The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |4.2|...|589|
 |.8.|6..|...|
 |..5|.9.|...|
 |---+---+---|
 |..9|..7|3.8|
 |.4.|.3.|.7.|
 |7.6|1..|4..|
 |---+---+---|
 |...|.1.|9..|
 |...|..9|.6.|
 |893|...|1.7|
 *-----------*


Play/Print this puzzle online

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 | 4     6     2     | 3     7     1     | 5     8     9     |
 | 9     8    a17    | 6     5     4     |a27    3     2-1   |
 | 3     17    5     | 2     9     8     | 67    14    146   |
 *-------------------+-------------------+-------------------|
 | 125   125   9     | 4     6     7     | 3     125   8     |
 | 125   4     8     | 9     3    *25    |b26    7   c*1256  |
 | 7     3     6     | 1     8    *25    | 4     9    *25    |
 *-------------------+-------------------+-------------------|
 | 6     27    47    | 8     1     3     | 9     245   245   |
 | 125   125   14    | 7     24    9     | 8     6     3     |
 | 8     9     3     | 5     24    6     | 1     24    7     |
 *-----------------------------------------------------------*


Uses UR 2/5 r56c69:

(1=72)r2c37 - (2=6)r5c7 - (6=1)r5c9[UR] => -1 r2c9 ; stte

[Marty R.]

Code: Select all

+------------+---------+-------------+
| 4   6   2  | 3 7  1  | 5  8   9    |
| 9   8   17 | 6 5  4  | 27 3   12   |
| 3   17  5  | 2 9  8  | 67 14  146  |
+------------+---------+-------------+
| 125 125 9  | 4 6  7  | 3  125 8    |
| 125 4   8  | 9 3  25 | 26 7   1256 |
| 7   3   6  | 1 8  25 | 4  9   25   |
+------------+---------+-------------+
| 6   27  47 | 8 1  3  | 9  245 245  |
| 125 125 14 | 7 24 9  | 8  6   3    |
| 8   9   3  | 5 24 6  | 1  24  7    |
+------------+---------+-------------+


Play this puzzle online at the Daily Sudoku site

DP125,r48c12. 1r4c12,1r8c12 yield common outcomes.

r4c12=1-(1=25)r4c8-254=1)r473c8-(1=7)r3c2-(7=2)r7c2
r8c12=1-(1-4)r8c3-(4=7)r7c3-r2c3=r3c2-(7=2r7c2=>r3c2=7,r7c2=2

[Leren]

Code: Select all

*--------------------------------------------------------------*
| 4     6     2      | 3     7     1      | 5     8     9      |
| 9     8     17     | 6     5     4      | 27    3     12     |
| 3     17    5      | 2     9     8      |b67    14   a146    |
|--------------------+--------------------+--------------------|
| 125   125   9      | 4     6     7      | 3     125   8      |
| 125   4     8      | 9     3     25     |c26    7    d256-1  |
| 7     3     6      | 1     8     25     | 4     9     25     |
|--------------------+--------------------+--------------------|
| 6     27    47     | 8     1     3      | 9     245   245    |
| 125   125   14     | 7     24    9      | 8     6     3      |
| 8     9     3      | 5     24    6      | 1     24    7      |
*--------------------------------------------------------------*

H2 Wing: (1=2) r2c9 - r2c7 = (2-6) r5c7 = (6) r5c9 => - 1 r5c9; stte

Leren

[pjb]

Code: Select all

 4       6       2      | 3      7      1      | 5      8      9     
 9       8       17     | 6      5      4      | 7-2    3     c12     
 3       17      5      | 2      9      8      | 67     14     146   
------------------------+----------------------+---------------------
 125     125     9      | 4      6      7      | 3      125    8     
 125     4       8      | 9      3      25     |a26     7     b16(25)   
 7       3       6      | 1      8      25     | 4      9      25     
------------------------+----------------------+---------------------
 6       27      47     | 8      1      3      | 9      245    245   
 125     125     14     | 7      24     9      | 8      6      3     
 8       9       3      | 5      24     6      | 1      24     7     


