The New Sudoku Players' Forum

[PeetNeef]

Hey guys another one! Please also have another look at #15!

https://ibb.co/Kb7SH3S

[PeetNeef]

Now with the good link:

https://ibb.co/Kb7SH3S

[Maxito_Bahiense]

Hi! Both links seem ok to me, showing the same grid.
At this stage, you can work with an XY-chain or an XY-wing to advance, for instance. Since I like colouring, I show here a Medusa colouring cluster that kills the sudoku:

Start colouring any of the bivalue coloured cells below [for instance, r1c1 with 1A, 4B]. Alternating colours using strong links, you can find the following grid:

Code: Select all

*--------------------------------------------------------------------*
 | 1A4B   1B5A   5B7A   | 27     279    4A79   | 8      3      6      |
 | 3      4A6B   6A7B   | 8      4B7A   5      | 1      9      2      |
 | 8      2      9      | 3      1      6      | 4      5      7      |
 *----------------------+----------------------+----------------------|
 | 2B4A   9      3568   | 256    2358   4B8A   | 7      1      58     |
 | 7      4B5A   58     | 9      4A58   1      | 26     26     3      |
 | 1B2A   1A56A  3568   | 2567   23578  78     | 9      4      58     |
 *----------------------+----------------------+----------------------|
 | 9      7      2      | 1      6      3      | 5      8      4      |
 | 5      38     1      | 4      78     2      | 36     67     9      |
 | 6      38     4      | 57     5789   789    | 23     27     1      |
 *--------------------------------------------------------------------*

Here, we find a cell colour wrap: candidates 1 and 6 in r7c2 have the same colour, so colour/parity A truth value is false, and all B candidates can be put in place. Singles to the end after that.

If you like a non-colour alternative, you have the XY-wing formed by cells r1c12, r6c2, for instance. These eliminations are included in the ones by the previous Medusa cluster.

[PeetNeef]

Thank you so much! I hate the fact that I missed the XY-wing...

To be honest; I don't really like the colouring techniques, but the Medusa one is interesting. I only have one question remaining about this technique:

*--------------------------------------------------------------------*
| 1A4B 1B5A 5B7A | 27 279 4A79 | 8 3 6 |
| 3 4A6B 6A7B | 8 4B7A 5 | 1 9 2 |
| 8 2 9 | 3 1 6 | 4 5 7 |
*----------------------+----------------------+----------------------|
| 2B4A 9 3568 | 256 2358 4B8A | 7 1 58 |
| 7 4B5A 58 | 9 4A58 1 | 26 26 3 |
| 1B2A 1A56A 3568 | 2567 23578 78 | 9 4 58|
*----------------------+----------------------+----------------------|
| 9 7 2 | 1 6 3 | 5 8 4 |
| 5 38 1 | 4 78 2 | 36 67 9 |
| 6 38 4 | 57 5789 789 | 23 27 1 |
*--------------------------------------------------------------------*


Why did you assign an A to '5' in r5c2? I understand every assigned 'color', but not that one...


Thanks for the help anyway, really appreciate it!

[PeetNeef]

I mean especially that r1c2 already has a 5 assigned with color A; isn't it already interfering with the assigned color A to 5 in r5c2?

[Maxito_Bahiense]

(edited)

Thank you so much!

You're welcome!

To be honest; I don't really like the colouring techniques, but the Medusa one is interesting. I only have one question remaining about this technique:

That's alright... For each person, his favourite set of techniques. Your sudoku had on a previous stage a lot of candidates for digit 4. Most players will see the x-wing or the 2-string kite. I'll try directly the x-colour technique watching all those links between the candidates. Of course it has to do with my set of abilities and (more importantly) my set of liabilities

Why did you assign an A to '5' in r5c2? I understand every assigned 'color', but not that one...


Thanks for the help anyway, really appreciate it!

For building the cluster, you start with a seed (for instance, the referred r1c1 1A). Then you proceed:

• If a candidate is a conjugate pair in a house to a candidate for the same digit marked A [resp. B], then you can colour the first candidate B [resp. A] (House)
• If in a bivalue cell one candidate is marked A [resp. B], then you can colour the other candidate B [resp. A] (Cell)
• If a bivalue cell with candidates x and y sees candidates x and y marked A and B in other cells, then candidate x can be marked B and y A (Importing).

Built this way, we can deduce that if any candidate's truth value is false (meaning said digit doesn't go in the cell), then any candidate with the same tag can be eliminated, and any candidate with the opposite mark can be written in.

You have (among possibly others) the following implications:

• If a candidate for digit x sees (other cells with) candidates for the same digit marked A and B, it can be safely removed (outer trap).
• If a candidate for digit x has candidate y in its cell marked A, and sees another cell with candidate x marked B, then we can discard first candidate for x (mixed trap).
• If in a multivalued cell, candidate x and y are marked A and B, respectively, then any extra candidate in that cell can be safely removed (inner trap).
• If a house has two candidates for the same digit marked A, then tag A can be assumed to have false truth value, and candidates marked with it can be discarded (House wrap).
• If a cell has two candidates marked A, then tag A can be assumed to have false truth value, and candidates marked with it can be discarded (Cell wrap).
• If a cell with candidates x1,... xn sees every candidate x1,... xn marked in other cells as A, then parity A's truth value can be assumed false [i.e., candidates with this tag can be removed] (Cell Void).
• If each of the n candidates for digit x in a house sees another cell out of the house with candidate x marked as A, then parity A's truth value can be assumed false [i.e., candidates with this tag can be removed] (House Void).
  

These are names that I employ for personal usage, I don't claim standarisation in any way .

Now, let's get to our cluster. Starting with r1c1 1A, we can go like this:

Code: Select all

 r1c1 1A (Seed), 4B (Cell); r1c2 1B (House), 5A (Cell); r1c3 5B (House), 7A (Cell); r2c3 7B (House), 6A (Cell); r2c2 6B (House), 4A (Cell); r2c5 4B (House), 5A (Cell);

In this way, we can continue colouring until we extend the cluster to the shown grid, if you wish. For you have already found a contradiction! As you have said, column 2 has two 5's marked A, which is a House wrap. I previously showed you a Cell wrap; both contradictions will eventually produce the same eliminations.

(Edited some typos, added House void.)