The New Sudoku Players' Forum

[tarek]

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+-------+-------+-------+
| . . . | . . 9 | . . . |
| 3 . . | . 4 . | 9 6 . |
| . 9 . | 8 3 . | . 5 . |
+-------+-------+-------+
| . 1 . | 3 . . | 8 . 5 |
| . . . | . . 2 | . . . |
| . 2 . | 7 . . | 3 . 4 |
+-------+-------+-------+
| . 8 . | 1 9 . | . 7 . |
| 2 . . | . 5 . | 1 3 . |
| . . . | . . 7 | . . . |
+-------+-------+-------+
.....9...3...4.96..9.83..5..1.3..8.5.....2....2.7..3.4.8.19..7.2...5.13......7...


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[SpAce]

Two not very interesting options. Hope to see better ones.

1) Boring: Show

Code: Select all

.-----------------------.------------.---------------------.
| 14568   456    124568 |  25   7  9 | 24     48    3      |
| 3      a5(7)  b2578   |  25   4  1 | 9      6   bc2(8)-7 |
| 47      9      247    |  8    3  6 | 247    5     1      |
:-----------------------+------------+---------------------:
| 79      1      79     |  3    6  4 | 8      2     5      |
| 45      345    345    |  9    8  2 | 67     1    d6(7)   |
| 68      2     b68     |  7    1  5 | 3      9     4      |
:-----------------------+------------+---------------------:
| 456     8      456    |  1    9  3 | 2456   7     26     |
| 2      a467*  b4679*  | c46*  5  8 | 1      3    d69*    |
| 14569   3456   134569 | c46   2  7 | 456   c48   c689    |
'-----------------------'------------'---------------------'

Code: Select all

(6-7)r8c2 = (7)r2c2
||
(6)r8c3 - (6=8)r6c3 - r2c3 = (8)r2c9
||
(6)r8c4 - (6=4)r9c4 - (4=8)r9c8 - r9c9 = (8)r2c9
||
(6)r8c9 - (6=7)r5c9

=> -7 r2c9; stte


8x8 PM:

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 8r2c9 8r2c3
       8r6c3 6r6c3
 8r2c9             8r9c9
                   8r9c8 4r9c8
                         4r9c4 6r9c4
 7r5c9                               6r5c9
 7r2c2                                     7r8c2
             6r8c3             6r8c4 6r8c9 6r8c2
------------------------------------------------
-7r2c9

2) Ridiculous: Show

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.-----------------------.-----------.-----------------.
|  14568  456   245+168 | 25+  7  9 | 24+     48  3   |
|  3      57    25(+7)8 | 25+  4  1 | 9       6   278 |
|  4-7    9     24(+7)  | 8    3  6 | 24(+7)  5   1   |
:-----------------------+-----------+-----------------:
| (7)9    1     79      | 3    6  4 | 8       2   5   |
|  45     345   345     | 9    8  2 | 67      1   67  |
|  68     2     68      | 7    1  5 | 3       9   4   |
:-----------------------+-----------+-----------------:
|  456    8     456     | 1    9  3 | 2456    7   26  |
|  2      467   4679    | 46   5  8 | 1       3   69  |
|  14569  3456  134569  | 46   2  7 | 456     48  689 |
'-----------------------'-----------'-----------------'

MUG (245)r1c347,r2c34,r3c37 using internals:

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(1)r1c3 - r9c3 = (197)r943c1 - r3c7 = (7-8)r2c9 = (8)r2c3 - ... = (7)r4c1
||
(6)r1c3 - (6=8)r6c3 - r6c1 = r1c1 - r1c8 = (8-7)r2c9 = (7)r3c7
||
(8)r1c3 - r1c8 = (8-7)r2c9 = (7)r3c7
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(7)r2c3
||
(8)r2c3 - r6c3|r2c9 = (6*)r6c3,(89*4)b9p968 - r9c4 = r8c4 - (4|*9|*6=7)r8c3 - r4c3 = (7)r4c1
||
(7)r3c37

=> -7 r3c1; stte

17x17 BTM:

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 7r2c3|               
 7r3c37 6r1c3       8r1c3       1r1c3                         8r2c3
        6r6c3 8r6c3
              8r6c1 8r1c1
                    8r1c8 8r2c9
 7r3c7                    7r2c9
                                1r9c3 1r9c1
                                      9r9c1 9r4c1
                                            7r4c1 7r3c1
                                                  7r3c7 7r2c9
                                                        8r2c9 8r2c3
                                                              8r6c3 6r6c3
                                                        8r2c9             8r9c9
                                                                          8r9c8 4r9c8
                                                                                4r9c4 4r8c4
                                                                          9r9c9             9r8c9
                                                                    6r8c3             4r8c3 9r8c3 7r8c3
 7r4c1                                                                                            7r4c3
-------------------------------------------------------------------------------------------------------
-7r3c1

3) (Added) For better or worse, this would be more like my usual style....