Regarding r5c9 as quantum cell 16, reduces to simple xy wing => -2 r2c7; stte
(or is it 2 steps and I'm cheating?)
Phil

[Ngisa]

Code: Select all

+------------+---------+-------------+
| 4   6   2  | 3 7  1  | 5  8   9    |
| 9   8   e17 | 6 5  4  | 27 3   2-1   |
| 3   17  5  | 2 9  8  | 67 a14  146  |
+------------+---------+-------------+
| 125 125 9  | 4 6  7  | 3  125 8    |
| 125 4   8  | 9 3  25 | 26 7   1256 |
| 7   3   6  | 1 8  25 | 4  9   25   |
+------------+---------+-------------+
| 6   27  d47 | 8 1  3  | 9  b245 c245  |
| 125 125 14 | 7 24 9  | 8  6   3    |
| 8   9   3  | 5 24 6  | 1  b24  7    |
+------------+---------+-------------+


(1=4)r3c8-r79c8=r7c9-(4=7)r7c3-(7=1)r2c3 => -1r2c9; stte

[sultan vinegar]

Regarding r5c9 as quantum cell 16, reduces to simple xy wing => -2 r2c7; stte
(or is it 2 steps and I'm cheating?)

That's two steps in my book.
Step 1 is the UR for 25 in r56c69 => r5c9 <> 2,5.
Step 2 is the XY-wing.

I don't see anything quantum about the elimination. The quantum term is commonly misunderstood. See my post from yesterday for some examples of what quantums are.

[SteveG48]

Code: Select all

 4       6       2      | 3      7      1      | 5      8      9     
 9       8       17     | 6      5      4      | 7-2    3     c12     
 3       17      5      | 2      9      8      | 67     14     146   
------------------------+----------------------+---------------------
 125     125     9      | 4      6      7      | 3      125    8     
 125     4       8      | 9      3      25     |a26     7     b16(25)   
 7       3       6      | 1      8      25     | 4      9      25     
------------------------+----------------------+---------------------
 6       27      47     | 8      1      3      | 9      245    245   
 125     125     14     | 7      24     9      | 8      6      3     
 8       9       3      | 5      24     6      | 1      24     7     


Regarding r5c9 as quantum cell 16, reduces to simple xy wing => -2 r2c7; stte
(or is it 2 steps and I'm cheating?)
Phil

I don't think it's two steps. Just write it as (2=1)r2c9 - (1=6)[UR] - (6=2)r5c7 => -2 r2c7

[Marty R.]

Would someone define "quantum cell"?

[pjb]

Thanks Steve. My use of "quantum" in this case was wrong. I found the following example where the 2 cells r6c89 can be regarded as (12) in an xy-wing. I think this represents a "quantum cell"

Code: Select all

 +--------------------------------------------------------------+
 |  7     2     48    |  1358  138   6     |  49    459   39    |
 |  5     6     1     |  4     37    9     |  8     27    23    |
 |  48    9     3     |  58    78    2     |  6     457   1     |
 |--------------------+--------------------+--------------------|
 |  23    5     7     |  1389  138   38    |  49    1249  6     |
 |  4-8   14    9     |  6     2     7     |  3    *18    5     |
 |  6     13   *28    |  139   5     4     |  7     89+12 89+2  |
 |--------------------+--------------------+--------------------|
 |  9     8     6     |  2     4     1     |  5     3     7     |
 |  1     7     5     |  38    9     38    |  2     6     4     |
 |  23    34    24    |  7     6     5     |  1     89    89    |
 +--------------------------------------------------------------+

Phil

[sultan vinegar]

Hi pjb,

That particular result can be explained with a standard grouped strong link through the AUR. I don't see why any quantum is necessary in this case.
Try and replicate those chains I posted without using quantums. You'll soon find that you need an assumption or memory to make the chain bidirectional, hence the quantum is necessary for those cases.

