## Quantums

Advanced methods and approaches for solving Sudoku puzzles

### Re: Quantums

DonM wrote:

Adding to the thought behind Luke's comment above: IMO, the particularly attractive feature of these 'quantum' moves is ...

We've been expressing chains with AURs for some time without the need to call anything a 'quantum' anything, unless there's Type 3, of course. What exactly is 'quantum' about this move to you? ("Steve K says it is" does not count.)

Aside: I find it interesting, but not necessarily constructive, that the lingo has gone from 'quantum cell' to 'quantum set' to 'quantum move.'
ronk
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### Re: Quantums

Steve K,

no doubt that you are a brilliant solver and i like the 4 samples here very much.

But i really have a problem with all this notation (and naming) stuff. Maybe with the exception of loops, which are well presented in an AIC, it only makes things more complicated for others (at least for me).
I dont need any AALS, sis, QNT, Almost Hub spoke rim, almost rim or QNPx8, not even an ALS or AIC to explain these moves to others.
Deadly patterns and subsets are enough for all of them.

Here is may way for your last example:

Code: Select all
` *-----------------------------------------------------------------------------*  | 2579    29      1       | 6       245789  2479    | 3       58      45789   |  | 5679    4       78      | 58      5789    3       | 2       1      *56789   |  | 235679 *2369    378     | 1       245789  2479    | 56789   568     456789  |  |-------------------------+-------------------------+-------------------------|  | 1       5       6       | 2       789     79      | 78      4       3       |  | 234     23      9       | 3458    345678  467     | 1      ^568    ^5678    |  | 8       7       34      | 345     13456  ^146     | 56      9       2       |  |-------------------------+-------------------------+-------------------------|  |@34679  #1369    347     | 34     #1346    8       |@569     2      #1569    |  |@346    #1368    5       | 9      #12346  @1246    |@68      7      #168     |  |@69     #1689    2       | 7      #16      5       | 4       3      #1689    |  *-----------------------------------------------------------------------------* `

To avoid a deadly pattern 16 in r789c259, 1 or 6 must be elsewhere in boxes 789. So one of the following must be true:
r789c1=6, r8c7=16, r78c7=6
Now we have
r789c1=6 => r3c2=6 => r2c9=6 => r78c7=6
and
r78c7=6 => r5c89=6 => r68c6=16 (hidden pair)

I dont see any reason to invent even another new notation for this.
eleven

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### Re: Quantums

Steve K wrote:Perhaps the use of the term quantum is overstretched.

Steve, I hope you won't be disuaded from using the term. IMO, it reasonably fits and to change it and try to find another term or more than one label for the situations where you have used 'quantum' would just make things more confusing. In any event, IMO, a certain amount of license is allowed for labels used in a puzzle game & I vote for its continued use.
DonM
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### Re: Quantums

eleven wrote: To avoid a deadly pattern 16 in r789c259, 1 or 6 must be elsewhere in boxes 789. So one of the following must be true:
r789c1=6, r8c7=16, r78c7=6
Now we have
r789c1=6 => r3c2=6 => r2c9=6 => r78c7=6
and
r78c7=6 => r5c89=6 => r68c6=16 (hidden pair)

I dont see any reason to invent even another new notation for this...But i really have a problem with all this notation (and naming) stuff. Maybe with the exception of loops, which are well presented in an AIC, it only makes things more complicated for others (at least for me).

Eleven, you obviously have the clever ability to look at a puzzle and see some of these relationships quickly and you apparently prefer to present them as above over standard notation. And that probably works fairly well for this type of situation, but my guess is that it doesn't work so well for the more difficult puzzles ie. when it comes to transferring the info clearly to others.

In any event, many of us (most of us more likely) prefer to use notation because we believe it makes things less complicated and good notation (ie. that others can understand clearly) requires labels. Those who don't like notation and the labels that come with it don't have to use them.
DonM
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### Re: Quantums

I hope, that none of you wants to discourage newcomers to follow your deductions.

Now suppose, you dont know these notations yet and read following:

6) Note the AALS (4789)r1c46. Note the Almost Hub (47)r8c5, with two spokes (7)r82c5, (4)r83c5 => almost Hub spoke rim, with AALS r1c46 as almost rim. We can, equivalently (for the purpose of the elimination it is equivalent) note that we have the quantum ALS(x89)r1c46, whereas x is no more than one of, but possibly none of,(47). With the ALS(189)r2c89, and the newly stronger (8)r3, we have a Wwing with ALSâ€™s:

(9)r1c46 = (QNPx8)r1c46 â€“ (8)r3c46 = (8)r3c7 â€“ (8)r2c8 = (np19)r2c89 => r2c5, r1c78<>9, depth 7

=> (lc9)r1c46 => r3c456<>9

If you dont run away, you might try to find out, what it means. If you do so, you will spend days, just to get an idea, what is the logic behind.

