Simple enough?

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Simple enough?

Postby tarek » Wed Oct 09, 2019 5:51 pm

Code: Select all
.2....89.1..6..4.5.......27....3......42.8...7..59..6.23..7......9.....65.63...1.

.2....89.
1..6..4.5
.......27
....3....
..42.8...
7..59..6.
23..7....
..9.....6
5.63...1.
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Re: Simple enough?

Postby ArkieTech » Wed Oct 09, 2019 8:02 pm

Code: Select all
 *-----------------------------------------------------------*
 | 6     2     357   | 47    45    3457  | 8     9     1     |
 | 1     89    78    | 6     28    279   | 4     3     5     |
 | 348   4589  358   | 89    1     359   | 6     2     7     |
 *-------------------+-------------------+-------------------|
 | 89    6     1258  | 47    3     147   | 1259  458   2489  |
 | 39    15    4     | 2     6     8     | 157   57    39    |
 | 7     18    1238  | 5     9     14    | 12    6     2348  |
 *-------------------+-------------------+-------------------|
 | 2     3     18    | 189   7     6     | 59    458   489   |
 | 48    1478  9     | 18    25    25    | 3     78    6     |
 | 5     78    6     | 3     48    49    | 279   1     289   |
 *-----------------------------------------------------------*
[83r45c1-(83=1)r6c237]-1r6c6; ste


Nice! what is it?
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Re: Simple enough?

Postby SpAce » Wed Oct 09, 2019 8:44 pm

ArkieTech wrote:[83r45c1-(83=1)r6c237]-1r6c6; ste

Nice! what is it?

Hi Dan! I don't quite understand your expression, but there's a Sue de Coq / Doubly-Linked ALS-XZ in those cells. I'd write it:

(8=9'3)r45c1 - (3=12'8)r4c723 - loop => -1 r6c6, -2 r6c9, -8 r4c3

Or as a Rank 0 pattern:

Alien 5-Fish (Rank 0): {45N1 6N237} \ {12r6 389b4} => -1 r6c6, -2 r6c9, -8 r4c3

--

Something less nice:

Code: Select all
.--------------------.------------------.-----------------.
|   6     2     357  | 47   c45    3457 | 8     9    1    |
|   1     89    78   | 6     28    279  | 4     3    5    |
|   48-3  4589  358  | 89    1   d(3)59 | 6     2    7    |
:--------------------+------------------+-----------------:
|  a89    6     1258 | 47    3     147  | 1259  458  2489 |
| a[3]9   15    4    | 2     6     8    | 157   57   39   |
|   7    a81    1238 | 5     9    b14   | 12    6    2348 |
:--------------------+------------------+-----------------:
|   2     3     18   | 189   7     6    | 59    458  489  |
|   48    1478  9    | 18    25    25   | 3     78   6    |
|   5     78    6    | 3    c48  bc49   | 279   1    289  |
'--------------------'------------------'-----------------'

(3=981)b4p418 - (14)r69c6 = (459)r91c5,r9c6 - (5|9=3)r3c6 => -3 r3c1; stte
-SpAce-: Show
Code: Select all
   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."
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Re: Simple enough?

Postby tarek » Wed Oct 09, 2019 8:53 pm

ArkieTech wrote:[83r45c1-(83=1)r6c237]-1r6c6

I'm trying to follow … you chose 1 as the restricted common which is correct, but 2 is also restricted and therefore gives you the loop that you need so that you eliminate more candidates along the weak links too

[Edit: corrected spelling mistake]
Last edited by tarek on Wed Oct 09, 2019 9:18 pm, edited 1 time in total.
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Re: Simple enough?

Postby eleven » Wed Oct 09, 2019 9:09 pm

ArkieTech wrote:[83r45c1-(83=1)r6c237]-1r6c6; ste

Strange notation, but i like the view, that one of r45c1 must be 3 or 8, and therefore the ALS 1238r6c237 must contain 1 and 2 (eliminating also 2r6c9).
or
5 digits in 5 cells, all must be there, because none can be twice (eliminating also the 8 r4c4).
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Re: Simple enough?

Postby SpAce » Wed Oct 09, 2019 10:24 pm

eleven wrote:
ArkieTech wrote:[83r45c1-(83=1)r6c237]-1r6c6; ste

Strange notation, but i like the view, that one of r45c1 must be 3 or 8, and therefore the ALS 1238r6c237 must contain 1 and 2 (eliminating also 2r6c9).