Code: Select all

.--------------------------.----------.------------------.
|   14568   456     124568 | 25  7  9 |  24    48   3    |
|   3      c57     d2578   | 25  4  1 |  9     6   d278  |
| ab47      9       247    | 8   3  6 | c247   5    1    |
:--------------------------+----------+------------------:
|  a79      1      a7[9]   | 3   6  4 |  8     2    5    |
|  a45      345     345    | 9   8  2 |  67    1   d67   |
|   68      2      d8(6)   | 7   1  5 |  3     9    4    |
:--------------------------+----------+------------------:
|  a45[6]   8       456    | 1   9  3 |  2456  7    26   |
|   2      d4(7)-6  47-69  | 46  5  8 |  1     3   d6(9) |
|   14569   3456    134569 | 46  2  7 |  456   48   689  |
'--------------------------'----------'------------------'

(6547,9)r7534c1,r4c3 = 7r3c1 - r2c2|r3c7 = ((7)r8c2 & (7,86,69)r2c9,r26c3,r58c9) => -6 r8c23, -9r8c3; stte

uncompressed variants: Show

(6549=7)r753c1,r4c3 - r4c3 = r3c1 - r2c2|r3c7 = r8c2&r2c9 - 7r2c2|7r5c9|8r2c9 = (7)r8c2,(86)r26c3,(69)r58c9
=> -6 r8c23, -9r8c3; stte

(69)r7c1,r4c3 = (457)r753c1|(7)r4c3 - r4c3 = r3c1 - r2c2|r3c7 = r8c2&r2c9 - 7r2c2|7r5c9|8r2c9 = (7)r8c2,(86)r26c3,(69)r58c9
=> -6 r8c23, -9r8c3; stte

10x8 pseudo-BTM: Show

Code: Select all

 6r7c1&9r4c3 5r7c1 4r7c1 7r4c3
             5r5c1 4r5c1
                   4r3c1 7r3c1
                         7r4c1 7r3c1
 7r8c2                         7r2c2
  &                            7r3c7 7r2c9
  &                                  8r2c9 8r2c3
 6r6c3                                     8r6c3
  &                                  7r5c9       6r5c9
 9r8c9                                           6r8c9
------------------------------------------------------
-6r8c23
-9r8c3

--
Edit. Hid the first two options. Minor cosmetic changes to the last one.

[SteveG48]

Code: Select all

 *-------------------------------------------------------------------------------*
 |  14568   456     124568  |  25      7       9       | 24      4-8     3       |
 |  3       57     e2578    |  25      4       1       | 9       6      f278     |
 | c47      9       247     |  8       3       6       | 247     5       1       |
 *--------------------------+--------------------------+-------------------------|
 | c79      1      d79      |  3       6       4       | 8       2       5       |
 | c45      345     345     |  9       8       2       | 67      1       67      |
 |  68      2      d68      |  7       1       5       | 3       9       4       |
 *--------------------------+--------------------------+-------------------------|
 |cb456     8       456     |  1       9       3       |a2456    7      a26      |
 |  2       467    d4679    |bc46      5       8       | 1       3     bc69      |
 |  14569   3456    134569  | a46      2       7       |a456    a48      69-8    |
 *-------------------------------------------------------------------------------*


(8=456)r9c478&(26)r7c79 - 6r7c1,r8c49 = (4579)r3457c1&(49)r8c49 - (4|9=678)r468c3 - 8r2c3 = 8r2c9 => -8 r1c8,r9c9 ; stte

[SpAce]

Hi Steve,

(8=456)r9c478&(26)r7c79 - 6r7c1,r8c49 = (4579)r3457c1&(49)r8c49 - (4|9=678)r468c3 - 8r2c3 = 8r2c9 => -8 r1c8,r9c9 ; stte

