The New Sudoku Players' Forum

[daj95376]

ronk and I have a new Exemplar to submit. (note: this puzzle has lots more to offer than this one pattern.)

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  Fig 4J inverse (daj95376: AKLM_1 #1 transformed)
  +-----------------------+
  | . . . | . . 1 | . 5 8 |
  | 3 . . | . . . | . 1 9 |
  | . . . | . . . | 4 . . |
  |-------+-------+-------|
  | . 3 . | . 9 8 | . . 5 |
  | 7 8 . | . . 2 | 9 3 . |
  | . . 6 | . . . | . 2 . |
  |-------+-------+-------|
  | . . . | . 6 . | . . 3 |
  | 8 . . | 1 . 9 | 6 . 2 |
  | 6 . 1 | 3 . . | . 8 . |
  +-----------------------+


Code: Select all

  +--------------------------------------------------------------+
  |  24    6     479   |  29    47    1     |  3     5     8     |
  |  3     57-4  4578  |  457   4578  6     |  2     1     9     |
  |  25    1     89    |  29    38    35    |  4     67    67    |
  |--------------------+--------------------+--------------------|
  |  1     3     2     |  46    9     8     |  7     46    5     |
  |  7     8     45    |  56-4  1     2     |  9     3     46    |
  |  9     45    6     |  457   3457  34    |  8     2     1     |
  |--------------------+--------------------+--------------------|
  |  45    2     47    |  8     6     457   |  1     9     3     |
  |  8     457   3     |  1     45    9     |  6     47    2     |
  |  6     9     1     |  3     2     47    |  5     8     47    |
  +--------------------------------------------------------------+


Code: Select all

  +-----------------------------------+   +-----------------------------------+
  |  .  /  .  |  *  X  *  |  .  /  .  |   |  .  *  .  |  /  X  /  |  .  *  .  |
  |  .  #  .  | **  X  *  |  .  #  .  |   |  . **  .  |  #  X  /  |  . **  .  |
  |  .  /  .  |  *  X  *  |  .  /  .  |   |  .  *  .  |  /  X  /  |  .  *  .  |
  |-----------+-----------+-----------|   |-----------+-----------+-----------|
  |  *  X  *  |  X  /  X  |  *  X  *  |   |  /  X  /  |  X *X  X  |  /  X  /  |
  |  .  /  .  |  #  /  /  |  .  /  .  |   |  .  *  .  | **  *  *  |  .  *  .  |
  |  *  X  *  |  X  /  X  |  *  X  *  |   |  /  X  /  |  X *X  X  |  /  X  /  |
  |-----------+-----------+-----------|   |-----------+-----------+-----------|
  |  .  /  .  |  .  /  .  |  .  /  .  |   |  .  *  .  |  .  *  .  |  .  *  .  |
  |  *  X  *  |  *  X  *  |  *  X  *  |   |  /  X  /  |  /  X  /  |  /  X  /  |
  |  .  /  .  |  .  /  .  |  .  /  .  |   |  .  *  .  |  .  *  .  |  .  *  .  |
  +-----------------------------------+   +-----------------------------------+
  Fig 4J: cccb\rrrb                       Fig 4J inverse: rrrb\cccb
  4-Fish c258b5\r468b2                    4-Fish r468b2\c258b5
  transpose = inverse                     transpose = normal
  franken jellyfish


[ronk]

Requesting suggestions and comments on a change of exemplar symbols

gsf has generously offered to add canonicalization ("c14n") of fishy exemplars and hidden patterns to his sudoku program. However, dealing with multiple character symbols is unnecessarily awkward, so symbols "*X" and "**" need to be replaced. My suggestions are '&' and '$' ... or 'e' and 'E', respectively, as illustrated below.