Marty,
I've never seen a definition of 'quantum cell'. I've seen plenty of people come up with what they think are new examples of quantums, but the only example that I've ever seen that cuts it as a quantum is the quantum version of the type 3 AUR. Note that there is also a standard version of the type 3 AUR that is not quantum. This point is also often misunderstood. I'm more than happy to add to the quantum collection if an example can be provided, however

[Marty R.]

Thank you, SV.

[JC Van Hay]

"Quantum ..." : see SteveK's blog pages 08/Aug/09, 10/Aug/09 and 02/Sep/09 here.

[sultan vinegar]

"Quantum ..." : see SteveK's blog pages 08/Aug/09, 10/Aug/09 and 02/Sep/09 here.

Thanks for these JC. There are mixed results here. Starting from the back, noting that two separate quantum examples were provided for 10 Aug:

2 Sep: (QNT147)bfg2 is three cells for three candidates so not a quantum.

10 Aug: (QNP16)e1f2 is two cells for two candidates so not a quantum.

The remaining ones for 10 Aug and 8 Aug can be solved with almost chains or counting arguments (I won't discuss these here), but I agree that a quantum interpretation is valid (and simpler) for these.

10 Aug: Steve uses branching further up his chain, but if we consider the business end of the elimination, one can 'get by' without quantums by using instead:

... - (6)g4 = (HP16)ef4 - (345)e4 = (NP16)e14 => e23 <> 16.

It does seem reasonable to me to write instead:

… - (6)f5 = (QNP16)e145 => e23 <> 16.

From left to right, given that by assumption f5 <> 6, so there are three cells remaining in box 5 for the two candidates 16, so at least one candidate must occur in e4 or e5 which then combines with e1 to make the QNP. Right to left also works under assumption e45 <> 1 or 6, because (1) is locked in ef4, forcing (6) into f5.

8 Aug: This has a similar structure to the previous case, but you can’t 'get by' with the same trick (without branching) because in this case we have:

(HP57)gh6 = (5h5, 7gi4) and you then need separate branches off the 5 and 7 respectively.

Again, I think it is reasonable to call this a quantum, and write (7)gi4 = (QNP57)h156, for similar reasons as before, specifically the constraints on where to place 57 in box 6. There was no branching in this elimination so we can write the full (alternate) chain:

(QNP57)h156 = (7)gi4 – (7=2)b4 – (2)b5 = (2-5)d5 = (NP57)h15 => h2 <> 57, h3 <> 5, h7 <> 7.

[DonM]

"Quantum ..." : see SteveK's blog pages 08/Aug/09, 10/Aug/09 and 02/Sep/09 here.

Thanks for these JC. There are mixed results here. Starting from the back, noting that two separate quantum examples were provided for 10 Aug:

2 Sep: (QNT147)bfg2 is three cells for three candidates so not a quantum.

10 Aug: (QNP16)e1f2 is two cells for two candidates so not a quantum.

The remaining ones for 10 Aug and 8 Aug can be solved with almost chains or counting arguments (I won't discuss these here), but I agree that a quantum interpretation is valid (and simpler) for these.

10 Aug: Steve uses branching further up his chain, but if we consider the business end of the elimination, one can 'get by' without quantums by using instead:
...

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.

Generally, he defined a quantum as a grouping of cells that could be used, if other things were equal, to form useful constructs that ordinarily, at first glance, wouldn't be apparent. He was never totally happy with the term, quantum, because some others (inexplicably) had an issue with it. At one point, he started using the term 'quasi' instead of quantum. Also, it is apparent that as Steve used of the term 'quantum', it was also a way of simplifying and shortening notation. Thus, in some circumstances, one could have probably expressed a solution in another, albeit more cumbersome, way.

The simplest example of a quantum -and the type that Steve first used- did relate to using the virtual cells available in Type 3 AURs to form constructs that could operate as almost locked sets (or locked sets as the case may be) in a chain. But he very quickly went beyond that in complexity and even came up with what almost amounted to a quantum guardian. It is true that many of his quantums used AURs in one way or another.

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.

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.)