But i am sure that many could understand this:
Code: Select all
` *-----------------------------------------------------------------------------*  | 1       678     567     |@489     2      @789     | 5689    489     3       |  | 789     378     4       | 5      #379     6       | 2      ^189    ^19      |  | 569     2       356     | 13489  #349     1389    |*5689    7       4569    |  |-------------------------+-------------------------+-------------------------|  | 3       1467    12567   | 129     569     129     | 1679    1249    8       |  | 268     9       1268    | 7       36      4       | 136     5       126     |  | 24567   1467    12567   | 12389   3569    12389   | 13679   12349   124679  |  |-------------------------+-------------------------+-------------------------|  | 267     167     9       | 236     8       2357    | 4       23      1257    |  | 2478    5       12378   | 2349   #3479    2379    | 1789    6       1279    |  | 24678   34678   23678   | 23469   1       23579   | 35789   2389    2579    |  *-----------------------------------------------------------------------------*`

In words:
In column 5 there are 2 strong links for 4 and 7 sharing r8c5. Since they cant both be in r8c5, one of r2c5=7 and r3c5=4 must be true (or both) and one of r1c4=4 and r1c6=7 must be false. This implies that one of the 2 cells r1c46 must be 8 or 9.
Now look at the case r1c46<>9. Then one of the cells must be 8, r3c46 cant be 8, r3c7=8, r2c8=19 and you have a pair 19 in r2c89.
So either r1c46 has a 9 or r2c89=19, in both cases r1c78 cant be 9 and you can eliminate them.

In a standard notation:
(1) (r2c5<>7 -> r8c5=7 -> r3c5=4) => (r2c5=7 or r3c5=4) => (r1c4 or r1c6)=89
(2) r1c46<>9 -> (1) (r1c4 or r1c6)=8 -> r3c46<>8 -> r3c7=8 -> r2c89=19
=> r1c78<>9

Not that i insist, that this always should be done. Basic AICs as standard notation are ok for me (hopefully there are good and clear explanations for it). But here we have a notation jungle, which takes you 100 times longer to understand than the logic behind the move (and i still dont know, what all that means above).
eleven

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### Re: Quantums

Steve
I would prefer to reserve the quantum label any pattern that depends on a derived inference (as you've said somewhere). So a quantum pattern would be one which couldn't be expressed within a linear elimination AIC. Thus of the first three examples here, only the first one would qualify and the last two wouldn't.

This keeps us in line with what happens when we set out on a Simple Colouring exercise and find an Xwing that we failed to spot earlier - it still stays an Xwing not a SC something. For the same reason I believe that there should be no such thing as a quantum method or move, and another term should be used for how you discover them.
David P Bird
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### Re: Quantums

One question to the notation guys. Did you understand that ?
(16)r8cc6 = (XWing6)[r5c9=r23c9r7c2 - r3c8 = r5c8 loop] - (6)r5c6

Or do i have to RTFM, before i may dare to ask that ?
eleven

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### Re: Quantums

ronk wrote: We've been expressing chains with AURs for some time without the need to call anything a 'quantum' anything, unless there's Type 3, of course. What exactly is 'quantum' about this move to you? ("Steve K says it is" does not count.)

Aside: I find it interesting, but not necessarily constructive, that the lingo has gone from 'quantum cell' to 'quantum set' to 'quantum move.'

Oh, I'm afraid I'm not about to answer your questions before you have answered mine. You devoted a sizable post to objecting to the use of the 'quantum' term without any substantive reference to a definition (as applied to sudoku) as the basis for the objection. Curiously, history seems to have something to do with it.

Steve has presented a number of constructs that he calls 'quantums' in his puzzles over the last few months in his blog and over at Eureka. Anyone who has looked at them closely can see a broad similarity that exists in them. One thing they have in common is that there isn't an existing term that can be applied to them and even though there may be some differences that exist among them, IMO, the term 'quantum' seems to work just fine. Rather than this being some sort of 'support for Steve K' as you would imply, I'm a syncophant for advanced solving methods & I'm actually more afraid that he is going to react by dumping the term and try to come up with more than one label where IMO one has sufficed.

However, what does this matter to you? You don't do any puzzle solving. I prefer the responses from those (such as eleven) who do, even if I don't totally agree with them. I repeat -coming into these threads devoted to practical solving subjects and making a stink over terminology, as almost a routine, unless grounded in objective substance having to do with things such as -will it interfere with understanding the construct/chain, does nothing but detract from the main objective of the thread. And, IMO, the fact that appreciation for the person having taken the time to start an interesting thread during a time when the forum is often 'dead' is practically never acknowledged only makes it worse.
DonM
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### Re: Quantums

eleven wrote:One question to the notation guys. Did you understand that ?
(16)r8cc6 = (XWing6)[r5c9=r23c9r7c2 - r3c8 = r5c8 loop] - (6)r5c6

Or do i have to RTFM, before i may dare to ask that ?