Code: Select all

IS NOW:
 .  .  . |  .  *  * |  *  X  *
 /  /  / |  /  X  X | *X  /  X
 .  .  . |  .  *  * |  *  X  *
---------+----------+----------
 .  .  . |  .  *  * |  *  /  .
 /  /  / |  /  X  X |  X  /  /
 .  .  . |  .  *  * |  *  /  .
---------+----------+----------
 .  .  . |  .  *  * | **  #  .
 /  /  / |  /  X  X |  X  @  #
 .  .  . |  .  *  * | **  #  .
 Fig 4W inverse: rrrc\cccb
 rccc\rrrb transpose


         Proposal A              OR           Proposal B

 .  .  . |  .  *  * |  *  X  *        .  .  . |  .  *  * |  *  X  *
 /  /  / |  /  X  X |  &  /  X        /  /  / |  /  X  X |  e  /  X
 .  .  . |  .  *  * |  *  X  *        .  .  . |  .  *  * |  *  X  *
---------+----------+----------      ---------+----------+----------
 .  .  . |  .  *  * |  *  /  .        .  .  . |  .  *  * |  *  /  .
 /  /  / |  /  X  X |  X  /  /        /  /  / |  /  X  X |  X  /  /
 .  .  . |  .  *  * |  *  /  .        .  .  . |  .  *  * |  *  /  .
---------+----------+----------      ---------+----------+----------
 .  .  . |  .  *  * |  $  #  .        .  .  . |  .  *  * |  E  #  .
 /  /  / |  /  X  X |  X  @  #        /  /  / |  /  X  X |  X  @  #
 .  .  . |  .  *  * |  $  #  .        .  .  . |  .  *  * |  E  #  .
 Fig 4W inverse: rrrc\cccb            Fig 4W inverse: rrrc\cccb
 rccc\rrrb transpose                  rccc\rrrb transpose

Remember that "*X" currently represents a candidate which is potentially eliminated even though it's a member of a base sector (unit). It's both a fish group member and a potential elimination, hence the '&'. The "**" represents a candidate eliminated whether or not any fin cell is eventually true. It's the "payoff" elimination for a finned fish, sashimi or non-sashimi, hence the '$'.

The 'e' and 'E' in the 2nd proposal? Well ... they just stand for potential "eliminations" of two different cases, with two different explanations. The '*' is a third case.

Other proposals and/or comments would be appreciated?

[ronk]

Here is a starfish (squirmbag) that is interesting for two reasons: 1) it is non-sashimi, and 2) it has diagonal, anti-diagonal and 180-degree rotation symmetry.

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..5...1..24.1....71.3..7.593..2..7.46.4.7..23.2.....1..7.4..5....2.3..7...1..2.9.   # AKLM_215(8) permuted

After SSTS and contrived elimination r8c7<>8
 7     689   5     | 689   2     3     | 1     4     68
 2     4    *689   | 1    *589   569-8 | 3    *68    7
 1     68    3     | 68    4     7     | 2     5     9
-------------------+-------------------+------------------
 3     15   *89    | 2    *15689 159-8 | 7    *68    4
 6     15    4     | 589   7     1589  | 89    2     3
*89    2     7     | 3    *689   4     | 69-8  1     5
-------------------+-------------------+------------------
*89    7    *689   | 4    *189   169-8 | 5     3     2
 45    689   2     | 5689  3     5689  | 4     7     1
 45    3     1     | 7    *58    2     |*468   9    *68

 unfinned franken starfish c1358b9\r24679 ==> r247c6, r6c7<>8

All digit 8 candidates in base set B = {c1358b9} are also candidates in cover set C = {r24679}. All candidates in B are "covered" by C. The difference set H = B\C (B minus C) -- the hidden set -- is void of candidates. Therefore, any candidates in difference set E = C\B -- the elimination set -- may be eliminated.

Without the contrived elimination r8c7<>8, r8c7 would be a fin cell, c7 would be a fin unit, and the only valid elimination would be r6c7<>8.

Many thanks to daj95376 for generating this puzzle and finding the finned franken starfish. Preferably without referring back to the pencilmarks above, see if you can find that starfish in his original (unpermuted) puzzle.

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1...5.7...5.7.9.21.97...43....3...7...1.4.2...7...2....12...36.53.2.1.4...4.7...2 # AKLM_215(8) original

elimination is r1c9<>8

starfish is r2478b2\c35679 with fin r1c4 ==> r1c9<>8

[RW]

Just asking for a little update on your fishing progress... With all the fishy patterns discovered so far, how many % of all nishio/template eliminations do you think you can explain as a fish?

RW

[daj95376]

Some hidden patterns can support a multitude of fish patterns -- often Remora. For the hidden pattern below, this fish pattern has the distinction of forcing one of its vertices to be true.

