The New Sudoku Players' Forum

[David P Bird]

**** RANT ALERT ****

I'm not a fan of quantum patterns as they tend to introduce confusion rather than clarity when they are used.

My take on quantums is that they allow patterns to be recognised and used that are local to the current puzzle and aren't common enough to warrant a name. However they may however contain named sub-patterns. Their role should be to make the balance of the solution easier to notate and comprehend.

They produce a derived inference that's available in the current puzzle (a term I prefer).

When a quantum pattern is identified it should be notated and declared. For example if it can be expressed as an AIC:
(a)r1c1 = ................ = (bc)r9c78 => quantum/derived inference [A]
Now (a)r1c2 =[A]= (bc)r9c78 can be used in any subsequent step.

Generally that will only be worthwhile if the inference will be used more than once or if it illustrates a logical construct that can be adapted to similar situations (which should be described).

If the aim is to find a linear solution to a puzzle then using a quantum inference that requires branching will clearly downgrade the solution.

Our aim should be to simplify rather than complicate our notations.

**** OVER & OUT ****

[sultan vinegar]

Hi Don,

Of course we disagree; we are using different definitions! I am using the definition from 21 October 2005, as defined <here>. You are using Steve K's definition from 8 August 2009 (almost four years later), as defined <here>. Which one is right? Everyone is entitled to their own point of view, so we are both right. My point of view is that Steve K's definition is four years late, and from your own words, he wasn't even happy with the term because it didn't have the support of the sudoku community! If you'd just call it 'quasi' as you suggested instead of 'quantum' then we'd be on the same page.

For a start, let's make something clear: Steve K introduced the use of the term 'quantum' so essentially telling Steve himself that what he's using is not a quantum is a little presumptuous. He actually did define the term if you read his quantum-related blogs and if you could have read his posts on the Eureka forum on the subject, the latter of which are no longer available.

The above links prove that Steve K did not introduce the term 'quantum'; it was introduced by MadOverlord almost four years before Steve K's blog entry. I'm not telling Steve K himself that he is wrong; I'm telling you that some of Steve K's quantum examples do not comply with the original definition. Of course, they do comply with Steve's definition.

Saying that "2 Sep: (QNT147)bfg2 is three cells for three candidates so not a quantum." is a gross oversimplification since the QNT147 construct is not simply a question of 3 cells and 3 candidates. The 3 cells containing 147 only have potential value as a NT because of two almost hidden pairs and even then, require an almost-Kite to allow for an elimination. I could go through the same general process discussing your dismissal of the therm quantum in the Aug 10 example, but life is too short.

Again, what I say is consistent with the original definition, just as what you say is consistent with Steve's definition, apart from your mention of the almost-Kite which occurs later in the net and is nothing to do with the quasi.

Also, I'm not sure what is served by pointing out that some of Steve's quantum-based solutions could have been solved or interpreted another way. I'm sure he would have admitted so himself. What he was doing was trying to educate solvers on what, at the time, was a new concept. He wasn't trying to prove that those constructs were the only way to arrive at a solution. (Also, please see my paragraph 2 above.)

I actually said that:

but I agree that a quantum interpretation is valid (and simpler) for these.

So I'm not sure what your point is with that one? How am I meant to show that the technique is worthwhile if I can't compare it with an alternate technique?


DPB,

Fair enough rant, but I'm sure that you could replicate a quantum type 3 AUR link with your #notation, and I'm sure you could replicate my full chain from the Aug 8 quantum example with your #notation. These 2 patterns warrant a name in my opinion.

[DonM]

Hi Don,

Of course we disagree; we are using different definitions! I am using the definition from 21 October 2005, as defined <here>. You are using Steve K's definition from 8 August 2009 (almost four years later), as defined <here>. Which one is right? Everyone is entitled to their own point of view, so we are both right. My point of view is that Steve K's definition is four years late, and from your own words, he wasn't even happy with the term because it didn't have the support of the sudoku community! If you'd just call it 'quasi' as you suggested instead of 'quantum' then we'd be on the same page.


The above links prove that Steve K did not introduce the term 'quantum'; it was introduced by MadOverlord almost four years before Steve K's blog entry. I'm not telling Steve K himself that he is wrong; I'm telling you that some of Steve K's quantum examples do not comply with the original definition. Of course, they do comply with Steve's definition.

