The New Sudoku Players' Forum

[denis_berthier]

Thanks totuan for this major contribution to science.

[totuan]

You're too and don't mention it...

[denis_berthier]

I have fun in Sudoku also, but in different ways. My fun is in trying to find the proper conditions for a pattern to be valid, in analysing its resolution power (wrt to other, simpler patterns) and in trying to extend it.

In the case of your pattern, it would lead me to ask the following questions, in order:
- what is the complexity of proving the "strong link" part?
- is the current presentation (involving all the cells in one row and all the cells in one column) the correct one?
- instead of fixing givens in some cells, wouldn't it be better and much more general to define the conditions by mentioning only allowed/disallowed candidates in the cells outside the block (and in the row or column) ? e.g. 9 must be present in t1c1, r1c9 and r9c1; 9 must be absent in r1c45678 and in r45678c1. This would make 12 cells to check, a huge number.
- considering the high complexity obtained above, is there any simpler way to write the conditions? Indeed, yes: instead of considering rc-cells, one has to consider only 1 rn-cell r1n9 and 1 cn-cell c1n9 => complexity reduced to 2.

As should be clear, this was not a final analysis of Shye's pattern; it was only me thinking loud about how I'd start the analysis.

After more thinking about it, it appears that not 2 but 3 CSP-Variables must be considered to prove the pattern: in terms of 2D-cells, not only rn-cell r1n9 and cn-cell c1n9 but also bn-cell b1n9.
As a result, in my measure of complexity, this adds 3 to any pattern it is a part of.

To take te above example:

Code: Select all

.--------------------.----------------------.--------------------.
|  1     *346   567  |*2347   8    *2347    | 256    27    9     |
|  4567   468   2    | 9      1-4   147     | 3      578  *4678  |
|f*347    9     78   | 6      234   5       | 28     1   f*2478  |
:--------------------+----------------------+--------------------:
|  9      7     3    | 5      12    128     | 4      6     128   |
|  26     1268  1568 | 23478  1234  1234678 | 12589  2389  1238  |
|  256    1268  4    | 238    9     12368   | 7      2358  1238  |
:--------------------+----------------------+--------------------:
|  236    5     169  | 238    7     238     | 1269   4     1236  |
|f*23467 *2346  67   | 1      5     9       | 268    2378  23678 |
|  8      123   179  | 234    6     234     | 129    2379  5     |
'--------------------'----------------------'--------------------'

kraken firework
7s multi-candidate strong link is true else repeat 7s in b1
||(7-3)r3c1 = (3-4)r1c2 = 4r1c46
||(7-4)r3c9 = 4r2c9
||(7-4)r8c1 = 4r8c2 - 4r1c2 = 4r1c46
-4r2c5 stte

the vertical bar should be assigned size 3 and the total size is:
- 3 for the vertical bar
- 3 for the first line (including 2 for the X-wing)
- 1 for the second line
- 2 for the 3rd line (not counting the x-wing, already counted before)
Total: 9

[marek stefanik]

Someone said: when someone doesn't want to understand, don't waste your time trying to explain.

- 3 for the first line (including 2 for the X-wing)

Thanks for the advice.

After more thinking about it, it appears that not 2 but 3 CSP-Variables must be considered to prove the pattern: in terms of 2D-cells, not only rn-cell r1n9 and cn-cell c1n9 but also bn-cell b1n9.

Correct, you need all three.
However, in the pattern they're semantically different.
The first two are equivalent to strong AIC links or the variables you write in your notation. For the reasoning to be correct at least one of the candidates must be true.
The last one is equivalent to weak AIC links. These aren't explicit in your notation. At most one of the candidates can be true.
Since you don't count those in other patterns, it wouldn't be consistent to count them here.

Marek

[denis_berthier]

After more thinking about it, it appears that not 2 but 3 CSP-Variables must be considered to prove the pattern: in terms of 2D-cells, not only rn-cell r1n9 and cn-cell c1n9 but also bn-cell b1n9.

Correct, you need all three.
However, in the pattern they're semantically different.
The first two are equivalent to strong AIC links or the variables you write in your notation. For the reasoning to be correct at least one of the candidates must be true.
The last one is equivalent to weak AIC links. These aren't explicit in your notation. At most one of the candidates can be true.
Since you don't count those in other patterns, it wouldn't be consistent to count them here.

I don't count strong or weak links. What I count is the number of CSP-Variables necessary to express the pattern.
In this case, there's no way of expressing the pattern without mentioning b1n9. If you don't agree with this, your job to find a way to do it.