Wow! That's a fun chain! However, in this case I must admit that reading it was tedious even for me. It probably means that it's incomprehensible to most people. I actually had to put it into a matrix so I wouldn't lose my train of thought. Here it is:

13x13 TM: Show

Code: Select all

 8r9c8 4r9c8
       4r9c4 6r9c4
       4r9c7 6r9c7 5r9c7
       4r7c7       5r7c7 26r7c79
             6r8c4               4r8c4
                         6r8c9         9r8c9
                         6r7c1               45r57c1
                                             4r3c1   7r3c1
                                                     7r4c1 9r4c1
                                                           9r4c3 7r4c3
                                 4r8c3 9r8c3                     7r8c3 6r8c3
                                                                       6r6c3 8r6c3
 8r2c9                                                                       8r2c3
----------------------------------------------------------------------------------
-8r1c8
-8r9c9

That often happens with my own chains too, so nothing new there, but in those cases I prefer to offer alternate expressions to make the deciphering a bit easier (for myself as well, if I have to come back to it later). In a case like this even a memory chain might be easier to read, but a full net diagram or a matrix wouldn't be a bad idea either.

(Btw, it's a bit funny that even though I regularly provide such deciphering aids in addition to my almost guaranteed-to-be-correct chains, my notations are the only ones that get s**t from certain people. It just tells me everything about their objectivity and judgment in general. But I digress.)

About the AIC itself, I presume you were just a bit careless when writing the first link and really meant:

(8)r9c8 = (456)r9c478&(26)r7c79

That said, you know that I'm not a big fan of that either, since the second half of the split node is not an independent (direct) result of the link. It makes the split node unbalanced and a bit baffling at first glance. However, as we both know, the alternatives to write it aren't that great either, which is why I don't hugely mind if people write it like that. It's just not as easy to follow because one side of the node is basically skipping a beat. I don't think it's incorrect, per se, because the derived link 8r9c8 == 26r7c79 is of course valid, but it's not showing clearly how it happens (i.e. that it depends on the other half to happen first). To quote someone's favorite term, I think it's one form of a "riddle" (and one that I wouldn't use, even though I'm the only one accused of writing them).

A couple of alternate ways to write it:

(8=645,26)r9c487,r7c79 - 6r8c49|r7c1 = ...

(8)r9c8 = (645)r9c487 -> (26)r7c79 - 6r8c49|r7c1 = ...

(8=6*45)r9c487 - (4|5=26)r7c79 - 6r7c1|r8c9*4 = ...

Personally I'd use the first one which combines the split node into a single node. (In fact, I just did in both end nodes of my own hideous chain.) The difference is subtle but significant (at least to me), since a single node implies any necessary digit interactions within those cells while a split node doesn't. It thus avoids any imbalance and spooky action despite being almost the same.

The second option is not standard, of course, but perhaps something to think about if one wants to improve readability and still avoid a memory chain (which would actually be the easiest to follow here, I think). Then again, it's still more or less a memory chain in disguise if both sides of that implication are used for the next weak link. In that situation (like here) I'd be tempted to add parentheses around the implication to make it look like a single node, but I think it actually breaks the normal link logic, which I can't accept. A bit of redundancy would avoid those traps, but it doesn't look very smart:

(8)r9c8 = (645)r9c487 -> (645)r9c487&(26)r7c79 - 6r8c49|r7c1 = ...

Anyway, like I said, there aren't really great options to deal with that dilemma. Personally I'd still go with the first option or a memory chain (or a net diagram and/or a matrix).

Another practice that would improve the readability (at least for me) of such a very complex chain is aligning the digits and the cells in the locked sets. I know you don't like that style, and perhaps it's not always a great idea either, but in this case I think it would really help. Otherwise it's pretty difficult to see how the links work, because it requires looking at both the chain and the grid at the same time to have any idea which cells are occupied by which digits. Any hints that would help that would be welcome.

Just some very biased suggestions A great chain anyhow!

[SteveG48]

About the AIC itself, I presume you were just a bit careless when writing the first link and really meant:

(8)r9c8 = (456)r9c478&(26)r7c79

That said, you know that I'm not a big fan of that either, since the second half of the split node is not an independent (direct) result of the link. It makes the split node unbalanced and a bit baffling at first glance.

Indeed, on both counts. I was too busy hating that first multi-sector node to be careful with it.