The New Sudoku Players' Forum

[ArkieTech]

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 *-----------*
 |.3.|...|.7.|
 |7.1|...|9.8|
 |.9.|7.8|.3.|
 |---+---+---|
 |..3|.2.|7..|
 |...|8.6|...|
 |..4|.5.|2..|
 |---+---+---|
 |.5.|9.2|.1.|
 |1.6|...|8.9|
 |.4.|...|.5.|
 *-----------*


Play/Print this puzzle online

[Leren]

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*---------------------------------------------------------*
| 24568  3    258  | 1246  1469  149  | 1456  7     12456 |
| 7      26   1    | 23456 346   345  | 9     246   8     |
| 2456   9    25   | 7     146   8    | 1456  3     12456 |
|------------------+------------------+-------------------|
| 569    168  3    | 14    2     149  | 7     4689  1456  |
| 259    127  2579 | 8     13479 6    | 1345  49    1345  |
| 69     1678 4    | 13    5     1379 | 2     689   136   |
|------------------+------------------+-------------------|
| 38     5    8-7  | 9     4678  2    | 346   1    a3467  |
| 1     d27   6    | 345   347   3457 | 8    c24    9     |
| 2389   4    2789 | 16    1678  17   | 36    5    b2367  |
*---------------------------------------------------------*

(7) r7c9 = (7-2) r9c9 = r8c8 - (2=7) r8c2 => - 7 r9c3; lclste

Leren

[Cenoman]

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 +------------------------+-------------------------+------------------------+
 |  24568   3      258    |  1246    1469    149    |  1456   7      12456   |
 |  7       26     1      |  23456   346     345    |  9      246    8       |
 |  2456    9      25     |  7       146     8      |  1456   3      12456   |
 +------------------------+-------------------------+------------------------+
 |  569     168    3      |  14      2       149    |  7      4689   1456    |
 |  259     127   y2579   |  8       13479   6      |  1345  z49     1345    |
 |  69      1678   4      |  13      5       1379   |  2      689    136     |
 +------------------------+-------------------------+------------------------+
 |  38      5     a78     |  9       4678    2      | b346    1     b3467    |
 |  1      A27     6      |  345     347     3457   |  8     B2-4    9       |
 |  2389    4     x2789   |  16      1678    17     | b36     5      2367    |
 +------------------------+-------------------------+------------------------+

Kraken box (7)b7p359
(7)r7c3-(7=364)b9p137
(7-2)r8c2=(2)r8c8
(7-9)r9c3=r5c3-(9=4)r5c8
=> -4 r8c8; ste

Added: congratulations, Dan, for the puzzle pattern !

[SteveG48]

Code: Select all

 *--------------------------------------------------------------------*
 | 24568  3      258    | 1246   1469   149    | 1456   7      12456  |
 | 7      26     1      | 23456  346    345    | 9      246    8      |
 | 2456   9      25     | 7      146    8      | 1456   3      12456  |
 *----------------------+----------------------+----------------------|
 |d569    168    3      | 14     2      149    | 7      4689   1456   |
 |d259    127   e2579   | 8      13479  6      | 1345  f49     1345   |
 |d69     1678   4      | 13     5      1379   | 2      689    136    |
 *----------------------+----------------------+----------------------|
 |c38     5     c78     | 9      4678   2      |b346    1     b3467   |
 | 1     b7-2    6      | 345    347    3457   | 8   abf24     9      |
 |c2389   4      2789   | 16     1678   17     |b36     5      367-2  |
 *--------------------------------------------------------------------*


2r8c8 = (3467)b9p1357&2r8c2 - (2|7=389)b7p137 - 9r456c1 = r5c3 - (9=24)r58c8 => -2 r8c2,r9c9 ; stte

[SpAce]

Code: Select all

.------------------------.--------------------.-----------------------.
| 24568   3      258     | 1246   1469   149  | 1456    7      12456  |
| 7       26     1       | 23456  346    345  | 9       246    8      |
| 2456    9      25      | 7      146    8    | 1456    3      12456  |
:------------------------+--------------------+-----------------------:
| 569     168    3       | 14     2      149  | 7       4689   1456   |
| 259     127   c2579    | 8      13479  6    | 1345   b49     1345   |
| 69      1678   4       | 13     5      1379 | 2       689    136    |
:------------------------+--------------------+-----------------------:
| 38      5      8-7     | 9      4678   2    | 346     1     d346(7) |
| 1      a2(7)   6       | 345    347    3457 | 8     ab24     9      |
| 2389    4     d28(9)-7 | 16     1678   17   | 36      5    bc2367   |
'------------------------'--------------------'-----------------------'

