Two-Candidate Notation

Everything about Sudoku that doesn't fit in one of the other sections

Postby Pat » Wed Aug 19, 2015 1:21 pm


    (off-topic)

      XOR (exclusive-or)
      is the same as NE (not-equal)

      symbol:

      Code: Select all
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Re: Two-Candidate Notation

Postby eleven » Wed Aug 19, 2015 2:26 pm

Ah thats nice, so you could write a skyscraper as A≠B-C≠D, which lets you know, that A=D :)
The implication A≠B => A=B is amusing too.
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Re: Two-Candidate Notation

Postby Pat » Wed Aug 19, 2015 3:43 pm

    yes, the abuse of the = has already been noted
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Re: Two-Candidate Notation

Postby ronk » Wed Aug 19, 2015 7:04 pm

sultan vinegar wrote:I too would be open to using another symbol for SK loops. Another option for consideration is to use a different symbol for the inferences in SK-loops rather than on the grouped candidates, given that (in general?) two truths are transported in an SK-loop compared with just one in an AIC. (I think the puzzle called Cigarette is the typical exception, I can't remember the details for sure?)

Although I recall the finding of an exception, Cigarette is not it. daj95376, do you have this recorded in your potpourri file? :)
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Postby daj95376 » Thu Aug 20, 2015 2:04 am

[Withdrawn: not relevant given ronk's update post below.]

_
Last edited by daj95376 on Thu Aug 20, 2015 9:38 pm, edited 1 time in total.
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Postby Pat » Thu Aug 20, 2015 10:24 am

daj95376 wrote:
    I barely recall that a puzzle named Cigarette existed,
    but I have no record of it.
    here it is:
    Cigarette by eleven (2011.Jan.26)
    Code: Select all
    12.3.....34....1....5......6.24..5......6..7......8..6..42..3......7...9.....9.8.
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Postby daj95376 » Thu Aug 20, 2015 4:17 pm

[Withdrawn: not relevant given ronk's update post below.]

_
Last edited by daj95376 on Thu Aug 20, 2015 9:38 pm, edited 1 time in total.
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Re: Two-Candidate Notation

Postby eleven » Thu Aug 20, 2015 6:13 pm

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Re: Two-Candidate Notation

Postby ronk » Thu Aug 20, 2015 7:17 pm

ronk wrote: ... though I recall the finding of an exception, Cigarette is not it. daj95376, do you have this recorded in your potpourri file? :)

daj95376 wrote:I must admit that I'm not certain what's being requested.

Sorry, I wasn't at all clear. perhaps this will help

Easter Monster (slightly morphed, I think)
001000002030004050600000700000058040000070000050903000007000600090300080200000001

Code: Select all
 45789 *478    1      | 5678   3689   5679   | 3489  *369    2
*789    3     *289    | 12678  12689  4      |*189    5     *689
 6     *248    24589  | 1258   12389  1259   | 7     *139    3489
----------------------+----------------------+---------------------
 1379   1267   2369   | 126    5      8      | 1239   4      3679
 13489  12468  234689 | 1246   7      126    | 123589 12369  35689
 1478   5      2468   | 9      1246   3      | 128    1267   678
----------------------+----------------------+---------------------
 13458 *148    7      | 12458  12489  1259   | 6     *239    3459
*145    9     *456    | 3      1246   12567  |*245    8     *457
 2     *468    34568  | 45678  4689   5679   | 3459  *379    1

Band 2 and stack 2 are omitted from the following diagrams.

Code: Select all
+--------------------+--------------------+
|  .    (478)   .    |  .    (369)    .   |
| (789)  .     (289) | (189)  .     (689) |
|  .    (248)    .   |  .    (139)    .   |
+--------------------+--------------------+
|  .    (148)   .    |  .    (239)    .   |
| (145)  .     (456) | (245)  .     (457) |
|  .    (468)    .   |  .    (379)    .   |
+--------------------+--------------------+

The Easter Monster solution has exactly one of the four k-loop "super-digits" in each mini-row and mini-col of the k-loop pattern.

