The New Sudoku Players' Forum

[eleven]

This was a bit much at once for me. To summarize my impression, we have
- Su de Coq (ev. extended)
- Doubly linked ALS
- Overlapping AHS's (MSHS - what does MS mean ?)
- Intersecting ANS's (MSNS)
- ALS loops

Now it seems to me (talking about 2 sets only):
All (but the loops) are base/cover examples.
A Dl-ALS can be expressed as ALS loop with the same eliminations.
Dl-ALS's are always in 2 lines of a band/stack, SDC/MSHS/MSNS in a line+box.
If so, you have 3*6 chances to find 2 lines for a DL-ALS, and 6*9 to find a box/line for the others, iow the effort to check 18 line pairs or 54 line/box pairs to find all of them.
A SDC (not extended) is an intersecting ANS.
There are DL-ALS eliminations, which cannot be expressed as SDC and vice versa.
Same for DL-ALS/MSHS, SDC/MSHS, MSHS/MSNS.

Methods for finding DL-ALS's and MSHS were described here by aran and David.
For finding SDC's check the line/box intersections, if they can be split into 2 disjoint ALS groups in the rest of the line and box resp. (the number of cells needed increases with each additional candidate).

Little is known about how common they are. But it seems, it's in the order SDC, DL-ALS, MSHS.

Please correct and comment.

[JC Van Hay]

An "homework" suggestion ... !?
Ask yourself :
1. Besides Locked Subsets, what are the simplest valid rank 0 logic in a puzzle ?
2. How is it possible to add SIS, one by one, to these patterns without changing the rank ?
3. What are the solutions of these patterns ?
4. Are there relations between these patterns ?

[DonM]

An "homework" suggestion ... !?
Ask yourself :
1. Besides Locked Subsets, what are the simplest rank 0 logic in a valid puzzle ?
2. How is it possible to add SIS, one by one, to these patterns without changing the rank ?
3. What are the solutions of these patterns ?
4. Are there relations between these patterns ?

And I would want to do that because....?

[eleven]

JC,
thanks for your nice questions.
[Added:] I don't understand no 3 . Does a pair have a solution ?
As to no 4, it coincides to mine in the post before. I do know, that there are relations, but i don't even have an exact definition for the 4 (or are there only 3 different) patterns.
So my question to you is:
What are the definitions of the above patterns and are my assumptions correct ?

[David P Bird]

I've been told before that my posts are difficult to understand so I'm sorry you haven't been able to follow me so far in this thread. However this summary is even terser!

I know the basic SdC pattern but I don't know it stops being a SdC when it gets extended. I therefore avoid the term.
Doubly Linked ALSs seem to cover most if not all of the various possibilities but I'm no expert on them and don't know if they are always contained in a single band of boxes.
However they cover a particular type of rank 0 pattern that can be represented by Multi-Sector Locked Sets.
These patterns can be expressed as truth and link sets – also known as base and cover sets.
They may also be translatable into AIC loops (when no digit will appear in more than two consecutive links).
As the basic SdC occupies one box and one line it is therefore a 2-sector naked set.
In this thread I've shown that the locked sets concerned can either be naked or hidden built up from overlapping (or intersecting) ANSs or AHS respectively in each sector.
For overlapping ANSs a hit happens when one of the digits that may be false in one ANS must be true in the other.
For overlapping AHSs a hit happens when one of the digits that isn't locked in one AHS is locked in the other.
Overlapping ANSs and AHSs can occur alone or both together

There are therefore 4 ways to find these patterns
a) look for a known SdC pattern
b) look for a doubly linked ANS loop
c) look for overlapping ANSs or AHSs that combine to give a MSLS
d) use a base and cover set approach

If you're good with AICs with embedded ANSs or AHSs sooner or later you should be able to find the same eliminations but perhaps by taking extra steps. This gives me the feeling that extending my approach to more than 2 sectors won't give me any new inferences.

[JC Van Hay]

JC,
thanks for your nice questions.
[Added:] I don't understand no 3 . Does a pair have a solution ?
As to no 4, it coincides to mine in the post before. I do know, that there are relations, but i don't even have an exact definition for the 4 (or are there only 3 different) patterns.
So my question to you is:
What are the definitions of the above patterns and are my assumptions correct ?

Before going into more details in this thread, I hope the following will help ...
I addressed myself these questions a few months ago in order to understand how to manually find multifishes.
I posted a partial synthesis with examples in the "Exotic patterns a resume" thread.
You will also find on the same page David P Bird's posts on the analysis of multifishes in terms of MSLS.