(72)r8c28 = (492)r85c8,r9c9 - (9)r5c3|(7)r9c9 = (97)r9c3,r7c9 => -7 r79c3; stte

Matrix: Show

Code: Select all

5x5 TM:

       | 7b1,9n3,7r7   2r8   4c8   9r5   9n9
-------+-------------------------------------
8N2    |    7r8c2     2r8c2
8N8    |              2r8c8 4r8c8
5N8    |                    4r5c8 9r5c8
2B9    |              2r8c8             2r9c9
9C3,7B9| 9r9c3&7r7c9              9r5c3 7r9c9
-------+-------------------------------------
       |  -7r79c3

Alien 6x7-Fish (Mixed Rank 2/1): {9C3 27B9 58N8 8N2} \ {9r5 7r7 2r8 4c8 7b1 9n39} => -7 r79c3 (Rank 1)
(set triplet 2r8c8 => Rank 1 on links 2r8,7b1)

...or M-Wing: (72)r8c28 = (27)r97c9 => -7 r7c3; lclste (same as Leren's)

[SpAce]

2r8c8 = (3467)b9p1357&2r8c2 - (2|7=389)b7p137 - 9r456c1 = r5c3 - (9=24)r58c8 => -2 r8c2,r9c9 ; stte

Hi Steve! As written, I'd rather conclude: +2 r8c8. However, it suggests that some simplifications are possible. I hope you don't mind that I (again) used your chain as a case study in matrix analysis:

Original: Show

Code: Select all

10x10 TM:

    |   8n8   4b9   2b7   36b9      7r7   8b7   3b7   9c1     9r5   4c8
----+-------------------------------------------------------------------
8N8 |  2r8c8 4r8c8
2R8 |  2r8c8       2r8c2
79N7|        4r7c7        36r79c7
7N9 |        4r7c9       (3|6)r7c9 7r7c9
7N3 |                              7r7c3 8r7c3
7N1 |                                    8r7c1 3r7c1
9N1 |              2r9c1                 8r9c1 3r9c1 9r9c1
9B4 |                                                9r456c1 9r5c3
5N8 |                                                        9r5c8 4r5c8
8N8 |  2r8c8                                                       4r8c8
----+-------------------------------------------------------------------
    | +2r8c8

(I wanted to break it into as small pieces as I could, but gave up with the 36r79c7 as it proved difficult to break.)

Anyway, here we can see that the result column (first) has just one value (proving a placement) and the same set (8N8) twice in the rows and also once in the columns, suggesting redundancy. Easy first fix: drop the last row and column.

Simplification #1: Show

Changed: (9=24)r58c8 -> (9=4)r5c8 (with the corresponding conclusion)

AIC: 2r8c8 = (3467)b9p1357&2r8c2 - (2|7=389)b7p137 - 9r456c1 = r5c3 - (9=4)r5c8 => -4 r8c8

Code: Select all

9x9 TM:

    | 8n8,4c8  4b9   2b7   36b9      7r7   8b7   3b7   9c1     9r5
----+--------------------------------------------------------------
8N8 |  2r8c8  4r8c8
2R8 |  2r8c8        2r8c2
79N7|         4r7c7        36r79c7
7N9 |         4r7c9       (3|6)r7c9 7r7c9
7N3 |                               7r7c3 8r7c3
7N1 |                                     8r7c1 3r7c1
9N1 |               2r9c1                 8r9c1 3r9c1 9r9c1
9B4 |                                                 9r456c1 9r5c3
5N8 |  4r5c8                                                  9r5c8
----+--------------------------------------------------------------
    | -4r8c8

Alien 10x11-Fish (Mixed Rank 2/1): {2R8 9B4 5N8 7N1379 8N8 9N17} \ {9r5 7r7 9c1 4c8 238b7 346b9 8n8} => -4 r8c8 (Rank 1)
(set triplet 2r8c8 => Rank 1 on link 8n8)

We still have the same set (8N8) as a row and a column header, suggesting some further redundancy.

Simplification #2: Show

Changed: 9r456c1 -> 9r9c3
Changed: (3467)b9p1357&2r8c2 -> (27)r97c9

AIC: (2)r8c8 = (27)r97c9 - (2|7=389)b7p137 - (9)r9c3 = r5c3 - (9=4)r5c8 => -4 r8c8; stte

Code: Select all

7x7 TM:

   | 8n8,4c8  9n9,9r9  7r7   8b7   3b7   9b7   9r5
---+-----------------------------------------------
2B9|  2r8c8    2r9c9
7B9|           7r9c9  7r7c9
7N3|                  7r7c3 8r7c3
7N1|                        8r7c1 3r7c1
9N1|           2r9c1        8r9c1 3r9c1 9r9c1
9C3|                                    9r9c3 9r5c3
5N8|  4r5c8                                   9r5c8
---+-----------------------------------------------
   | -4r8c8