That's how I read it too (though 83r45c1 implies 8 AND 3; should have been (8|3)). It's possibly the simplest way to see those eliminations, but it's actually a compacted forcing chain and not an AIC. Basically the same as this (which is an AIC if stretched out):

(8)r45c1 - (83=12)r6c237
||
(3)r45c1 - (38=12)r6c237

=> +12 r6c237

One kludgy way to write it as a compact AIC is to start with a DP (contradiction) node [!]:

([!]=8|3)r45c1 - (83=12)r6c237 => +12 r6c237

That way the chain has two strongly-linked end-points like a normal AIC. One of them just happens to be a known false, which makes the other one true.
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Re: Simple enough?

Postby tarek » Wed Oct 09, 2019 10:49 pm

So as you all noticed this indeed a double linked ALS-XZ, VWXYZ-Wing or a Sue-De-Coq … It is now caught by Sukaku Explainer VWXYZ-Wing technique

Code: Select all
+----------------+----------------+----------------+
| 6    2    357  | 47   45   3457 | 8    9    1    |
| 1    89   78   | 6    28   279  | 4    3    5    |
| 348  4589 358  | 89   1    359  | 6    2    7    |
+----------------+----------------+----------------+
|%89   6    125-8| 47   3    147  | 1259 458  2489 |
|%39   15   4    | 2    6    8    | 157  57   39   |
| 7   %18  %1238 | 5    9   -14   |*12   6   -2348 |
+----------------+----------------+----------------+
| 2    3    18   | 189  7    6    | 59   458  489  |
| 48   1478 9    | 18   25   25   | 3    78   6    |
| 5    78   6    | 3    48   49   | 279  1    289  |
+----------------+----------------+----------------+
Double-linked VWXYZ-wing *:r6c7 %:r45c1 r6c23 => r4c3<>8  r6c6<>1 r6c9<>2

The following is what I thought is best to be presented as an explanation with SE:
Hidden Text: Show
VWXYZ-Wing 2410
The five cells r6c2, r4c1, r5c1, r6c3 and r6c7 form a double-linked VWXYZ-Wing: The four cells r6c2, r4c1, r5c1 and r6c3 form an almost locked set linked to the bivalue cell r6c7 through both values 2 and 1. Regardless of the final value of cell r6c7, the double-link would force the other 4 cells from the pattern to have different values to that one. The 5 different values will be in 5 cells therefore forming a locked set.
Other occurrences of any of the values of the Wing pattern can therefore be removed from any cells sharing a row, column or block with all Wing cells containing that value.
The largest cell of the wing has 4 candidates and the 5 cells of the VWXYZ-Wing have a total of 12 candidates.


Here are 2 bonus gifts for people who enjoy these types of eliminations (I also enjoy watching you struggle with your AIC notation :lol: )
Code: Select all
+-------------------+-------------------+-------------------+
| 137   579   8     | 2356  1367  257   | 134   12579 2347  |
| 137   79    2     | 8     4     57    | 136   15679 137   |
| 6     4     135   | 23    137   9     | 13    1257  8     |
+-------------------+-------------------+-------------------+
| 8     3     9     | 4     5     6     | 2     17    17    |
| 2     1     4     | 7     9     8     | 5     3     6     |
| 5     6     7     | 1     2     3     | 8     4     9     |
+-------------------+-------------------+-------------------+
| 134   2     136   | 9     367   47    | 1346  8     5     |
| 347   57    356   | 2356  8     1     | 9     26    234   |
| 9     8     1356  | 2356  36    245   | 7     126   1234  |
+-------------------+-------------------+-------------------+
+-------------------+-------------------+-------------------+
| 679   56    179   | 156   367   8     | 4     37    2     |
| 678   68    127   | 126   367   4     | 379   5     19    |
| 3     245   24    | 25    9     17    | 6     17    8     |
+-------------------+-------------------+-------------------+
| 2     7     8     | 4     5     3     | 1     9     6     |
| 5     9     34    | 7     1     6     | 2     8     34    |
| 1     34    6     | 8     2     9     | 5     347   347   |
+-------------------+-------------------+-------------------+
| 467   1     237   | 9     8     5     | 37    23467 347   |
| 678   368   5     | 16    4     2     | 379   367   19    |
| 469   26    29    | 3     67    17    | 8     1246  5     |
+-------------------+-------------------+-------------------+
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Re: Simple enough?

Postby ArkieTech » Wed Oct 09, 2019 11:23 pm

SpAce wrote:
eleven wrote:
ArkieTech wrote:[83r45c1-(83=1)r6c237]-1r6c6; ste

Strange notation, but i like the view, that one of r45c1 must be 3 or 8, and therefore the ALS 1238r6c237 must contain 1 and 2 (eliminating also 2r6c9).

That's how I read it too (though 83r45c1 implies 8 AND 3; should have been (8|3)).