[eleven]

JC, it is not of big help, when instead of answering my questions you open a new chapter.
Multifish have not been a topic here so far. And i wonder, if it will be one ever for me, because - as i already told aran here - i don't even like to look for a swordfish (but i would make your fish elimination of today with an x-chain). Of course, if you have a method, how to spot multifish easily on paper, i would like to know it - in another thread or later.

[eleven]

I've been told before that my posts are difficult to understand so I'm sorry you haven't been able to follow me so far in this thread.

Oh, i am rather happy with what i could follow. Looking at this post i have the feeling, that i understood more of your patterns than you know about the others.

I know the basic SdC pattern but I don't know it stops being a SdC when it gets extended. I therefore avoid the term.

... and replace it by MSNS. This does it for you, but not for me, who is not interested to learn things twice, which are probably the same.

Doubly Linked ALSs seem to cover most if not all of the various possibilities but I'm no expert on them and don't know if they are always contained in a single band of boxes.

Yes, that's what i also (don't) know about them.

However they cover a particular type of rank 0 pattern that can be represented by Multi-Sector Locked Sets.

I have to admit, that i did not know, what rank 0 means, until aran wrote "rank = base-cover". So i did not miss much. Both a single and any grid are rank 0 patterns, and some sets between, fine.

These patterns can be expressed as truth and link sets – also known as base and cover sets.

So MSLS and base/cover are the same. Nice to know.

They may also be translatable into AIC loops (when no digit will appear in more than two consecutive links).

Ah yes, AIC's only see black or white.

As the basic SdC occupies one box and one line it is therefore a 2-sector naked set.

This does not change with the extensions described in the hodoku doc. So now i think, that 2SNS and SDC are simply the same. SDC sees it as 3 sets, 2SNS as two ?
[Edit:]This is probably a misunderstanding, because i guess that 2 sectors also can be 2 (parallel) lines. So now i see both DL-ALS and SDC's as subsets of 2SNS and conversely i don't believe, that there are other 2SNS, which are not covered by DL-ALS and SDC, so that we would have 2SNS=DL-ALS+SDC. Unfortunateley i will not get a confirmation by the experts, because the one does not know, what the other does.

In this thread I've shown that the locked sets concerned can either be naked or hidden built up from overlapping (or intersecting) ANSs or AHS respectively in each sector.
For overlapping ANSs a hit happens when one of the digits that may be false in one ANS must be true in the other.
For overlapping AHSs a hit happens when one of the digits that isn't locked in one AHS is locked in the other.

I had got that.

Overlapping ANSs and AHSs can occur alone or both together

So you confirm, that here are MSHS with no MSNS equivalent and vice versa. However, examples would be fine.

There are therefore 4 ways to find these patterns
a) look for a known SdC pattern
b) look for a doubly linked ANS loop
c) look for overlapping ANSs or AHSs that combine to give a MSLS
d) use a base and cover set approach

a)-c) are base and cover set approachs too, are'nt they ?

[aran]

Eleven on a couple of points
Just to be clear on "base/cover" :
Any sudoku construct can be expressed in base cover terms : what will change is the rank.
Example : take the AIC
xr1c1=xr9c1-xr9c9=xr9c2 => <x>r9c1
In base cover :
two truths in the base xr1 and xr9
but impossibe to cover with less than three truths, eg xc1+xc9+xc3 or xc1+xc9+xb7
So rank = cover - base = 3-2=1.
btw rank = cover-base (and not base-cover as I did write : changes nothing, just means rank is always a positive number)

All the "noblest" sudoku objects have rank 0
eg fish loops DL-ALS.
Put another way, anything that generates multiple eliminations is very likely a rank 0 object (not than rank 0 objects necessarily generate multiple eliminations)

Do DL-ALS occur in the same stacks or bands ?
No.
Construct the following hypothetical object (it looks "existable" but there may be some other consideration)
r1c1= abc r1c9 = pqr
r3c1 = abd r3c9 = pqrd
r5c1 = abce r5c9 = pqe
r7c1 = abc r7c9 = pqr
r8c1 = abcdex r8c9 = pqdey
r9c1 = abcdx r9c9 = pqdy
then it would appear that
r1357c1 = {abcde}
r1357c9 = {pqrde}
with dual links on d/e ie {abcde} {edpqr} => <abc>r89c1 <pq>r89c9 <d>r3c2..8 <e>r5c2..8

[eleven]

aran,

your example nicely shows, why i don't like A. Barkers vocabulary. It's more confusing than helpful for me. Truth, link, base, cover, it's never clear, what is what. So no surprise, that even you mixed the terms.
I can well understand the above patterns and there eliminations without thinking in these terms.

