The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|5..|.2.|
 |..6|...|4..|
 |.3.|.7.|..6|
 |---+---+---|
 |1..|2..|.9.|
 |..8|.5.|3..|
 |...|..1|...|
 |---+---+---|
 |.7.|.8.|.5.|
 |2..|1..|9..|
 |..4|...|..2|
 *-----------*


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[Ngisa]

Two steps for me today

Code: Select all

+-----------------------+------------------------+---------------+
| 479      49      79   | 5         1       6    | 8    2     3  |
| 5        1       6    | 38        2       38   | 4    7     9  |
| 8        3       2    | 49        7       49   | 5    1     6  |
+-----------------------+------------------------+---------------+
| 1        456     35   | 2         346     348  | 7    9     58 |
| 4679     2       8    | 4679      5       479  | 3    46    1  |
| 34679    4569    3579 | 346789    3469    1    | 2    46    58 |
+-----------------------+------------------------+---------------+
| 39       7       1    | 39        8       2    | 6    5     4  |
| 2       d568     35   | 1        c346    b345  | 9    38    7  |
| 369     e5689    4    | 3679      369   fa5-379| 1    38    2  |
+-----------------------+------------------------+---------------+


1): (5)r9c6 = (5-4)r8c6 = (4-6)r8c5 = (6-8)r8c2 = (8-5)r9c2 = (5)r9c6 => - 379r9c6

Code: Select all

+-------------------+------------------+---------------+
| 479     49     79 | 5       1     6  | 8    2     3  |
| 5       1      6  | g38     2     38 | 4    7     9  |
| 8       3      2  | 4       7     9  | 5    1     6  |
+-------------------+------------------+---------------+
| 1       6     c35 | 2       4    e38 | 7    9    d58 |
| 49      2      8  | 69      5     7  | 3    46    1  |
| b3479   459    79 | f3689   39    1  | 2    46    58 |
+-------------------+------------------+---------------+
| a39     7      1  | 9-3     8     2  | 6    5     4  |
| 2       58     35 | 1       6     4  | 9    38    7  |
| 6       89     4  | 7       39    5  | 1    38    2  |
+-------------------+------------------+---------------+


2): (3)r7c1 = r6c1 - (3=5)r4c3 - (5=8)r4c9 - r4c6 = r6c4 - (8=3)r2c4 => - 3r7c4; stte

Clement

[SpAce]

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Original

Code: Select all

.---------------------.----------------------.---------------.
|  479     49      79 | 5        1      6    | 8    2     3  |
|  5       1       6  |e38       2     e38   | 4    7     9  |
|  8       3       2  | 49       7      49   | 5    1     6  |
:---------------------+----------------------+---------------:
|  1       456    c35 | 2        346   d348  | 7    9    c58 |
| C4679    2       8  | 4679     5      479  | 3    46    1  |
| C34679  D4569   D79 | 346789  E3469   1    | 2    46    58 |
:---------------------+----------------------+---------------:
| B39      7       1  |f39       8      2    | 6    5     4  |
|  2     Aa56(8)  b35 | 1       f346   f345  | 9    3-8   7  |
|GB369     569-8   4  |f3679   Fg369   g3579 | 1  Gg3(8)  2  |
'---------------------'----------------------'---------------'

Kraken Cell (568)r8c2

(8)r8c2
||
(5)r8c2 - (5=3*)r8c3 - (3=58)r4c39 - r4c6 = (8,3)r2c64 - r79c4,*r8c56 = (38)r9c568
||
(6*)r8c2 - (6=39)r97c1 - r65c1 = r6c23 - r6c5 = r9c5 - (9|*6=38)r9c18

=> -8 r8c8, r9c2; stte

Code: Select all

.--------------------.-----------------------.---------------.
| 479     49      79 |  5        1      6    | 8    2     3  |
| 5       1       6  | d38       2     d38   | 4    7     9  |
| 8       3       2  |  49       7      49   | 5    1     6  |
:--------------------+-----------------------+---------------:
| 1      B456    b35 |  2       C346   c348  | 7    9    b58 |
| 4679    2       8  |  4679     5      479  | 3    46    1  |
| 34679   4569    79 |  346789   3469   1    | 2    46    58 |
:--------------------+-----------------------+---------------:
| 39      7       1  | e39       8      2    | 6    5     4  |
| 2     Aa56(8)  a35 |  1      De346   e345  | 9    3-8   7  |
|E369     569-8   4  |Ee3679  EDf369   f3579 | 1  Ef3(8)  2  |
'--------------------'-----------------------'---------------'

Kraken Cell (568)r8c2

(8)r8c2
||
(53*)r8c23 - (3=58)r4c39 - r4c6 = (8,3)r2c64 - r79c4,*r8c56 = (38)r9c568
||
(6)r8c2 - r4c2 = r4c5 - r89c5 = (6398)r9c4158

=> -8 r8c8, r9c2; stte

PS. What would you guys think of this option for the second branch:

(53*)r8c23 - (3=58)r4c39 - r4c6 = (8,3)r2c64 - r7c4 = r7c1 - r8c3*56 = (3)r8c8

The interesting bit is the (3)r8c3 acting as Schrödinger's cat in the r8c3*56 node. Weird but valid logic, isn't it?