Alien 7x9-Fish (Mixed Rank 2/1): {9C3 27B9 5N8 7N13 9N1} \ {9r59 7r7 4c8 389b7 8n8 9n9} => -4 r8c8 (Rank 1)
(link triplet 2r9c9 => Rank 1 in 8n8)

That's as much as I could reduce based on the matrix alone. However, some grid analysis revealed more:

Simplification #3: Show

Changed: (2|7=389)b7p137 -> (2|7)b7p73 = (27-9)b7p59

AIC: (2)r8c8 = (27)r97c9 - (2|7)b7p73 = (27-9)b7p59 = r5c3 - (9=4)r5c8 => -4 r8c8; stte

Code: Select all

5x5 TM:

    | 8n8,4c8  9n9,9r9  7r7  8n2,9n3  9r5         
----+-------------------------------------
2B9 |  2r8c8    2r9c9
7B9 |           7r9c9  7r7c9
27B7|           2r9c1  7r7c3 27b7p59
9C5 |                         9r9c3  9r5c3
5N8 |  4r5c8                         9r5c8
----+-------------------------------------
    | -4r8c8

Alien 6x8 -Fish (Mixed Rank 2/1): {9C5 27B79 5N8} \ {9r59 7r7 4c8 8n28 9n39} => -4 r8c8 (Rank 1)
(link triplet 2r9c9 => Rank 1 in 8n8)

Conclusion:

• Matrix size: 10 -> 5.
• Strong sets used: 11 -> 6.
• A (subjectively) simpler AIC.

Matrices are a pretty nice tool, I'd say! Thanks again, Cenoman, for very helpful instruction on them!

PS. Here's what I got for Cenoman's solution proving the same elimination:

Matrix for the 7B7 kraken: Show

Code: Select all

5x5 PM/TM:

        |  4b9,4c8,8n8  36b9,7r7    9r5   9n3   8n2
--------+-------------------------------------------
7N79,9N7|  4r7c79       367b9p173
5N8     |  4r5c8                   9r5c8
9C3     |                          9r5c3 9r9c3
7B7     |                 7r7c3          7r9c3 7r8c2
2R8     |  2r8c8                               2r8c2
--------+-------------------------------------------
        | -4r8c8

Alien 7x9-Fish (Rank 2) {2R8 9C3 7B7 5N8 7N79 9N7} \ {9r5 7r7 4c8 346b9 8n28 9n3} => -4 r8c8 (Rank 2)

The fish is one size bigger and the elimination is Rank 2, but on the other hand it's not using any triplets, so the logic is inherently simpler.

[SteveG48]

2r8c8 = (3467)b9p1357&2r8c2 - (2|7=389)b7p137 - 9r456c1 = r5c3 - (9=24)r58c8 => -2 r8c2,r9c9 ; stte

Hi Steve! As written, I'd rather conclude: +2 r8c8.

Or -4 rc8c8

I tend to write it the way I did because that's the conclusion that we'd reach if it were a pincer chain. Of course in this case the ends of the chain lie on top of one another.

hope you don't mind that I (again) used your chain as a case study in matrix analysis:

Not at all. Always fun.

[SpAce]

2r8c8 = (3467)b9p1357&2r8c2 - (2|7=389)b7p137 - 9r456c1 = r5c3 - (9=24)r58c8 => -2 r8c2,r9c9 ; stte

Hi Steve! As written, I'd rather conclude: +2 r8c8.

Or -4 r8c8

Strictly speaking, it's not the same thing, even though the effect is the same (as it is with either of your original eliminations). I do, however, think it's the second best option if one insists on showing an elimination without modifying the chain. (The best option is to cut the chain and then show that elimination.)

I tend to write it the way I did because that's the conclusion that we'd reach if it were a pincer chain. Of course in this case the ends of the chain lie on top of one another.

That's one way to look at it, and it's not wrong. However, in that case I think one should list all of the direct eliminations of the fused end points, as we do with other chains too:

-4 r8c8, -2 r2c8,r8c2,r9c9

Yet, isn't it much faster and cleaner to replace the whole list (which could be much longer) with +2 r8c8? Easier to read too. Randomly picking just some (or one) from that list seems like the most confusing option to me, though the cell elimination seems the best in that case. A placement is a stronger conclusion anyway, so it makes sense to show one if the chain proves it directly. Otherwise, why not shorten the chain? If a chain proves a placement, it seems like an unnecessary step backwards to express it as an elimination (or a list of those) which leads to the same placement right after.

Of course none of this really matters. It's just a matter of aesthetics and efficiency to me. When a chain indicates that a direct placement is available, the most efficient option is almost always (here as well) to shorten the chain and show an elimination. But, for that reason too I think it's a good habit to show placements when available, because it alerts to the fact that there's probably a shorter chain available with the same effect.