The New Sudoku Players' Forum

[denis_berthier]

xNy is equivalent to rxcy; for example, 3N1=r3c1

Even now, I can't guess what the other symbols mean: 2R3, 3B2, 5c1... There's a total lack of consistency in this notation.

2R3=r3n2(L R)
3B2=b2n3(L R)
5C1=c1n5(L R)

OK, I see: when N is present in the notation, it is not present in the cell component; and when N is not present in the notation, it is present in the cell component. Absolutely great!
So, these 7 "Truths" {2R3 3N13 4N135 3B2} are Xsudo disguised way of writing the 7 CSP-Variables: r3n2 r3c1 r3c3 r4c1 r4c3 r4c5 b2n3
Now, the problem with this is, in order to find a possible correspondence with a whip, one would have to find the proper order of these CSP-Variables. There are 7! possibilities, which is much work to test.

I was nevertheless curious about size 7 and I tried if there was a 1-step solution using a braid[7] instead of a whip[8]. There is one indeed:
braid[7]: r3n2{c6 c5} - b2n3{r3c5 r2c5} - r4c5{n3 n7} - r3c1{n4 n5} - r3c3{n4 n9} - r4c1{n5 n8} - r4c3{n9 .} ==> r3c6 ≠ 4
and you can check that it uses the same 7 CSP-Variables, but in a totally different order.
So, my best guess is, Xsudo somehow finds something that does the same elimination as this braid. (Xsudo can't make any difference between a whip and a braid; it knows none of these patterns.)

[yzfwsf]

In fact, this solution path is not found by Xsudo, but found by my solver (Forcing Net). I just typed Xsudo to verify it, so that it can be compared with your solution.

BTW:I think the csp parameter of your original whip(8) does not seem to be consistent.The red part has no correlation with the neighboring nodes behind.
whip[8]: r3n2{c6 c5} - r3n3{c5 c2} - b2n3{r3c6 r2c5} - r4c5{n3 n7} - r5n7{c5 c2} - r8c2{n7 n8} - r7c2{n8 n4} - r1c2{n4 .} ==> r3c6 ≠ 4

[denis_berthier]

In fact, this solution path is not found by Xsudo, but found by my solver (Forcing Net). I just typed Xsudo to verify it, so that it can be compared with your solution.

There's no chance that a general Forcing net will find a braid[7]. If your "forcing nets" rely on the number of CSP-Variables instead of the number of "nodes", they are not "forcing nets" but a disguised form of braids or forcing braids.

BTW:I think the csp parameter of your original whip(8) does not seem to be consistent.The red part has no correlation with the neighboring nodes behind.
whip[8]: r3n2{c6 c5} - r3n3{c5 c2} - b2n3{r3c6 r2c5} - r4c5{n3 n7} - r5n7{c5 c2} - r8c2{n7 n8} - r7c2{n8 n4} - r1c2{n4 .} ==> r3c6 ≠ 4

Correlation means nothing in a whip. What means something is continuity. And the red part perfectly satisfies this condition.

[yzfwsf]

What means something is continuity.

Means no branch in path.

Please provide a picture instead of your whip(8), just like the introduction in the BUM chapter "A quick graphical introduction to the most basic chain rules" in CSP-Rule. I think your whip(8) has a branch, but there is no branch introduced in BUM.

[denis_berthier]

I think your whip(8) has a branch, but there is no branch introduced in BUM.

There's no branch.
There's just a z-candidate in r3n3, namely n3r3c6 (which is linked to target z=n4r3c6). z-candidates are not part of the whip.

[yzfwsf]

Does the z-candidate have to directly link the target (4r3c6) and the end point (r1c2)? Is there a z-cell (a cell directly links the target and the end point)?

[denis_berthier]

Does the z-candidate have to directly link the target (4r3c6) and the end point (r1c2)?

By definition, a z-candidate is a candidate linked to the target z. That's the only condition. If the target was True, any z-candidate would be False.

Is there a z-cell (a cell directly links the target and the end point)?

No. A cell linked to anything has no meaning. Only candidates are linked.

[yzfwsf]

I made this picture, but I still think there is a branch.

whip7.png (14.74 KiB) Viewed 447 times

[denis_berthier]

I'll suppose you're still talking of this whip[8]:

Code: Select all

whip[8]: r3n2{c6 c5} - r3n3{c5 c2} - b2n3{r3c6 r2c5} - r4c5{n3 n7} - r5n7{c5 c2} - r8c2{n7 n8} - r7c2{n8 n4} - r1c2{n4 .} ==> r3c6 ≠ 4

(You call your pic whip[7].)

I wonder why you write the two CSP-Variables r3n3 and b2n3 on the same column. As a result, you fail to write the link n3r3c2 — n3r3c6 and to see the continuous line between all the llcs and rlcs.
That's the problem with such representations that make no difference between the llcs and rlcs (which are part of the whip) and the other candidates (z- and t- candidates): everything gets confused and the main (linear, continuous) chain structure becomes hidden in a lot of useless details.
As you ay have noticed, I've changed the representation in the BUM, so that llcs and rlcs are in black but z- and t- candidates are in light grey

[yzfwsf]

Please provide a picture of the whip(8) for learning and reference, thank you.

[denis_berthier]

Please provide a picture of the whip(8) for learning and reference, thank you.

I have a much better idea for learning.
Modify your picture along the following lines:
1) put b2n3 in a separate column after the column for r3n3 (strictly following the whip order of the CSP-Variables);
2) add the link I mentioned above;
3) use larger size and bold for the llcs and rlcs than for the z- and t- candidates;
4) use thicker lines for the associated links (i.e. those that show continuity of the chain) (or dotted lines for the other links).


Now, if you meant a clean picture on the grid, that's very easy to do:
1) totally forget the z- and t- candidates;
2) draw the continuous line z-llc1-rlc1-llc2-rlc2....

[yzfwsf]

The CSP-Variables r3n2 and b3n3 are not directly related, but b3n3 is directly related to r3n2.

[denis_berthier]

The CSP-Variables r3n2 and b3n3 are not directly related.

CSP-Variables are not "related". This means nothing.
The only relations to consider are:
- a candidate C is a candidate for a CSP-Variable V
- 2 candidates C1 and C2 are linked.

b3n3 is never used in this whip.
If it's a typo and you meant r3n3 and b2n3, it's likely you failed to see the link : r3n3c2 - b2n3r3c6

[yzfwsf]

b3n3 is never used in this whip.
If it's a typo and you meant r3n3 and b2n3, it's likely you failed to see the link : r3n3c2 - b2n3r3c6

Yes, it is indeed a typo.
But I still don't understand that it is not a branch, but a continuous relationship. Please provide your own pictures to help me learn. Again, please provide pictures instead of text.

[denis_berthier]

b3n3 is never used in this whip.
If it's a typo and you meant r3n3 and b2n3, it's likely you failed to see the link : r3n3c2 - b2n3r3c6

Yes, it is indeed a typo.
But I still don't understand that it is not a branch, but a continuous relationship. Please provide your own pictures to help me learn. Again, please provide pictures instead of text.

The best way to learn is to do exercises. I've given you all the necessary tips allowing you to modify your own pic.
The reason why you don't see continuity seems to turn around the link: r3n3c2 - b2n3r3c6. So, the question is, do you see this link or not?