The New Sudoku Players' Forum

by **sultan vinegar** » Fri May 29, 2015 11:54 am

Eleven,

I couldn't agree more. The problem with those 'quanta' is that there is no rigorous definition of the pattern. If it was defined and suitably notated then those eliminations would be no harder to understand than an ALS elimination.

DPB,

Sure, we're on the same page as far as avoiding over-egging the pudding! I was just illustrating some different methods for daj who didn't understand the original solution. Not everyone learns the same way. As for your solution:

Using #n: (9=478#2)r1c46 - (48)r3c46 = (8)r3c7 - (8=19)r2c89 => r1c78,r2c5 <> 9.

I'm struggling with the (48)r3c46 = (8)r3c7 link, both from left to right and from right to left. I'm sure you need to take into consideration the constraints due to column 5 somehow?

As for CoALS, if it's such a useful way to find MSLS then why wouldn't you notate your solution with a CoALS link if it exists so that the reader too can learn to find the MSLS as you did?

As for quanta, given your proficiency with the #n notation I can see why you think that quanta are superfluous. It doesn't help that Steve K's examples often have branching further up the net, even though the quantum link may be OK. I guess I've only fully understood the #n notation in the last week or so; I was using it incorrectly for a while. But to me the quantum idea seems so intuitive; a specific pattern to recognise that you can just eye-ball, rather than trawling through on a case by case basis trying to make the #n count add up.

by **David P Bird** » Fri May 29, 2015 1:31 pm

sultan vinegar wrote:Using #n: (9=478#2)r1c46 - (48)r3c46 = (8)r3c7 - (8=19)r2c89 => r1c78,r2c5 <> 9.

I'm struggling with the (48)r3c46 = (8)r3c7 link, both from left to right and from right to left. I'm sure you need to take into consideration the constraints due to column 5 somehow?

You're right, it's unsound. I just quickly translated Luke's notation which has an error in it.
He wrote (9)r1c46 = (QNPx8)r1c46
I took this to mean (9)r1c46 and (8x)r1c46 can't both be false where x = 4 or 7, however (47)r1c46 makes both arguments false.
In my haste I thought I'd fixed it but I just moved the problem to the next strong link.

On re-checking that thread I found I had already tackled the problem - see <my post of Fri Aug 20, 2010 5:23 pm>

by **blue** » Fri May 29, 2015 4:38 pm

sultan vinegar wrote:Eleven,

I couldn't agree more. The problem with those 'quanta' is that there is no rigorous definition of the pattern. If it was defined and suitably notated then those eliminations would be no harder to understand than an ALS elimination.

DPB,

(...)

But to me the quantum idea seems so intuitive; a specific pattern to recognise that you can just eye-ball, rather than trawling through on a case by case basis trying to make the #n count add up.

You seem to be contradicting yourself.
I think there's an elimination to be had

Probably it's the idea that "quantum <XYZ>" has any particular meaning, other than that it's referring to something that (for varying and typically unspecified reasons, and in the context in which it is offered) "functions just like an actual <XYZ>".

P.S.: Sorry, I'm tired and I was trying to be funny

In all earnestness though, I think the reason that there hasn't been a "rigorous definition", has everything to do with the "varying [and typically unspecified] reasons" part of my last remark.

by **ronk** » Fri May 29, 2015 5:34 pm

blue wrote:Probably it's the idea that "quantum <XYZ>" has any particular meaning, other than that it's referring to something that (for varying and typically unspecified reasons) "functions just like an actual <XYZ>".

That's true. In the puzzle under discussion and once the effect of weak link (4)r1c4-(7)r1c6 (2nd image) is accounted for, (8=9)r1c46 functions like a bivalued single cell. So consistent with the definition by madOverlord in 2005, r1c46 is a bivalued quantum cell ultimately holding a quantum single.

sultan vinegar wrote:]7 Truths = {8R3 47C5 1N46 2N89}
10 Links = {1r2 9r12 8n5 4789b2 89b3}
3 Eliminations --> r1c78<>9, r2c5<>9

Xsudo tends to overstate the links and eliminations for a single "move" The 1-rank logic set is:

7 Truths = {8R3 47C5 1N46 2N89}
8 Links = {9r1 8n5 478b2 189b3}
2 Eliminations --> r1c78<>9
when techniques are revealed such as locked candidates, locked subsets, etc. I was wrong in thinking locked candidates were involved here.

by **blue** » Fri May 29, 2015 6:56 pm

ronk wrote:
blue wrote:Probably it's the idea that "quantum <XYZ>" has any particular meaning, other than that it's referring to something that (for varying and typically unspecified reasons) "functions just like an actual <XYZ>".

