   |
 | 2    8    7    |  5    3    69  |  19   16   4   |
 | 1   +59   4    |  2    8    69  |  3   -56   7   |
 *--------------------------------------------------*


As pointed out by Ruud and Tracy, where the same colour occurs twice in a group, in this case column 5 as designated by the [-] sign then the 5's can be excluded from both these cells r4c5 and r6c5. This leaves one remaining 5 to fill cell r5c5 which in turn excludes the other 5's in row5. Alternatively, this coloring technique could also have excluded the 5's in row5, ie.cells r5c2 and r5c7 because of their identical coloring in this row to give the same result as above.

Cec

[FEARDIZ]

thanks for the replys, I'm confused with another puzzle with colors

Code: Select all

 *-----------*
 |.5.|...|9..|
 |...|98.|..1|
 |1..|.6.|37.|
 |---+---+---|
 |.45|.7.|.18|
 |...|...|...|
 |71.|.9.|65.|
 |---+---+---|
 |.78|.1.|..5|
 |2..|.35|...|
 |..1|...|.9.|
 *-----------*


 *-----------*
 |.5.|...|986|
 |...|98.|5.1|
 |189|56.|37.|
 |---+---+---|
 |945|.7.|218|
 |8..|.5.|7.9|
 |71.|.98|65.|
 |---+---+---|
 |.78|.19|4.5|
 |294|835|167|
 |5.1|...|89.|
 *-----------*

 
 *-----------------------------------------------------------*
 | 34    5     237   | 137   24    137   | 9     8     6     |
 | 346   236   2367  | 9     8     37    | 5     24    1     |
 | 1     8     9     | 5     6     24    | 3     7     24    |
 |-------------------+-------------------+-------------------|
 | 9     4     5     | 36    7     36    | 2     1     8     |
 | 8     236   236   | 124   5     124   | 7     34    9     |
 | 7     1     23    | 24    9     8     | 6     5     34    |
 |-------------------+-------------------+-------------------|
 | 36    7     8     | 26    1     9     | 4     23    5     |
 | 2     9     4     | 8     3     5     | 1     6     7     |
 | 5     36    1     | 2467  24    2467  | 8     9     23    |
 *-----------------------------------------------------------*


here is the color list the program wants to do
 *-----------------------------------------------------------*
 | 34    5     -237   | 137   +24    137   | 9     8     6     |
 | 346   236   2367  | 9     8     37    | 5     -24    1     |
 | 1     8     9     | 5     6     -24    | 3     7     +24    |
 |-------------------+-------------------+-------------------|
 | 9     4     5     | 36    7     36    | 2     1     8     |
 | 8     236   236   | 124   5     124   | 7     34    9     |
 | 7     1     23    | 24    9     8     | 6     5     34    |
 |-------------------+-------------------+-------------------|
 | 36    7     8     | -26    1     9     | 4     +23    5     |
 | 2     9     4     | 8     3     5     | 1     6     7     |
 | 5     36    1     | 2467  -24    2467  | 8     9     -23    |
 *-----------------------------------------------------------*


why do I only color these and not the other 2's from box 1,4,5 and the other 2 2's in 8

thanks
[/code]

[Ruud]

why do I only color these and not the other 2's from box 1,4,5 and the other 2 2's in 8

Hi,

You only color conjugate pairs.

If you want to continue coloring, you would end up with a picture like this:



The uncolored candidates in box 1, 4, 5 and 8 are not part of any conjugate pair.

For simple coloring you can only use a single chain. Even when you would use multi-coloring (multiple chains), the extra colors would not have made any difference.

Ruud.

[Cec]

"..why do I only color these and not the other 2's from box 1,4,5 and the other 2 2's "

I too was confused with this same dilemma which is why I particularly mentioned in my above post that the coloring technique applies to an individual candidate, in this case the 2's, which occupies only two cells in a group (row, column or box) to form a conjugate pair with another candidate in that group.

You will see from ruud's above grid that the conjugate pairs for the 2's correctly occupy only two cells for the groups being in rows 1,3 and 7 and in columns 5,8 and 9. Coloring the additional 2's in boxes 1,4,5 and 8 which you have questioned would result in more than two cells being colored in these groups (boxes) which contravenes the above criteria for coloring conjugate pairs (two cells) in a given group. Hope this also helps.

Cec