The New Sudoku Players' Forum

[FEARDIZ]

I'm working on a shogun puzzle so this part has many solutions, but together it has only 1
so

Code: Select all

 *-----------*
 |...|...|...|
 |...|.8.|...|
 |7.9|2.1|...|
 |---+---+---|
 |5..|...|..1|
 |8.3|...|9..|
 |...|5.8|.2.|
 |---+---+---|
 |.3.|.7.|..5|
 |..6|4..|2..|
 |..8|.52|...|
 *-----------*


 *-----------*
 |215|...|48.|
 |364|.85|..2|
 |789|241|563|
 |---+---+---|
 |5.7|...|8.1|
 |8.3|...|956|
 |6.1|5.8|.2.|
 |---+---+---|
 |.32|87.|..5|
 |.56|4..|278|
 |.78|.52|...|
 *-----------*

 
 *-----------------------------------------------------------*
 | 2     1     5     | 3679  369   3679  | 4     8     79    |
 | 3     6     4     | 79    8     5     | 17    19    2     |
 | 7     8     9     | 2     4     1     | 5     6     3     |
 |-------------------+-------------------+-------------------|
 | 5     249   7     | 369   2369  3469  | 8     34    1     |
 | 8     24    3     | 17    12    47    | 9     5     6     |
 | 6     49    1     | 5     39    8     | 37    2     47    |
 |-------------------+-------------------+-------------------|
 | 149   3     2     | 8     7     69    | 16    149   5     |
 | 19    5     6     | 4     139   39    | 2     7     8     |
 | 149   7     8     | 169   5     2     | 136   1349  49    |
 *-----------------------------------------------------------*


the programs wants to color the 9's like this

Code: Select all

 *-----------*
 |...|...|...|
 |...|.8.|...|
 |7.9|2.1|...|
 |---+---+---|
 |5..|...|..1|
 |8.3|...|9..|
 |...|5.8|.2.|
 |---+---+---|
 |.3.|.7.|..5|
 |..6|4..|2..|
 |..8|.52|...|
 *-----------*


 *-----------*
 |215|...|48.|
 |364|.85|..2|
 |789|241|563|
 |---+---+---|
 |5.7|...|8.1|
 |8.3|...|956|
 |6.1|5.8|.2.|
 |---+---+---|
 |.32|87.|..5|
 |.56|4..|278|
 |.78|.52|...|
 *-----------*

 
 *-----------------------------------------------------------*
 | 2     1     5     | 3679  369   3679  | 4     8     +79    |
 | 3     6     4     | +79    8     5     | 17    -19    2     |
 | 7     8     9     | 2     4     1     | 5     6     3     |
 |-------------------+-------------------+-------------------|
 | 5     249   7     | 369   2369  3469  | 8     34    1     |
 | 8     24    3     | 17    12    47    | 9     5     6     |
 | 6     49    1     | 5     39    8     | 37    2     47    |
 |-------------------+-------------------+-------------------|
 | 149   3     2     | 8     7     69    | 16    149   5     |
 | 19    5     6     | 4     139   39    | 2     7     8     |
 | 149   7     8     | 169   5     2     | 136   1349  -49    |
 *-----------------------------------------------------------*



somehow the 9 at r9c4 gets excluded.. how is that possable when there are more 9's in c4 and r9


thanks[/code]

[Animator]

- is the opposite of +

So if r2c4 is not the number 9 then r9c9 has to be the number 9 (remember: it's the opposite).
If r9c9 is not the numbe r9 then r2c4 has to be the number 9.

Which one is the number 9 is irrelevant. What you can see is that r9c4 can never be 9. since it sees both a + and a -. (Either r2c4 or r9c9 is 9)

[RW]

[Edit: post removed, Animator said the same thing while I was writing]

[FEARDIZ]

thanks for the reply
what I'm confused about is there is 2 other 9's in C4 and 2 other 9's in R9, so how can the 9 in C4R9 be conjugate with C4R2 or C9R9 ?

thanks

[Animator]

Wheter or not there are other cells in that row or column that can have the number 9 is irrelevant.

What is relevant:

• there are two cells in row 2 that can have the number 9,
• two cells in box 3 that can have the number 9,
• two cells in column 9 that can have the number 9
  

This allows you to come to these conclusions:

• row2: r2c8 is the opposite of r2c4 (one of them is true, one is false: remember: only 2 candidates for the number 9 on that row)
• box3: r1c9 is the opposite of r2c8 (or: r1c9 is the same as r2c4)
• column 9: r9c9 is the opposote of r1c9 (or: r9c9 is the opposite of r2c4)
  

Assume:

• r2c4 = 9 ==> r2c8 != 9 ==> r9c1 = 9 ==> r9c9 != 9
• r2c4 != 9 ==> r2c8 = 9 ==> r9c1 != 9 ==> r9c9 = 9.
  

Either r2c4 is the number 9 or it isn't. In both cases this lead to r9c4 seeing a 9: either in the column 4 (r2c4) or in row 9 (r9c9).

Which one it really is is impossible to tell at this moment... But what you know for sure is that r9c4 can never be the number 9.

For example, if r9c4 is the number 9, then r9c9 can't be 9 and then r2c4 has to be 9 (r2c4 is the opposite of r9c9): this would mean that you have the number 9 twice in column 4.

Does this makes sense?

[Cec]

"..what I'm confused about is there is 2 other 9's in C4 and 2 other 9's in R9, so how can the 9 in C4R9 be conjugate with C4R2 or C9R9 ?.."

The following extract from this Thread may also help you understand why the 9 in c4r9 can't be "conjugate" with c4r2 or c9r9.

"..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..."

* Note: for your latest puzzle this of course would mean the 9's.

To meet this criteria the 9 in c4r9 cannot be "conjugate" with another pair in either column4 or in row9, because the 9's occur in more than two cells in these particular two groups. For "conjugate pairs" an individual candidate, in this case 9, can only occupy two cells in a group (row, column or box). Understanding this concept will help you understand the "colouring" technique.

Cec

[FEARDIZ]

thanks Animator that makes sence.. this seems like a varation of coloring

with 'basic' coloring you can't color the 9 at c4r9
but since that cell intersects with opposite colors it can't be true

[TKiel]

Most of the time, the cell in which an exclusion is made using colouring is not one of the cells that is coloured. The colouring merely highlights the relationship (the fact that they must be opposites) between cells, so one can see that a particular cell that is not part of the chain shares a grouping with both colours of the chain and can be excluded.

Tracy