That's true. (...)

Thanks ronk,

In case someone else quotes that bit, I'm about to add a qualifier to "(for varying and typically unspecified reasons)".

BTW: Nice take on the connection with MadOverlord's definition !

by **sultan vinegar** » Sat May 30, 2015 3:08 am

ronk wrote:Xsudo tends to overstate the links and eliminations for a single "move"

Sure. I contemplated doing that but then I feared someone would complain about the other elimination being missing. Of course all that's going on is that the ends of my chain are structurally the same as a simple skyscraper, and as you say, its a two-step "move".

blue wrote:You seem to be contradicting yourself.
I think there's an elimination to be had

Nice joke! But damn right there's eliminations to be had with these quanta. Hence a first draft of the quantum guide below. Once we've ironed out the kinks as a group then I'll get a 'clean' version of it moved to a new thread in Advanced Solving Techniques. It isn't meant to be a complete list yet, but someone's just got to start somewhere!

Edited following feedback received up to Don M's post

The Draft Ultimate Quantum Guide

A quantum locked set is an almost locked set that due to some derived inference functions as though it is a locked set. As with locked sets they may be used in alternating inference chains. The derived inference may take any form in theory. Examples of derived inferences used in this guide include the almost unique rectangle (AUR) and the almost hidden set (AHS). Credits to <MadOverlord>, <ronk>, and <Steve K>, for the various discoveries and <blue> for the suggested definition.

Selection of examples:

1. Quantum Naked Triple (QNT) from an AUR.

Hidden Text: Show

2. Quantum Naked Pair (QNP) from an AUR.

Hidden Text: Show

3. Quantum Naked Single (QNS) from an AUR. The quantum notation is superfluous here because the end result is just a grouped link for a single candidate.

Hidden Text: Show

4. Almost Quantum Naked Pair (QNP) from an AUR. This shows how to use an almost QNP in a chain.

Hidden Text: Show

5. Naked Pair from an AUR. This example clarifies the difference between a standard naked pair and a quantum naked pair. A naked pair is two candidates locked in two cells. A quantum naked pair is two candidates locked in three cells.

Hidden Text: Show

6. Quantum Naked Pair from an AHS. Conceptual example only.

Hidden Text: Show

7. Quantum Naked Single from an AHS. Compare with examples 3 and 6.

Hidden Text: Show

8. Quantum Naked Pair from an AAHS.

Hidden Text: Show

by **daj95376** » Sat May 30, 2015 10:30 am

[Withdrawn: SV's post has changed and my comments are now irrelevant.]

_

by **ronk** » Sat May 30, 2015 3:02 pm

sultan vinegar wrote:
ronk wrote:Xsudo tends to overstate the links and eliminations for a single "move"
.. all that's going on is that the ends of my chain are structurally the same as a simple skyscraper ...

You're right. I hastily and erroneously thought locked candidates were involved. :oops:

Post edited.

by **David P Bird** » Sun May 31, 2015 12:10 am

SV, as I declared in my rant I'd like to dispose of the quantum term altogether as the process is one of identifying derived inferences. However I can appreciate that having found a derived inference the effect is to produce a quantum object such as a 'quantum naked pair' or a 'quantum bi-value' as in your first two cases which may be of help to players when considering their options.

However just as there are a large number of chains that will produce an elimination there are a large number of ways quantum objects can arise but which generally will recur infrequently. We don't try to categorise and name every chain configuration, only the short commonly recurring ones. I therefore feel that your approach of trying to categorise the different ways quantum objects can be produced is going in the wrong direction – no-one would be able remember them all.