Thanks SpAce My mistake; should be [8|3r45c1-(83=1)r6c237]-1r6c6; ste

My eagerness for simplicity sometimes goes awry.
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Re: Simple enough?

Postby ArkieTech » Wed Oct 09, 2019 11:45 pm

Code: Select all
 *--------------------------------------------------------------------*
 | 137    579    8      | 2356   1367   257    | 134    12579  2347   |
 | 137    79     2      | 8      4      57     | 136    15679  137    |
 | 6      4      135    | 23     137    9      | 13     1257   8      |
 *----------------------+----------------------+----------------------|
 | 8      3      9      | 4      5      6      | 2      17     17     |
 | 2      1      4      | 7      9      8      | 5      3      6      |
 | 5      6      7      | 1      2      3      | 8      4      9      |
 *----------------------+----------------------+----------------------|
 | 134    2      136    | 9      367    47     | 1346   8      5      |
 | 347    57     356    | 2356   8      1      | 9      26     234    |
 | 9      8      1356   | 2356   36     245    | 7      126    1234   |
 *--------------------------------------------------------------------*
[7|2r12c6-(72=13)r3c457]-13r3c3; ste
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Re: Simple enough?

Postby ArkieTech » Thu Oct 10, 2019 12:12 am

Code: Select all
 *--------------------------------------------------------------------*
 | 679    56     179    | 156    367    8      | 4      37     2      |
 | 678    68     127    | 126    367    4      | 379    5      19     |
 | 3      245    24     | 25     9      17     | 6      17     8      |
 *----------------------+----------------------+----------------------|
 | 2      7      8      | 4      5      3      | 1      9      6      |
 | 5      9      34     | 7      1      6      | 2      8      34     |
 | 1      34     6      | 8      2      9      | 5      347    347    |
 *----------------------+----------------------+----------------------|
 | 467    1      237    | 9      8      5      | 37     23467  347    |
 | 678    368    5      | 16     4      2      | 379    367    19     |
 | 469    26     29     | 3      67     17     | 8      1246   5      |
 *--------------------------------------------------------------------*
[3|7r7c7=37r8c4789]-37r7c89; singles to bug
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Re: Simple enough?

Postby SpAce » Thu Oct 10, 2019 9:39 am

ArkieTech wrote:[3|7r7c7=37r8c4789]-37r7c89; singles to bug

Hi Dan! I don't see how that's supposed to work. Can you elaborate on how it should be interpreted? Even if the strong link (3|7=37) were valid (which I don't see either) it wouldn't give us the eliminations (you'd need 37=37).

With that starting cell, your original way doesn't produce those eliminations either:

(3|7)r7c7 - (37=196)r8c4789 => -6 r8c12

But this does:

(1|6)r8c4 - (16=937)b9p1456 => -37 r7c89

Any of the Rank-0 approaches {SDC, DL-VWXYZ-Wing, DL-ALS-XZ, Alien Fish} gives both at the same time:

(3=7)r7c7 - (7=169'3)r8c4789 - loop => -6 r8c12, -37 r7c89

{7N7 8N4789} \ {169r8 37b9} => -6 r8c12, -37 r7c89
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Re: Simple enough?

Postby ArkieTech » Thu Oct 10, 2019 11:06 am

SpAce wrote:
ArkieTech wrote:[3|7r7c7=37r8c4789]-37r7c89; singles to bug

Hi Dan! I don't see how that's supposed to work. Can you elaborate on how it should be interpreted? Even if the strong link (3|7=37) were valid (which I don't see either) it wouldn't give us the eliminations (you'd need 37=37).

With that starting cell, your original way doesn't produce those eliminations either:

(3|7)r7c7 - (37=196)r8c4789 => -6 r8c12

But this does:

(1|6)r8c4 - (16=937)b9p1456 => -37 r7c89

Any of the Rank-0 approaches {SDC, DL-VWXYZ-Wing, DL-ALS-XZ, Alien Fish} gives both at the same time:

(3=7)r7c7 - (7=169'3)r8c4789 - loop => -6 r8c12, -37 r7c89

{7N7 8N4789} \ {169r8 37b9} => -6 r8c12, -37 r7c89



Code: Select all
 *--------------------------------------------------------------------*
 | 679    56     179    | 156    367    8      | 4      37     2      |
 | 678    68     127    | 126    367    4      | 379    5      19     |
 | 3      245    24     | 25     9      17     | 6      17     8      |
 *----------------------+----------------------+----------------------|
 | 2      7      8      | 4      5      3      | 1      9      6      |
 | 5      9      34     | 7      1      6      | 2      8      34     |
 | 1      34     6      | 8      2      9      | 5      347    347    |
 *----------------------+----------------------+----------------------|
 | 467    1      237    | 9      8      5      | 37     23467  347    |
 | 678    368    5      | 16     4      2      | 379    367    19     |
 | 469    26     29     | 3      67     17     | 8      1246   5      |
 *--------------------------------------------------------------------*
[3|7r7c7=37r8c4789]-37r7c89

r7c7 is going to be a 3 or 7
if it is a 3 then set r8c4789 must contain a 7
if it is a 7 then set r8c4789 must contain a 3
3 and 7 must be in r7c7,r8c4789 therefore cannot be in r7c89