Don't feel like the lone stranger, I haven't figured it out yet either. Indeed, after your simpler presentation, there probably won't be another attempt.
ronk
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### Re: Quantums

DonM wrote:
ronk wrote: We've been expressing chains with AURs for some time without the need to call anything a 'quantum' anything, unless there's Type 3, of course. What exactly is 'quantum' about this move to you? ("Steve K says it is" does not count.)

Aside: I find it interesting, but not necessarily constructive, that the lingo has gone from 'quantum cell' to 'quantum set' to 'quantum move.'

DonM, I'm afraid you're being deliberately obtuse. In a variety of forms, you've only asked me for the definition of 'quantum' I'm using. I've already told you I'm using MadOverlord's original 2005 definition which you mentioned first, so you must have the link. If you search this forum for 'quantum' by user 'ronk', you'll see posts where I've used the term in the sense of that definition.
ronk
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### Re: Quantums

David P Bird wrote:I would prefer to reserve the quantum label any pattern that depends on a derived inference (as you've said somewhere). So a quantum pattern would be one which couldn't be expressed within a linear elimination AIC. Thus of the first three examples here, only the first one would qualify and the last two wouldn't.

Carcul has used impossible helping patterns (TILA). Isn't in the first example r1c46=47->r23c5<>47->r8c5=47 such a TILA? (Ron ?)
If thats correct, i ask, what would be the difference between quantum and TILA then ?

[Added]After reading the TILA explanation i guess, that Carcul would not have any problem to write this chain with TILA or ATILA, though i dont know, how he would formulate it exactly (and i am sure, that only a few would understand it).

So my opinion is, that the problem for both Carcul and Steve K is, that they were fixed to a notation (NL and AIC resp.), which is not able to express their brilliant ideas. So both always had to extend it, until it was totally unreadable for others.
eleven

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### Re: Quantums

Blind men should not post in forums. I have done this, and with the ancient spectacles I currently am wearing rather than ones that actually provide sight, I am farily certain that my post above is laden with errors. I have corrected the ones that I found. Hopefully some of the confusion is lessened.

One of the other deductions needs to be addressed:
Code: Select all
` *-----------------------------------------------------------------------------*   | 1       678     567     |*489     2      *789     | 5689    489     3       |  | 789     378     4       | 5       379     6       | 2       189     19      |  | 569     2       356     | 13489   349     1389    | 5689    7       4569    |  |-------------------------+-------------------------+-------------------------|   | 3       1467    12567   | 129     569     129     | 1679    1249    8       |  | 268     9       1268    | 7       36      4       | 136     5       126     |  | 24567   1467    12567   | 12389   3569    12389   | 13679   12349   124679  |  |-------------------------+-------------------------+-------------------------|   | 267     167     9       | 236     8       2357    | 4       23      1257    |  | 2478    5       12378   | 2349    3479    2379    | 1789    6       1279    |  | 24678   34678   23678   | 23469   1       23579   | 35789   2389    2579    |  *-----------------------------------------------------------------------------*  (9)r1c46 = (QNPx8)r1c46 - (8)r3c46 = (8)r3c7 - (8)r2c8 = (np19)r2c89 => r2c5, r1c78<>9`

That, by itself, is horrible. One needs to actively reference the two sis, (47)c5, specifically, (4)r3c5 = (4-7)r8c5 = (7)r2c5. If both (4)r3c5, (7)r2c5 saw an ALS involving (47), one would have a continuous loop known as a Hub, Rim, Spoke configuration. However, they see an AALS at r1c46. This AALS is effectively now an ALS concerning candidates (89), therefor (9=8)r1c46 is justified.
To rewrite the chain, perhaps someone can suggest how they would write it. Here is another attempt:
(9)r1c46 = [(NT478)r1c46r23c5, since (4)r3c5 = (4-7)r8c5 = (7)r2c5] - (8)r3c46 = (8)r3c7 - (8)r2c8 = (np19)r2c89 => r2c5, r1c78<>9

Eleven, you present me with a real problem. When, once, I posted AIC's and deductions without referring to past patterns, I was criticized for not recognizing they were part of the deduction. Now, I am criticized for including them. Truly, it makes little difference to me which presentation is preferred.

Nevertheless, I will submit that recognizing that these atypical groupings of almost patterns we already know is helpful in finding potential links to them. Of course, it takes some practice to do so. To condemn the entire idea without really understanding it is contempt before investigation. I do recognize that the errors above have not helped the situation one bit.

