The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|12.|.3.|
 |.6.|..7|.21|
 |...|..4|7..|
 |---+---+---|
 |53.|4..|8..|
 |48.|...|.92|
 |..6|..8|.74|
 |---+---+---|
 |..4|9..|...|
 |87.|2..|.6.|
 |.9.|.53|...|
 *-----------*


Play/Print this puzzle online

[SpAce]

Code: Select all

.------------------.------------------.----------------.
| 7     4    58    |   1      2     9 | 6     3   58   |
| 39    6    3589  |   58     38    7 | 4     2   1    |
| 123  c125  12358 | ab568    368   4 | 7   cd58  9    |
:------------------+------------------+----------------:
| 5     3    79    |   4      9-7   2 | 8     1   6    |
| 4     8    17    |  a6(7)   16-7  5 | 3     9   2    |
| 129   12   6     |   3      19    8 | 5     7   4    |
:------------------+------------------+----------------:
| 123  d125  4     |   9    e(7)8   6 | 12   e58  3578 |
| 8     7    35    |   2      4     1 | 9     6   35   |
| 6     9    12    |   8-7    5     3 | 12    4   78   |
'------------------'------------------'----------------'

(76)r53c4 = (5|8)r3c4 - (58)r3c28 = (5)r7c2,r3c8 - (5=87)r7c85 => -7 r45c5,r9c4; stte

(There's obviously a simpler route using the ALS (568)r3c48:

(7=6)r5c4 - (6=85)r3c48 - r3c2 = (587)r7c285 => -7 r45c5,r9c4; stte

...but that's not how I first saw it.)

[Sudtyro2]

Code: Select all

+--------------------+-----------------+-----------------+
| 7     4     58*    |  1     2     9  | 6    3    58*   |
| 39    6    b3589*  | a58#   38*   7  | 4    2    1     |
| 123  c125  A12358# | 568   A368#  4  | 7   B58*  9     |
+--------------------+-----------------+-----------------+
| 5     3     79     |  4     79    2  | 8    1    6     |
| 4     8     17     |  67    167   5  | 3    9    2     |
| 129   12    6      |  3     19    8  | 5    7    4     |
+--------------------+-----------------+-----------------+
| 123  d125   4      |  9     7-8*  6  | 12  e58*  3578# |
| 8     7     35     |  2     4     1  | 9    6    35    |
| 6     9     12     |  78    5     3  | 12   4    7-8   |
+--------------------+-----------------+-----------------+

In 8s, a 7-link oddagon(*) with four guardians(#).
(8-5)r2c4 = r2c3 - r3c2 = r7c2 - (5=8)r7c8; abcde
8r3c35 - r3c8 = 8r7c8; ABe
8r7c9;
=> -8r7c5,r9c9; stte

Prefer a single-sequence kraken lasso (a la DAJ) for the four guardians?
8r7c9=[8r7c8=r3c8-r3c35=(8-5)r2c4=r2c3-r3c2=r7c2-(5=8)r7c8] => -8r7c5,r9c9; stte

SteveC

[Ngisa]

Code: Select all

+-----------------------+-------------------+--------------------+
| 7       4       58    |  1      2       9 | 6      3      58   |
| 39      6       3589  |  58     38      7 | 4      2      1    |
| 123    g125     12358 |ga6-58   368     4 | 7     g58     9    |
+-----------------------+-------------------+--------------------+
| 5       3       79    |  4      79      2 | 8      1      6    |
| 4       8       17    | b67     167     5 | 3      9      2    |
| 129     12      6     |  3      19      8 | 5      7      4    |
+-----------------------+-------------------+--------------------+
| 123    f125     4     |  9      78      6 | 12    e58     3578 |
| 8       7       35    |  2      4       1 | 9      6      35   |
| 6       9       12    | c78     5       3 | 12     4     d78   |
+-----------------------+-------------------+--------------------+


(6)r3c4 = (6-7)r5c4 = r9c4 - (7=8)r9c9 - (8=5)r7c8 - r7c2 = (586)r3c248 => - 58r3c4; stte

Clement

[SteveG48]

Code: Select all

 *--------------------------------------------------------------------*
 | 7      4      58     | 1      2      9      | 6      3      58     |
 | 39     6     c3589   | 58    b38     7      | 4      2      1      |
 | 123    125    12358  | 568    368    4      | 7      58     9      |
 *----------------------+----------------------+----------------------|
 | 5      3      79     | 4      79     2      | 8      1      6      |
 | 4      8      17     | 67     167    5      | 3      9      2      |
 | 129    12     6      | 3      19     8      | 5      7      4      |
 *----------------------+----------------------+----------------------|
 | 123    125    4      | 9     b7-8    6      | 12   ae58    a3578   |
 | 8      7     d35     | 2      4      1      | 9      6     e35     |
 | 6      9      12     | 78     5      3      | 12     4      7-8    |
 *--------------------------------------------------------------------*