[37r7c7,r8c4789]-37r7c89

might be better
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Re: Simple enough?

Postby SpAce » Thu Oct 10, 2019 11:38 am

ArkieTech wrote:[3|7r7c7=37r8c4789]-37r7c89

r7c7 is going to be a 3 or 7
if it is a 3 then set r8c4789 must contain a 7
if it is a 7 then set r8c4789 must contain a 3
3 and 7 must be in r7c7,r8c4789 therefore cannot be in r7c89

While that's true, the chain does not depict it in any way. Remember that '=' means OR in Eureka. I think something like this might work instead (using your ubercompact style):

[3|7r7c7->37r7c7,r8c4789]-37r7c89

Even then it doesn't do a great job explaining why the implication is true.

[37r7c7,r8c4789]-37r7c89

might be better

Well, at least it's a valid statement, but it's basically starting with the conclusion. It would be nice to display a piece of logic that explains why 37 must be locked in those cells. Otherwise I could just as well say: (6)r1c4,r8c8,r9c5 => -6 r8c4; stte. Isn't it obvious why 6 must be in (at least) one of those cells? :D

Added. I think something like this would suffice:

{Rank 0 pattern name}: (13679)r7c7,r8c4789 => -37 r7c89, -6 r8c12

I do think it needs to be accompanied with a pattern name (SDC, DDS, ...) or a textual explanation in eleven's style, to provide an explicit reason why all of the digits are locked in those cells. Without that extra piece of information it's asking a lot of the reader. (On the other hand, a loop or an alien fish make the Rank 0 logic explicit, so they work just as well without any pattern names. That's why I'd generally prefer them.)

"Everything should be made as simple as possible, but no simpler."
Last edited by SpAce on Thu Oct 10, 2019 2:18 pm, edited 2 times in total.
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Re: Simple enough?

Postby SpAce » Thu Oct 10, 2019 12:04 pm

In case it wasn't obvious...

Code: Select all
.--------------------.------------------.----------------------.
|  d679  d56    d179 | c15(6)   367  8  |   4    k{37}     2   |
| df678  d68    e127 |  126    B367  4  |  f379    5       19  |
|   3     245    24  |  25      9    17 |   6      17      8   |
:--------------------+------------------+----------------------:
|   2     7      8   |  4       5    3  |   1      9       6   |
|   5     9     j34  |  7       1    6  |   2      8      j34  |
|   1     34     6   |  8       2    9  |   5    k{37}4    347 |
:--------------------+------------------+----------------------:
|  g467   1    hi237 |  9       8    5  | gh37     23467   347 |
|  g678   368    5   |  1-6     4    2  |   379  k{376}    19  |
|   469   26     29  |  3     A[6]7  17 |   8      1246    5   |
'--------------------'------------------'----------------------'

(6=7)r9c5 - r2c5 = [(6=1|5)r1c4 - (15=9867)b1p12345 - (7)r2c3 = r2c17 - r78c1&r7c7 = (7)r7c3|(3)r7c7 - (3)r7c3 = (3,4)r5c39 - (4=376)r618c8] => -6 r8c4; stte

as a kraken: Show
Code: Select all
(7)r2c1 - r78c1 = (73-4)r75c3 = r5c9 - (4=376)r618c8
||
(7)r2c3 - (7869=15)b1p45123 - (1|5=6)r1c4
||
(7)r2c5 - (7=6)r9c5
||
(7)r2c7 - (7=3)r7c7 - r7c3 = (3,4)r5c39 - (4=376)r618c8

=> -6 r8c4; stte

as a 9x9 TM: Show
Code: Select all
 6r9c5     7r9c5
 6r1c4           1|5r1c4
                 15r1c23 9867b1p12345
 673r816c8                            4r6c8
                                      4r5c9 4r5c3
                                            3r5c3 3r7c3
                                                  7r7c3 7r78c1
                                                  3r7c7        7r7c7
           7r2c5         7r2c3                          7r2c1  7r2c7
--------------------------------------------------------------------
-6r8c4
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