Code: Select all
+--------------------+--------------------+
|  .    (7  )   .    |  .    (6  )    .   |
| (   )  .     (2  ) | (1  )  .     (   ) |
|  .    (   )    .   |  .    (   )    .   |
+--------------------+--------------------+
|  .    (1  )   .    |  .    (2  )    .   |
| (   )  .     (6  ) | (   )  .     (7  ) |
|  .    (   )    .   |  .    (   )    .   |
+--------------------+--------------------+

The alternative I remember being found and am looking to re-find, has the two super-digits in one mini-row or mini-col, as in the following example.

Code: Select all
+--------------------+--------------------+
|  .    (7  )   .    |  .    (   )    .   |
| (   )  .     (   ) | (1  )  .     (6  ) |
|  .    (2  )    .   |  .    (   )    .   |
+--------------------+--------------------+
|  .    (   )   .    |  .    (2  )    .   |
| (1  )  .     (6  ) | (   )  .     (   ) |
|  .    (   )    .   |  .    (7  )    .   |
+--------------------+--------------------+


eleven wrote:Ron, you might mean this (?) http://forum.enjoysudoku.com/post203235.html#p203235

Thanks for posting that. I'd forgotten about it.
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Re: Two-Candidate Notation

Postby JC Van Hay » Thu Aug 20, 2015 9:58 pm

Danny, your "withdrawn" (?) chain
Code: Select all
+------------------+---------+--------------+
| .      (345)  .  | .  .  . | -3  -3    -3 |
| .      .      .  | .  .  . | .   .     .  |
| -3     -3     -3 | .  .  . | .   (39)  .  |
+------------------+---------+--------------+
| .      .      .  | .  .  . | .   .     .  |
| .      .      .  | .  .  . | .   .     .  |
| .      (45)   .  | .  .  . | .   .     .  |
+------------------+---------+--------------+
| (678)  .      .  | .  .  . | .   (89)  .  |
| .      (46)   .  | .  .  . | .   .     .  |
| .      (57)   .  | .  .  . | .   .     .  |
+------------------+---------+--------------+
3r1c2 4r1c2 5r1c2
     -------------------------
     |4r6c2 5r6c2            |
     |4r8c2       6r8c2      |
     |      5r9c2       7r9c2|
     |            6r7c1 7r7c1|8r7c1
     -------------------------
                              8r7c8 9r7c8
                                    9r3c8 3r3c8
can be rewritten as

(3=45)r1c2 - XYRing[(4=5)r6c2 - (5=7)r9c2 -(7=*6)r7c1 - (6=4)r8c2]=*8r7c1 - (8=9)r7c8 - (9=3)r3c8
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Re: Two-Candidate Notation

Postby ronk » Sat Aug 22, 2015 3:49 pm

daj95376 wrote:
Code: Select all
+------------------+---------+--------------+
| .      (345)  .  | .  .  . | -3  -3    -3 |
| .      .      .  | .  .  . | .   .     .  |
| -3     -3     -3 | .  .  . | .   (39)  .  |
+------------------+---------+--------------+
| .      .      .  | .  .  . | .   .     .  |
| .      .      .  | .  .  . | .   .     .  |
| .      (45)   .  | .  .  . | .   .     .  |
+------------------+---------+--------------+
| (678)  .      .  | .  .  . | .   (89)  .  |
| .      (46)   .  | .  .  . | .   .     .  |
| .      (57)   .  | .  .  . | .   .     .  |
+------------------+---------+--------------+

daj95376, even though you deleted the above, it deserves a reply, especially since it ties in with the topic of this thread.

Code: Select all
(3=45)r16c2 - (45=67)r89c2 - (67=8)r7c1 - (8=9)r7c8 - (9=3)r3c8 ==> r1c789<>3, r3c123<>3

No extra symbols required IMO.
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Re: Two-Candidate Notation

Postby daj95376 » Sat Aug 22, 2015 5:39 pm

ronk wrote:
daj95376 wrote:
Code: Select all
+------------------+---------+--------------+
| .      (345)  .  | .  .  . | -3  -3    -3 |
| .      .      .  | .  .  . | .   .     .  |
| -3     -3     -3 | .  .  . | .   (39)  .  |
+------------------+---------+--------------+
| .      .      .  | .  .  . | .   .     .  |
| .      .      .  | .  .  . | .   .     .  |
| .      (45)   .  | .  .  . | .   .     .  |
+------------------+---------+--------------+
| (678)  .      .  | .  .  . | .   (89)  .  |
| .      (46)   .  | .  .  . | .   .     .  |
| .      (57)   .  | .  .  . | .   .     .  |
+------------------+---------+--------------+

daj95376, even though you deleted the above, it deserves a reply, especially since it ties in with the topic of this thread.

