The New Sudoku Players' Forum

[JeffInCA]

I have been working on the puzzle below using Simple Sudoku

Code: Select all


*-----------------------------------------------------------*
 | 5     16    7     | 2     9     16    | 3     4     8     |
 | 2     168   3     | 4     578   168   | 156   17    9     |
 | 4     168   9     | 15    578   3     | 1256  127   57    |
 |-------------------+-------------------+-------------------|
 | 1     5     6     | 7     2     4     | 8     9     3     |
 | 9     7     2     | 8     3     5     | 4     6     1     |
 | 8     3     4     | 19    6     19    | 7     5     2     |
 |-------------------+-------------------+-------------------|
 | 3     2     15    | 6     4     89    | 159   178   57    |
 | 7     4     15    | 359   58    2     | 159   138   6     |
 | 6     9     8     | 35    1     7     | 25    23    4     |
 *-----------------------------------------------------------*



At this point I ask Simple Sudoku for a hint and it tells me I can make an elimination in r3c4 based on "Multiple Colors"

I have looked at this and see nothing interesting on the 1's.

On the 5's I see three independent conjugates that don't seem to be chained to any others

1) [r2c5]=5=[r2c7] (Is this notation correct?)

2) [r3c9]=5=[r7c9] (I guess r3c9 is technically "weak linked" to r2c7)

3) [r9c7]=5=[r9c4] (and here r9c7 is "weak linked" to r7c9)


I'm not sure, but it seems this may be an example of a forcing chain, nice loop or other related technique in this family which I haven't mastered yet.

However, I thought I had a pretty good handle on coloring, and I don't see how we make a coloring-based elimination here. (I will look into applying the other techniques on my own as an exercise, but I'm most interested in how "multiple colors" applies to this example.)


Thanks,

Jeff

[angusj]

Hi Jeff.
Yes the conjugate 5's in row 2 and row 9 are the key ones here.
There's also a weak link between r2c7 & r9c7.

See Type 2 Multicolors for more info here: http://www.setbb.com/phpbb/viewtopic.php?p=2575&mforum=sudoku#2575

[Jeff]

Hi Jeff, This multi-colouring example can also be expressed as 2 x-cycles of length 7. Refer here for details.

[angusj]

Hi Jeff, This multi-colouring example can also be expressed as 2 x-cycles of length 7

It's also a Turbot fish. But regardless, there are only 5 cells of particular interest at this point:



And to explain the multicolor logic here ...
It's not possible for both the blue and pink cells to be 'true' so either or both the bright green and the orange cells are 'true'. Therefore the yellow highlighted cell can have its '5' candidate excluded.

[Jeff]

It's also a Turbot fish. But regardless, there are only 5 cells of particular interest at this point:

Hi Angus, you are right.
There is also another turbot fish:
[r3c4]-5-[r3c9]=5=[r7c9]-5-[r9c7]=5=[r9c4]-5-[r3c4] => r3c4<>5

[Wolfgang]

All these different notations are a bit confusing. So i try to say in words, how (with at least 3 methods and 4 notations) you also can eliminate 5 from r8c5:

Either r2c5 or r2c7 must be 5.
If r2c7 is 5, then not r3c9, then r7c9 and not r7c3, then r8c3.
So either r2c5 or r8c3 must be 5, and r8c5 cannot be 5.

[JeffInCA]

Thanks for all your help guys.

Believe it or not, I actually saw the Turbot fish, but I wanted to see it from coloring, because I usually find those patterns easier to spot and use coloring before trying to look for more complex patterns.

Also, after reviewing "Type 2 coloring" I found that you can also use the conjugate in column 9 (r37c9) with the one in row 9 (r9c47) to make the same deduction.

Thanks again,

Jeff