8r7c89 = (38)r27c5 - 3r2c3 = r8c3 - (3=58)b9p25 => -8 r7c5,r9c9 ; stte

[Sudtyro2]

(6)r3c4 = (6-7)r5c4 = r9c4 - (7=8)r9c9 - (8=5)r7c8 - r7c2 = (586)r3c248 => - 58r3c4; stte

Hi Clement,
Would it be clearer to replace your last node with something like: 5r3c2 - (58=6)r3c48?

SteveC

[SpAce]

(6)r3c4 = (6-7)r5c4 = r9c4 - (7=8)r9c9 - (8=5)r7c8 - r7c2 = (586)r3c248 => - 58r3c4; stte

Hi Clement,
Would it be clearer to replace your last node with something like: 5r3c2 - (58=6)r3c48?

For someone, maybe, but not to me. I like Clement's concluding node, though it could be shortened to (58)r3c28. Both with the original (586)r3c248 and your suggestion I'd rather conclude +6 r3c4, however, because the chains prove the placement directly (6r3c4 at both ends). Of course the effect is exactly the same either way. All roads lead to Rome, so I'm fine with many possibilities here. I'd probably write the chain like this:

(6,7,8)r359c4 = (85)b9p92 - r7c2 = (58)r3c28 => -58 r3c4; stte

...or with a nice symmetry for the first two nodes:

(58)r3c28 = (58)r7c28 - r9c9 = (8,7,6)r953c4 => -58 r3c4; stte

Edit: once again, added commas for correctness.

[SpAce]

In 8s, a 7-link oddagon(*) with four guardians(#).

Nice!

Prefer a single-sequence kraken lasso (a la DAJ) for the four guardians?
8r7c9=[8r7c8=r3c8-r3c35=(8-5)r2c4=r2c3-r3c2=r7c2-(5=8)r7c8] => -8r7c5,r9c9; stte

Actually I do prefer that. However, I'd also prefer the '==' notation here to mark the non-native links, or otherwise it's kind of hard to read. I'd also add whitespace and combine some links to make it even easier on the eyes (well, my eyes):

8r7c9 == [8r7c8 = r3c8 - r3c35 == (8,5)r2c43 - r3c2 = (58)r7c28] => -8r7c5,r9c9; stte

PS. What do you mean by "lasso"? I haven't seen that term used by anyone but Denis Berthier (not that I know what it means in his vocabulary either), and I don't see anything resembling his notation here.

[Sudtyro2]

In 8s, a 7-link oddagon(*) with four guardians(#).

PS. What do you mean by "lasso"? I haven't seen that term used by anyone but Denis Berthier (not that I know what it means in his vocabulary either), and I don't see anything resembling his notation here.

These are my only notes on the Lasso...

3-value Kraken (SIS) written as Lasso...
Given SIS:
A - EE (or can also have A - .. = F - EE)
||
B - .. = D - EE
||
C - .. = D - EE

Can write as A = [B=C], but then bracket can be written:
[D = .. - B = C - .. = D] => D is true, so A = D.

Full AIC: A = [D = .. - B = C - .. = D] => -EE

(or F = .. - A = [D = .. - B = C - .. = D] => -EE
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Re: Network 6/21/2014
by daj95376 » Sun Jun 22, 2014 4:03 pm

Code: Select all

 +--------------------------------------------------------------------------------+
 |  3489    234589  34589   |  7       2349    359     |  3489    1       6       |
 |  3489    25      6       |  39      12      15      |  3489    38      7       |
 |  349     7       1       |  8       349     6       |  349     5       2       |
 |--------------------------+--------------------------+--------------------------|
 |  18      158     2       |  6       7       4       |  58      9       3       |
 |  36789   389     3789    |  1       5       389     |  2       8-6     4       |
 |  34689   34589   34589   |  2       389     389     |  568     7       1       |
 |--------------------------+--------------------------+--------------------------|
 |  134789  13489   34789   |  39      6       1389    |  13      2       5       |
 |  2       1369    39      |  5       139     7       |  13-6    4       8       |
 |  5       1368    38      |  4       138     2       |  7       36      9       |
 +--------------------------------------------------------------------------------+

 # 104 eliminations remain
 Kraken Cell r6c7:

Code: Select all

 6r6c7                                                                  - 6r5c8,r8c7
   ||
 8r6c7 - r6c5 = (8-1)r9c5                           = (1-6)r9c2 = 6r9c8 - 6r5c8,r8c7
   ||
 5r6c7 - r6c3 = r1c3 - (5=2)r2c2 - (2=1)r2c5 - r9c5 = (1-6)r9c2 = 6r9c8 - 6r5c8,r8c7