Code: Select all
(3=45)r16c2 - (45=67)r89c2 - (67=8)r7c1 - (8=9)r7c8 - (9=3)r3c8 ==> r1c789<>3, r3c123<>3

No extra symbols required IMO.

I noticed that neither you nor JC started the chain at r3c8. Please show it without any special symbols or networking.

Hidden Text: Show
Code: Select all
(3=9)r3c8 - (9=8)r7c8 - 8r7c1 = 6r7c1 - (645=453)r168c2 \
                                  ||                       =>  -3 r1c789,r3c123
                              = 7r7c1 - (745=453)r169c2 /

Reading this from r-to-l, the logic is two, three-cell ALS streams merging in a forcing chain. At this point, a Kraken Cell on r7c1 is possibly the best solution.

_
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Re: Two-Candidate Notation

Postby David P Bird » Sat Aug 22, 2015 7:38 pm

daj95376 wrote:
ronk wrote:
daj95376 wrote:
Code: Select all
+------------------+---------+--------------+
| .      (345)  .  | .  .  . | -3  -3    -3 |
| .      .      .  | .  .  . | .   .     .  |
| -3     -3     -3 | .  .  . | .   (39)  .  |
+------------------+---------+--------------+
| .      .      .  | .  .  . | .   .     .  |
| .      .      .  | .  .  . | .   .     .  |
| .      (45)   .  | .  .  . | .   .     .  |
+------------------+---------+--------------+
| (678)  .      .  | .  .  . | .   (89)  .  |
| .      (46)   .  | .  .  . | .   .     .  |
| .      (57)   .  | .  .  . | .   .     .  |
+------------------+---------+--------------+

daj95376, even though you deleted the above, it deserves a reply, especially since it ties in with the topic of this thread.

Code: Select all
(3=45)r16c2 - (45=67)r89c2 - (67=8)r7c1 - (8=9)r7c8 - (9=3)r3c8 ==> r1c789<>3, r3c123<>3

No extra symbols required IMO.

I noticed that neither you nor JC started the chain at r3c8. Please show it without any special symbols or networking.

I'd like to make a comment here, but I'm afraid Jason would moderate it.

By all means start a new dialect for left to right alternating inference streams but give it a new name to be cited when it is used - but hey, that's extra key-strokes!

Then a reference document is required explaining the scope of the modifications and what understandings are required such as when there are more than two digits involved. (I or probably DonM would be willing to write one for the classic approach if asked.)

Can anyone explain how the benefits that this would bring would justify the effort involved?
.
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Re: Two-Candidate Notation

Postby eleven » Sat Aug 22, 2015 10:07 pm

daj95376 wrote:I noticed that neither you nor JC started the chain at r3c8. Please show it without any special symbols or networking.

Modern style: (3=9)r3c8 - (9=8)r7c8 - (8=67)r7c1 - (67=3)r1689c2
Personally i would prefer (3=9)r3c8 - (9=8)r7c8 - (8=67)r7c1 - (6&7=4|5)r89c2 - (4&5=3)r16c2, because it is more like you could find it.
(i spare you to write it in my notation)
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Re: Two-Candidate Notation

Postby daj95376 » Sat Aug 22, 2015 10:13 pm

DPB: Since I know that Jason would moderate my reply, I'll just move on.


ronk: I was attempting to show that your solution didn't quite fall in with the topic of the thread. I'm trying to derive a new connector that would be bidirectional for a pair of values in two cells. A symbol that would work on said pair as if they were a single item. You provided a chain that you said didn't need special symbols. My first objective was to show that it wasn't bidirectional ... and inappropriate for my new connector. As it turns out, the interchange in r7c1 puts a crimp on everything.

Now, I could go on and discuss how your chain is appropriate in terms of what I call a DAJC, but I'm afraid that DPB would throw another tantrum.

_
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