The nice it is to have aesthetical patterns with multiple eliminations, it also should be said, that these are mostly weak in regard to the progress in the puzzle (similar to cannibalistic uniqueness eliminations). This is inherent to them, because e.g. an x-wing elimination still leaves 2 digits in the x-wing line, while a kite elimination has chances in all 3 units to be the next to last digit.

Thanks for the sample with DL-ALS in different stacks. But i read out also, that a useful real world example is not known yet. So i will resign to look for them.

[aran]

i don't like A. Barkers vocabulary. It's more confusing than helpful for me. Truth, link, base, cover, it's never clear, what is what.

When the concept is understood, the jargon doesn't matter.
I regard Allan Barker's contribution as one of the finest, if not the finest, that I have encountered.

This is inherent to them, because e.g. an x-wing elimination still leaves 2 digits in the x-wing line

It's not what's left behind, it's what's eliminated...that is of interest...

[eleven]

I regard Allan Barker's contribution as one of the finest, if not the finest, that I have encountered.

Ok. You like it and i dont need it

I know that champagne could downrate a lot of puzzles based on this concept. But suppose, we would have searched for the hardest the other way round. Collecting the puzzles, which are hardest to solve with base/cover. Denis would have had a lot of fun to show, how relatively easy chains could crack top rated puzzles.
Also in my view contradiction is not something, which excludes beauty or elegancy. Just think of Gödel’s Incompleteness Theorem (the #1 mathematical discovery of the 20th century).

[David P Bird]

Eleven, from your reactions it's clear that I've failed to live up to your expectations and have wasted your time telling you things you didn't want to know. I apologise for that, but I hope you understand that when you asked your questions it confused me. I'll endeavour not to do it again.

[eleven]

I am sorry for that. I have learned a lot from you. Please forgive me to demand more. Guess i should be quiet, until this fever is gone.

[David P Bird]

Aran, thanks for your hypothetical dual linked ANSs in 2 columns with 2 RCCs weakly linked in different rows. Looking at it, it seems that of necessity each RCC can only occur once in each ANS. This means that each ANS can be reduced to 3 smaller ones by removing the cells containing them either individually or together. There will therefore be 16 choices of ANSs that can be used in AIC constructions to give a variety of paths that will probably pick off the eliminations available from the pattern one by one. I would therefore guess that unless a search for one is made very early on, it's very unlikely that such a pattern would survive long enough to be recognisable.

Here's a stripped down version that looks feasible in a puzzle:

Code: Select all

|---------|-------|---------|
| p1  . . | . . . | . . x1  |   RCCs = 1 & 2
| pq  . . | . . . | . . y12 |   
| 6   . . | . . . | . . 7   |   p = 3 and/or 4   (1234)ANS:r149c1
|---------|-------|---------|   q = 5 and/or 7   (57+1234)AHS:r267c1
| p   . . | . . . | . . 8   |   
| 9   . . | . . . | . . xy  |   x = 4 and/or 5   (1245)ANS:r169c9
| pq  . . | . . . | . . x   |   y = 6 and/or 9   (69+1245)AHS:r258c9
|---------|-------|---------|
| q12 . . | . . . | . . 3   |
| 8   . . | . . . | . . xy  |
| p2  . . | . . . | . . x2  |
|---------|-------|---------|

(134=234)r1c9c1 – (245=145)r169c9 – Loop => r26c1> 34, r58c9 <> 45, r1c2345678 <> 1, r9c2345678 <> 2

MSNS:(1)r1,(2)r9,(34)c1,(45)c9: 6 digits/constrained cells

The other possible ANSs in c1 are (34)r4c1, (134)r14c1, & (234)r49c1

[Edit] (12) added back to r7c1 & r2c9 - mistakenly deleted earlier.

Eleven, if your fever has died down by now, classifying all 4 methods of looking for these locked sets 'base and cover approaches' is somewhat misleading. If you like, the first 3 look for symptoms that will diagnose the condition without needing to X-ray the patient which is the 4th choice.