[SteveG48]

Code: Select all

 *-----------------------------------------------------------------------------*
 | 479     49      79      | 5       1       6       | 8       2       3       |
 | 5       1       6       |a38      2      b38      | 4       7       9       |
 | 8       3       2       | 49      7       49      | 5       1       6       |
 *-------------------------+-------------------------+-------------------------|
 | 1      g456    d35      | 2      h346    c348     | 7       9      d58      |
 | 4679    2       8       | 4679    5       479     | 3       46      1       |
 | 34679   4569    79      | 346789  3469    1       | 2       46      58      |
 *-------------------------+-------------------------+-------------------------|
 |a39      7       1       | 9-3     8       2       | 6       5       4       |
 | 2      f568    e35      | 1      i346    i345     | 9       38      7       |
 | 369    f5689    4       | 3679    369     3579    | 1       38      2       |
 *-----------------------------------------------------------------------------*


(3=89*)r2c4,r7c1 - 8r2c6 = r4c6 - (8=35)r4c39 - (3=5**)r8c3 - (5|*9=68)r89c2 - 6r4c2 = r4c5 - (**5|6=34)r8c56 => -3 r7c4 ; stte

[SteveG48]

PS. What would you guys think of this option for the second branch:

(53*)r8c23 - (3=58)r4c39 - r4c6 = (8,3)r2c64 - r7c4 = r7c1 - r8c3*56 = (3)r8c8

The interesting bit is the (3)r8c3 acting as Schrödinger's cat in the r8c3*56 node. Weird but valid logic, isn't it?

That's pretty weird, all right, using 3 as being both true and not true in the same term. You're collapsing the wave function from undefined to both dead and alive at the same time. Even Schrödinger might call it a day.

I think I would prefer to write it as:

5r8c2 - (5=3)r8c3 - 3r4c3,r8c56* = (58)r4c39 - 8r4c6 = r2c6 - (8=3)r2c4 - r7c4 = r7c1 - 3r8c3*56 = 3r8c8

That kind of conceals the change in the status of 3 in r8c3. Alternately, just declare a contradiction, indicating that that branch can't occur.

[SpAce]

That's pretty weird, all right, using 3 as being both true and not true in the same term. You're collapsing the wave function from undefined to both dead and alive at the same time. Even Schrödinger might call it a day.

You're right!

I think I would prefer to write it as:

5r8c2 - (5=3)r8c3 - 3r4c3,r8c56* = (58)r4c39 - 8r4c6 = r2c6 - (8=3)r2c4 - r7c4 = r7c1 - 3r8c3*56 = 3r8c8

That kind of conceals the change in the status of 3 in r8c3.

Kind of, but not very well (results in duplication too). It would also be against my chosen habit of not storing negative memories. I think it's clearer if all memories are stored after a strong link and recalled after a weak link. Until this example I haven't had trouble staying consistent with that principle. In this case it just happens to cause some paranormal activity. I admit that your way does seem more normal because the effects of 3r8c3(alive) happen before it dies and can be considered historical facts. I guess my way needs to be interpreted as a ghost doing its thing

Alternately, just declare a contradiction, indicating that that branch can't occur.

I once suggested that as an option with troublesome kraken branches, but it wasn't received well and I wouldn't really like it myself either. It has a taste of two separate steps and seems like an easy way out anyway. Although a contradiction finish is perfectly fine logically -- nullifying that branch -- I think all branches should preferably end with the same (or functionally similar) conclusion. As far as I understand, it should be always possible as well, since any found contradiction can be moved around and used to prove pretty much anything.

But thanks for the comments and suggestions! I kind of doubt there's a clean way to do what I intended, which is why I chose a different option for that branch. Logically I don't think it really makes a difference, though, as the (3)r8c3 is in direct and obvious conflict with the final conclusion anyway, so however it's used seems a bit weird (like turning off r8c45 but not r8c8). The nature of false candidates is to cause weird and wonderful things in chaining logic.