I've never had much use for a lasso until lately. They often occur when I rewrite a three-value Kraken Cell as a single sequence. Here, we get 6r6c7=6r9c8:
6r6c7=[6r9c8=(6-1)r9c2=(1-8)r9c5=r6c5-(8=5)r6c7-r6c3=r1c3-(5=2)r2c2-(2=1)r2c5-r9c5=(1-6)r9c2=6r9c8] =>  -6 r5c8,r8c7
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Hope this helps...
SteveC

[SpAce]

These are my only notes on the Lasso...

3-value Kraken (SIS) written as Lasso...
...

I've never had much use for a lasso until lately. They often occur when I rewrite a three-value Kraken Cell as a single sequence. Here, we get 6r6c7=6r9c8:
6r6c7=[6r9c8=(6-1)r9c2=(1-8)r9c5=r6c5-(8=5)r6c7-r6c3=r1c3-(5=2)r2c2-(2=1)r2c5-r9c5=(1-6)r9c2=6r9c8] =>  -6 r5c8,r8c7

Thanks for attempting to explain, Steve. I'm well aware of how to convert a Kraken into an AIC like you did, and sometimes use it myself, but I've never heard it called "lasso". Personally I call them "almost-AICs" or "nested AICs", which I think is quite descriptive (since the inner AIC is used as a boolean term within the outer AIC -- like any other pattern). So my real question is where you picked up the term and how widely used it is for this purpose.

Like I said, I've only seen "lasso" used by Denis Berthier and his followers (*), and since he wasn't an AIC user, I doubt it means the same thing. I'm not a big fan of overloaded terms because they cause confusion. I'm pretty sure Denis tried to pick terms (lasso, whip, belt,...) that didn't conflict with existing ones (with the unfortunate exception of "braids", though I don't know who used that term first), which was a good thing because it kept the contexts clearly separated. I think AIC users also owe his system the same respect. I've never bothered to learn what his terms actually mean, so I guess it's possible that your "lasso" is in fact the same thing as his, but even in that case I wouldn't use the term with AICs because the context is different.

(*) A little search revealed that DAJ has indeed used that term a lot. Still I have no idea if he meant the same thing as Denis or not (but I have no clue what Denis meant). I'm no longer quite sure what DAJ meant either, as here he gives weird definition (highlighted by me):

Note: the above chain can be turned into a lasso (discontinuous loop) by reversing the chain at the contradiction

Based on that and some of his other thoughts on the matter, it seems that he wasn't necessarily seeing them as almost/nested AICs (like I do). Here's an example of how I do it.

[Sudtyro2]

...
I've never had much use for a lasso until lately. They often occur when I rewrite a three-value Kraken Cell as a single sequence. Here, we get 6r6c7=6r9c8:
6r6c7=[6r9c8=(6-1)r9c2=(1-8)r9c5=r6c5-(8=5)r6c7-r6c3=r1c3-(5=2)r2c2-(2=1)r2c5-r9c5=(1-6)r9c2=6r9c8] =>  -6 r5c8,r8c7

So my real question is where you picked up the term and how widely used it is for this purpose.

Just to be clear, the quote above is from DAJ and not from me. I picked up the "lasso" term solely from DAJ's several postings in the April, 2014 time frame. I also think his reference to a "discontinuous loop" refers (accurately) only to the bracketed portion of the single-sequence chain, in this case the loop beginning and ending with strong-strong inference to the same digit.

SteveC

[SpAce]

Just to be clear, the quote above is from DAJ and not from me.

Yes, I noticed it at some point but forgot to correct the quote (done now). Of course it would have been clearer in the first place if you'd used the "quote" tag too

I picked up the "lasso" term solely from DAJ's several postings in the April, 2014 time frame.

Ok. So you have no idea if it was based on Denis' lasso or not?

I also think his reference to a "discontinuous loop" refers (accurately) only to the bracketed portion of the single-sequence chain, in this case the loop beginning and ending with strong-strong inference to the same digit.

That's how I understood it. The question is, does it mean that DAJ's lasso would always require that property? I just noticed that your own chain had that too. If that's a requirement for the "lasso", then it's weaker than the "almost-AIC" because it would only work with a subset of krakens (ones with three branches where two of them end up with the same candidate turned on). The almost-AIC way works with every kraken, no matter how many branches and end points. Of course it won't be very readable with deeper nesting. (In fact I think Krakens are almost always more readable, but sometimes I still prefer the AIC approach.)