## (Dunno if it's a) New Technique

Advanced methods and approaches for solving Sudoku puzzles

### (Dunno if it's a) New Technique

I used this method to solve a sudoku puzzle just a while ago.
Code: Select all
` *-----------* |5.3|2.4|...| |8..|3..|1..| |74.|.9.|..3| |---+---+---| |...|...|4.7| |1..|6.3|..8| |9.4|...|...| |---+---+---| |6..|.3.|.89| |..9|..7|..4| |...|5.9|3.1| *-----------* *-----------* |513|284|..6| |89.|37.|14.| |74.|19.|8.3| |---+---+---| |.6.|9..|4.7| |1..|643|..8| |9.4|7..|6..| |---+---+---| |6.1|432|.89| |..9|817|.64| |4..|569|3.1| *-----------*  *--------------------------------------------------* | 5    1    3    | 2    8    4    | 79   79   6    | | 8    9    26   | 3    7    56   | 1    4    25   | | 7    4    26   | 1    9    56   | 8    25   3    | |----------------+----------------+----------------| | 23B  6    58   | 9    25G  18   | 4    13   7    | | 1    27-  57   | 6    4    3    | 29K  259  8    | | 9    238* 4    | 7    25B  18   | 6    13   25-  | |----------------+----------------+----------------| | 6    57   1    | 4    3    2    | 57   8    9    | | 23   235  9    | 8    1    7    | 25M  6    4    | | 4    278M 78   | 5    6    9    | 3    27K  1    | *--------------------------------------------------*`

I put the filter on candidate 2 and started colouring.

I later saw that there were easier eliminations which would do the same thing. But I saw this nonetheless.

B,G,K, and M are the four colours that I have used. B and G form one conjugate pair while K and M form another.

- are the cells from which 2 can be eliminated.

That would have been obvious if I had remembered to colour r8c1 with G.

I would have also been able to eliminate the 2 in r6c2 by use of the naked pair of 2 and 5 on row 6.

In the method I used, I used saw that the absence of 2 in the * cell would have allowed me to colour the - cells with G and thus eliminate all Gs since the Gs would see both K and M. As things stood, I could at least eliminate the - cells because of one piece of observation.

If 2 is in the * cell, the - cells can be eliminated.
If 2 is not in the * cell, the - cells can be eliminated.

This may afterall have been a useless post. I restarted this puzzle and tried to set up a position where the move I used would be necessary to solve the puzzle. I was able to avoid the naked pair, but I couldn't establish another 2 in column 1.

Here is a virtual example though.

Code: Select all
` *--------------------------------------------------* | 5    1    38   | 2    38   4    | 79   79   6    | | 238  9    286  | 38   7    56   | 1    4    25   | | 7    4    26   | 1    9    56   | 38   25   38   | |----------------+----------------+----------------| | 23B  6    58   | 9    25G  18   | 4    13   7    | | 1    27-  57   | 6    4    38   | 29K  259  38   | | 9    238* 4    | 7    125B 18   | 6    13   25-  | |----------------+----------------+----------------| | 6    57   1    | 4    38   2    | 57   38   9    | | 23   235  9    | 38   1    7    | 25M  6    4    | | 4    278M 78   | 5    6    9    | 38   27K  1    | *--------------------------------------------------*`

This is the position at which my method works even though you might want to eliminate the 2 from r2c1 before you apply this method. However, I noticed that simple sudoku says this puzzle has 316 solutions. I have not used any uniqueness conditions and was able to solve this puzzle. So, can this have more than one solution? Or is this a BUG in the program?

This example is slightly better because even though one doesn't need to apply my technique here if he filters 3 or 8 first. Yet, if 2 is filtered first, you can see the link between two unconnected conjugate sets.
Finlip

Posts: 49
Joined: 15 July 2005

Since r5c2 both sees K- and M-colored cells you can elimate the 2 with simple coloring (or 2 strong links/turbot fish).
ravel

Posts: 998
Joined: 21 February 2006

Posting two different PM for the same puzzle is a bit confusing. In either case, the XYZ-Wing in [r9c2] could be the next step.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

Do you guys read everything that's posted or just copy the puzzle and solve.
Finlip

Posts: 49
Joined: 15 July 2005