Finally, I am notoriously obscure in my ramblings, and for that I apologize. I shall attempt to be more clear, and post when I can see what I write.
Steve K

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### Re: Quantums

SK, as you may remember, I'm not terribly in favour of using derived inferences as for me they trivialise the moderately hard puzzles I pitch at, although I accept there is a place for them in solving monsters. Consequently I'm only vaguely familiar with your work in this area, and hope that this thread will help me get a better appreciation.

There's always two parts to the story when explaining a solution path - how the opening was found, and the Boolean logic that proves the deduction. Your ability to think in SIS patterns gives you an advantage in finding the opening and your explanations help readers to get an appreciation of your approach. However, when this approach quickly homes-in on a straightforward chain (as in examples 2 and 3 in the opening post) I believe that's how the proof should be presented. It seems you're trying to get the notation alone to do both these jobs but that's far too ambitious an aim.

eleven, with my limited knowledge on manipulating SIS deductions I canâ€™t make any fine judgements about the definitions of quantum patterns or how they relate to Carcul's deductions. The points I made were therefore far more general, which I hoped would help other contributors reach a consensus. This is not the place to start a debate on the differences between NL and Eureka notation styles.
David P Bird
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### Re: Quantums

Steve K wrote:(9)r1c46 = (QNPx8)r1c46 - (8)r3c46 = (8)r3c7 - (8)r2c8 = (np19)r2c89 => r2c5, r1c78<>9
...
One needs to actively reference the two sis, (47)c5, specifically, (4)r3c5 = (4-7)r8c5 = (7)r2c5. (4)r3c5, (7)r2c5 saw an ALS involving (47), one would have a continuous loop known as a Hub, Rim, Spoke configuration. However, they see an AALS at r1c46. This AALS is effectively now an ALS concerning candidates (89), therefor (9=8)r1c46 is justified.

Agreed, and it is analagous to a UR Type 3. Due to a weak link, two cells effectively contain the bivalue <89>, at least one of which must ultimately be true. The two cells 'behave' as a single cell, so r1c46 may IMO be properly referred to as a quantum cell. The result would be the same if r1c4 and r1c6 both contained <4789>, just as for a Type 3 UR.

Steve K wrote:To rewrite the chain, perhaps someone can suggest how they would write it. Here is another attempt:
(9)r1c46 = [(NT478)r1c46r23c5, since (4)r3c5 = (4-7)r8c5 = (7)r2c5] - (8)r3c46 = (8)r3c7 - (8)r2c8 = (np19)r2c89 => r2c5, r1c78<>9

A suggestion here is not so easy, but I sorta like David P Bird's method of showing the proof for a derived inference on a separate line.
David P Bird wrote:
1: (8|9=4)r1c4 - (4)r89c4 = (4-7)r8c5 = (7)r789c6 - (7=8|9)r1c6 => *[A] (8=9)r1c46
at least one of r1c4 and r1c6 must contain 8 or 9, so taken together these cells must contain at least one of these digits = derived inference [A].

2: (9=[A]=8)r1c46 - (8)r3c46 = (8)r3c7 - (8=19)AHS:r2c89 => r2c5, r1c78<>9
starts with the derived inference to build up the rest of the deduction.

It might be modified a bit to ...

1a: (8|9=4)r1c4 - (4)r89c4 = (4-7)r8c5 = (7)r789c6 - (7=8|9)r1c6 => (8=9)QC:r1c46
1b: (9=8)QC:r1c46 - (8)r3c46 = (8)r3c7 - (8=19)AHS:r2c89 => r2c5, r1c78<>9

... where 'QC' stands for [i]quantum cell.
ronk
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### Re: Quantums

eleven wrote:Carcul has used impossible helping patterns (TILA). Isn't in the first example r1c46=47->r23c5<>47->r8c5=47 such a TILA? (Ron ?)
If thats correct, i ask, what would be the difference between quantum and TILA then ?

[Added]After reading the TILA explanation i guess, that Carcul would not have any problem to write this chain with TILA or ATILA, though i dont know, how he would formulate it exactly (and i am sure, that only a few would understand it).

I don't believe there's a Two-Incompatible-Loop-Argument (TILA) here, at least not for this same deduction using the same inferences. If there were, asserting r1c78=9 would yield two discontinuous nice-loops yielding either 1) two contradictory eliminations, or 2) two contradictory placements or 3) a contradictory elimination and placement.

There aren't even two nice loops AFAICS. BTW Carcul may have been the only one to ever use TILA.

eleven wrote:So my opinion is, that the problem for both Carcul and Steve K is, that they were fixed to a notation (NL and AIC resp.), which is not able to express their brilliant ideas. So both always had to extend it, until it was totally unreadable for others.

I think there's another commonality. Both summarize a deduction in one expression but, as complexity increases, a single expression eventually becomes obfuscatory.
ronk
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