The essence of SK's thinking was to check for strong inference sets that might overlap or otherwise interact through a connecting structure to provide a derived inference and somehow that should be a condition to be satisfied. The product is then an envelope of cells containing that inference which can be called the quantum object. Otherwise we'll find players calling every almost pattern they find a quantum something or other.

We have a very adequate way of notating AICs which players should be familiar with before they want to progress to more advanced techniques. Admittedly some will have made every mistake possible in the process and others will suffer from AIC dyslexia, but ask yourself would they be any the better for it with your prototype quantum notations – I think not.

Three people, Eleven, Blue, and myself, have made similar points about using standard notations to declare the discovery of a quantum object and you yourself agreed that we should avoid over-egging the pudding but now you've gone in completely the opposite direction!

Personally I'd prefer it if you devoted your talents in other areas, but if you're bent on quantum matters then I'd suggest a change of overall approach, perhaps by tabulating the possible sources of strong inference sets that can interact. For example your first case is an AUR and an AALS that overlap, and perhaps that’s top of the list of those that could be named.

DPB

by **DonM** » Sun May 31, 2015 2:18 am

David P Bird wrote:...However just as there are a large number of chains that will produce an elimination there are a large number of ways quantum objects can arise but which generally will recur infrequently. We don't try to categorise and name every chain configuration, only the short commonly recurring ones. I therefore feel that your approach of trying to categorise the different ways quantum objects can be produced is going in the wrong direction – no-one would be able remember them all.

Fwiw: I agree. Perhaps there is some interest value in seeing which categories of derived inferences allow for notating a 'quantum', but in the end it might create more confusion ie. a newer solver might think that it was necessary to learn all the listed categories.

The essence of SK's thinking was to check for strong inference sets that might overlap or otherwise interact through a connecting structure to provide a derived inference and somehow that should be a condition to be satisfied. The product is then an envelope of cells containing that inference which can be called the quantum object.

When it comes to how SK introduced and used 'the concept of a quantum', that's about as good a description one could come up with. I've never understood why you are against the use of the term. It's really nothing more than a way of notating something that would, otherwise, be too cumbersome to describe. You state the SIS/derived inference and then you have an 'effective', 'quasi', 'virtual', 'quantum' this or that pattern. The reason it was picked up and used by advanced solvers after SK used it as he did was because it was so intuitive and useful.

by **sultan vinegar** » Sun May 31, 2015 3:08 am

Guide edited following feedback. More comments good and bad are welcome.

DonM wrote:Perhaps there is some interest value in seeing which categories of derived inferences allow for notating a 'quantum', ... The reason it was picked up and used by advanced solvers after SK used it as he did was because it was so intuitive and useful.

Hopefully the guide will reflect these excellent points.

by **David P Bird** » Sun May 31, 2015 11:10 am

DonM wrote:I've never understood why you are against the use of the term. It's really nothing more than a way of notating something that would, otherwise, be too cumbersome to describe. You state the SIS/derived inference and then you have an 'effective', 'quasi', 'virtual', 'quantum' this or that pattern. The reason it was picked up and used by advanced solvers after SK used it as he did was because it was so intuitive and useful.

To expand further on my previous rant:

1) People have been using differing personal interpretations of a badly defined term without a proper source reference causing confusion. Just look how of often steps using quantum objects are questioned in the forum and the recent spat over the MadOverlord and SK versions.

2) Inferences from quantum nodes are often inserted into chains without any previous mention. This requires the reader to validate that they are sound for themselves which is not the purpose of a notation.

3) There are three categories of derived inferences represented by a quantum node:

Just citing the quantum node therefore can conceal which of these categories is involved.

4) I'm opposed to introducing unnecessary arcane terms as they make our threads virtually inaccessible to tyros and improvers. A quantum node is simply a container for a derived inference, a more intuitive term which a newcomer could take in in passing without needing to refer to a definition. Of the alternative options you list I find 'virtual' to be the most descriptive (and now might be a good time to adopt that as a better name).

These objections would go if quantum nodes were as common as say XYWings but, as they are relatively rare, when they are encountered many readers will be either unaware of them or only have vague recollections of what they are.

DPB

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