Well, no. I'm afraid you were wrong because you proclaimed that both those examples provided by JC Hay were not quantums. You didn't say 'They are not quantums based on a 2005 definition by MadOverlord'. (In fact, I couldn't see anywhere above that you made it clear you were relying on MadOverlord's definition from the outset of your post(s) on the subject- my apologies if I missed it.) Since, you (above) apparently do acknowledge Steve's definition, that would mean that those examples were actually quantums.

But on the subject of which definition of 'quantum' is the accepted one in manual solving:
You are now only the 2nd person (the first was ronk) on the entire planet to raise the issue of MadOverlord's first use of the term 'quantum' in 2005. MadOverlord's use of the term 'quantum' was a one-time event. After that mention, he didn't follow up in the days and weeks thereafter with solutions using the term, nor did anyone else. From that initial mention in 2005 until Steve introduced his use of the term in 2009 there was NO mention, or use, of the term 'quantum'. I repeat: No one ever provided a solution using the term 'quantum' until Steve K did in 2009!

On the other hand, after Steve K first introduced it in 2009, it was picked up and used by myself and several others in the Eureka forum. It was also the subject of a 'Quantums' thread that lasted several weeks on this forum in mid-2009 and it has been used in many solutions here. It was used by both Steve K and ttt in the solving of some very advanced puzzles (ER >9.0) after mid 2009.

So, which definition is the one that is accepted: The one that was never used in practice in 2005 or even mentioned thereafter or the one that was used in advanced manual solving over a period of years after early-mid 2009?

Btw: I suspect that you have posted under another handle in the sudoku past. If so, what might that be?

[daj95376]

I've yet to see a winner when people argue semantics on a definition. However, I do have a question/observation on the first SteveK example in Luke's thread on Quantums. Here is the (edited) grid and its use of "quantum". Unfortunately, the referenced SteveK post isn't available.

Code: Select all

 *-----------------------------------------------------------------------------*
 | 1       678     567     |*489     2      *789     | 5689    489     3       |
 | 789     378     4       | 5      #39+7    6       | 2       189     19      |
 | 569     2       356     | 13489  #39+4    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   #39+47   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


Now, the QNP(x8) apparently claims that the absence of <9> forces the presence of <8> in r1c46. How?

If <9> is missing from r1c46, then the possible combinations become: <47>, <48>, and <87>. However, <47> is invalid in r1c46 because of the chain:

Code: Select all

(4)r1c4 - (4)r3c5 = (4-7)r8c5 = (7)r2c5 - (7)r1c6


This leaves <48> and <87> as the only possible combinations in r1c46. Is it possible that SteveK used similar logic?

_

[DonM]

I've yet to see a winner when people argue semantics on a definition.

This isn't an argument over 'semantics on a definition'. It's nothing more than pointing out the obvious: One definition was accepted by its use in practical solving over a period of years; the other wasn't...at all.

[blue]

Now, the QNP(x8) apparently claims that the absence of <9> forces the presence of <8> in r1c46. How?

If <9> is missing from r1c46, then the possible combinations become: <47>, <48>, and <87>. However, <47> is invalid in r1c46 because of the chain:

Code: Select all

(4)r1c4 - (4)r3c5 = (4-7)r8c5 = (7)r2c5 - (7)r1c6


This leaves <48> and <87> as the only possible combinations in r1c46. Is it possible that SteveK used similar logic?

Almost certainly, I would think.
It's not that I have any idea what he actually did, just that it seems like there aren't any other options.

P.S.: I would agree with David, that at the very least, the derived weak link [ 4r1c4 - 7r1c6 ] should be displayed as part of the solution, along with some kind of note indicating its connection with the QNP (or QANP).

[daj95376]

Thanks blue. I was tempted to write:

Code: Select all

(9)r1c46 = [(8=4)r1c4 - (4)r3c5 = (4-7)r8c5 = (7)r2c5 - (7=8)r1c6] ...


But I was afraid that others might consider it an alternative instead of being an expansion of SteveK's QNP() logic.

_

[blue]

I was tempted to write:

Code: Select all

(9)r1c46 = [(8=4)r1c4 - (4)r3c5 = (4-7)r8c5 = (7)r2c5 - (7=8)r1c6] ...


I like it ... JC's style
I don't know what David thinks.

I should apoligize in advance, for coming late, to the conversation, and not reviewing the entire thing.
[ I saw that DonM referenced a couple of JC's solutions, and I haven't tried to find them ].

[sultan vinegar]

What term do you propose I use for the MadOverlord Quantum then Don?

I do have a question/observation on the first SteveK example in Luke's thread on Quantums.

Below is my interpretation of how Steve K came to call this a quantum:

Start with the almost multi-sector locked set:

Sector 1: (4789)r1c46
Sector 2: (345679)r23456c5

Together, these two sectors form an almost multi-sector locked set, because there are 7 cells, but at most 8 possible candidates (note that candidate 9 needs to be counted twice because it might occur in sector 1 and sector 2). I don't know how to notate this, but something like: (9r1c46=8r1c46)AMSLS(34567899)r1c46r23456c5 - (8)r3c7 ...



10 Truths = {8R3 1N4 23456N5 1N6 2N8 2N9}
13 Links = {1r2 9r12 3569c5 4789b2 89b3}
3 Eliminations --> r1c78<>9, r2c5<>9.

Now what I think Steve has done is write sector 2 in hidden form rather than locked form, i.e. AHS47r238c5. So we now have an almost multi-sector set with one sector in locked form and one sector in hidden form, i.e. an almost 'hybrid' or 'atypical' or 'quasi' set. I have absolutely no idea how to notate that!



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

[sultan vinegar]

You can also do this with MJs CoALS from 21 Sep 2006 (or is that technique void now too because MJ hasn't followed up with solutions using the term in that thread since 2006?)

Code: Select all

*-----------------------------------------------------------------------------*
 | 1       678     567     | 489A     2      789A    | 5689    489     3       |
 | 789     378     4       | 5      379AB    6       | 2       189     19      |
 | 569     2       356     | 13489  349AB    1389    | 5689    7       4569    |
 |-------------------------+-------------------------+-------------------------|
 | 3       1467    12567   | 129     569B    129     | 1679    1249    8       |
 | 268     9       1268    | 7       36B     4       | 136     5       126     |
 | 24567   1467    12567   | 12389   3569B   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    |
 *-----------------------------------------------------------------------------*

Digits in overlap cells: 3,4,7,9
Digits not in overlap cells: 5,6,8

(3479=568)CoALSr1c46|r23456c5 - (8)r46c3 = (8)r3c7 - (8=19)ALSr2c89 => r1c78 <> 9, r2c5 <> 9.

[daj95376]

Thanks SV. I was afraid that it was something that I might understand and then try to implement. Something like:

Code: Select all

Legend:  a+b  -->  both are true/false in context


(8+9=4+7)r1c46 - [(4)r3c5,(7)r2c5] = (4+7)r8c5; contradiction  =>  (9=8)r1c46


_

[DonM]

You can also do this with MJs CoALS from 21 Sep 2006 (or is that technique void now too because MJ hasn't followed up with solutions using the term in that thread since 2006?)

Ignoring for the moment that the comment in brackets sidesteps the fact that the two situations are apples and oranges, Myth's CoALS thread was among many of his that I saved and it had some influence in my including the ALSs that have overlap in the Simple Sudoku graphics #5 and #8 (from the top) here:
http://forum.enjoysudoku.com/advanced-als-chains-a-tutorial-asi-3b-t30098.html

[eleven]

In my opinion Steve was great in spotting and combining (grouped) implications, but not in notation and terminology.

When i looked at the samples from Aug 8 and 10, then they were not hard to understand from the SIS and links he listed, but i never would have found the eliminations from his final notation alone.
So i prefer a description in words to any notation here, e.g. this way.

For Aug 10:
He shows that either there is a pair 16 in r6c56, which implies a pair 16 in r69c5, or a pair 16 in r8c6,r9c5.
The MUG gives the SIS {6r3c2,r8c6,6r78c7} (great spot!), with the implication 6r6c7=>6r8c6 (because 6r6c7 kills both 6r3c2 and 6r78c7).
That's it: if there is no pair in r6c56, then 6r6c7 => 6r8c6 and 1r9c5

Similar for Aug 8:
Here there is either a pair 57 in r4c78 (implying a pair 57r49c8) or a pair 57r59c8.
If r4c78 is not 57, then either 5 is outside and must be in r5c8, or 7 goes to r4c3, again implying 5r5c8, which gives the pair with r5c9.

In the grid, Danny posted above, it is obvious, that either r2c5=7 or r3c5=4 (both with strong links in c5 and a common cell). So not both can be in r1c46, leaving 89 in one of the cells.

Often notations makes things more complicated than they are.

[sultan vinegar]

Actually, on second reading I'm not sure if MJ would approve of my CoALS elimination because of the two separate instances of digit 9. The elimination is still valid but it doesn't fit the pattern as defined by MJ. The combined structure is seven digits in seven cells but it is not locked because digit 9 can occur at most twice. I should have labelled them 9a and 9b. This represents an extension of MJ's definition.

[David P Bird]

SV It's mentally stimulating to explore alternative search methods such as quantums and CoALS to find eliminations but we should avoid over-egging the pudding in inventing new ways to notate them when simpler methods exist. I consider it's far more informative to briefly describe the discovery method separately although DonM has different views.

The analogy I used in the quantums thread still applies; using colouring if we fall on an XWing that we failed to spot earlier we don't then call it a colouring deduction.

Your quantum example:

Code: Select all

 *-----------------------*-----------------------*-----------------------*
 | <1>    678    5678    | 489a   <2>    789a    | 5689   489    <3>     |
 | 789    378    <4>     | <5>    379    <6>     | <2>    189d   19d     |
 | 569    <2>    356     | 13489b 349    1389b   | 5689c  <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    1367   <9>     | 236    <8>    2357    | <4>    123    1257    |
 | 2478   <5>    12378   | 2349   3479   2379    | 13789  <6>    1279    |
 | 24678  34678  23678   | 23469  <1>    23579   | 35789  2389   2579    |
 *-----------------------*-----------------------*-----------------------*

<Lukes notation> : (9)r1c46 = (QNPx8)r1c46 - (8)r3c46 = (8)r3c7 - (8)r2c8 = (np19)r2c89 => r2c5, r1c78<>9

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

To spell out the first weak link in words; two digits from (478)r1c46 and both digits in (48)r3c46 can't be simultaneously true.
[Edit Sorry this is flawed - see my next post]

Looking for CoALS patterns is a way to find Multi-Sector Locked Sets which can be expressed as AIC chains or nets.

Code: Select all

 *--------------------------*--------------------------*--------------------------*
 | 3569    5689    68       | 79      <2>     1379     | 369     <4>     15679    |
 | 359     <7>     24       | 489     1348    <6>      | 2389    1235    1259     |
 | 369     <1>     24       | <5>     3478    34789    | 23689   2367    2679     |
 *--------------------------*--------------------------*--------------------------*
 | <2>     356     <7>      | 49c     1456    149      | 3469    <8>     14569    |
 | 156     568     168      | <3>     4568b   2489bd   | <7>     256     24569ae  |
 | <4>     3568    <9>      | 278     15678   1278     | 236     12356   1256     |
 *--------------------------*--------------------------*--------------------------*
 | 79      249     <5>      | <6>     478     2478     | <1>     29      <3>      |
 | <8>     26      <3>      | <1>     <9>     <5>      | 246     267     2467     |
 | 1679    2469    16       | 247     347     2347     | <5>     269     <8>      |
 *--------------------------*--------------------------*--------------------------*

The AIC is (4)r5c9 = (4)r5c56 - (4=9)r4c4 - (9)r5c6 = (9)r5c9 - Loop => r4c56 <> 4, r4c6 <> 9, r5c9 <> 256

The MSLS is MS-HS:(49)r5,(25678)b5 (7 candidates/cells) => Elims:14r4c5, 256r5c9, 1r6c5, 1r6c6

Follow-on eliminations produce the same end result.

<Harvard's original notation> was
A{[r5c125]-56-[r5c1235](56|18|4)-4-[r5c5]} -4- B{[r4c4](4|9)} -9- C{[r5c6]-9-[r5c123568](9|1248|56)-56-[r5c1258]}

A: Almost Locked Set in the cells [r5c1235] with the numbers (14568).
B: Almost Locked Set in the cells [r4c4] with the numbers (49).
C: Almost Locked Set in the cells [r5c123568] with the numbers (1245689).

[r5c9]<>5.
[r5c9]<>6.

However note that it's not always possible to translate XSudo rank 0 patterns into MSLSs when extensive use is made of truth and link sets confined to cells. They must be converted to house sets and that isn't always possible.

PS I see Eleven has posted while I've been writing - scanning but not digesting it, it seems we're on the same song sheet.