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5-Fish r39c39b5\r14c4b19   [r1c12345678],[r2c124],[r4c12478],[r78c478]
note: [r1c9]=X
+-----------------------------------+
|  *  * *X  |  *  *  *  |  *  * +X  |
|  *  *  X  |  *  .  .  |  .  .  /  |
|  X  X  /  |  X  /  /  |  /  /  /  |
|-----------+-----------+-----------|
|  *  *  X  | *X  X  X  |  *  *  X  |
|  .  .  /  |  X  /  /  |  .  .  /  |
|  .  .  /  |  X  /  /  |  .  .  /  |
|-----------+-----------+-----------|
|  .  .  /  |  *  .  .  |  *  *  X  |
|  .  .  /  |  *  .  .  |  *  *  X  |
|  /  /  /  |  X  /  /  |  X  X  /  |
+-----------------------------------+


[ronk]

Just asking for a little update on your fishing progress... With all the fishy patterns discovered so far, how many % of all nishio/template eliminations do you think you can explain as a fish?

I think the best answer to your question is what ...

after generating 1.000.000 random sudokus, filtering leaves only about 20 puzzles that can be solved with templates but not with any kind of Ultimate Fish patterns (opposed to ~500 for every 10.000 puzzles before I included Ultimate Fish).

If I interpret Obi-Wahn's statement correctly, that would be approximately (1-(20/(100*500)) or 99.96%. daj95376's solver might be close to being able to confirm that number.

Unfortunately finding the larger fish manually, particularly the mutants, remains very difficult.

Sorry for the delayed response. I somehow missed your post until yesterday.[/quote]

[ronk]

For the hidden pattern below, this fish pattern has the distinction of forcing one of its vertices to be true.

Code: Select all

5-Fish r39c39b5\r14c4b19   [r1c12345678],[r2c124],[r4c12478],[r78c478]
note: [r1c9]=X
+-----------------------------------+
|  *  * *X  |  *  *  *  |  *  * +X  |
|  *  *  X  |  *  .  .  |  .  .  /  |
|  X  X  /  |  X  /  /  |  /  /  /  |
|-----------+-----------+-----------|
|  *  *  X  | *X  X  X  |  *  *  X  |
|  .  .  /  |  X  /  /  |  .  .  /  |
|  .  .  /  |  X  /  /  |  .  .  /  |
|-----------+-----------+-----------|
|  .  .  /  |  *  .  .  |  *  *  X  |
|  .  .  /  |  *  .  .  |  *  *  X  |
|  /  /  /  |  X  /  /  |  X  X  /  |
+-----------------------------------+


I see no starfish pattern to support that placement. Indeed, if we have a fish theory to support any placement, I'm not aware of it. (My one trial balloon at a fishy placement was immediately shot down, ironically by you IIRC.)

However, there is a jellyfish that eliminates candidates in c9 such that r1c9 is a hidden single.

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 *  *  X |  *  .  . |  .  . +X
 *  *  X |  *  .  . |  .  .  /
 X  X  / |  X  /  / |  /  /  /
---------+----------+----------
 *  *  X | *X  X  X |  *  *  *
 .  .  / |  X  /  / |  .  .  /
 .  .  / |  X  /  / |  .  .  /
---------+----------+----------
 .  .  / |  *  .  . |  *  *  *
 .  .  / |  *  .  . |  *  *  *
 /  /  / |  X  /  / |  X  X  /
 mutant jellyfish r39c3b5\r4c4b19 ==> r12c124, r4c124789, r78c4789<>X

And one might first spot this swordfish ...

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 *  *  X |  *  .  . |  .  . +X
 *  *  X |  *  .  . |  .  .  /
 X  X  / |  X  /  / |  /  /  /
---------+----------+----------
 *  *  X | *X  X  X |  *  *  *
 .  .  / |  X  /  / |  .  .  /
 .  .  / |  X  /  / |  .  .  /
---------+----------+----------
 .  .  / |  *  .  . |  .  .  .
 .  .  / |  *  .  . |  .  .  .
 /  /  / |  *  /  / |  X  X  /
 mutant swordfish r3c3b5\r4c4b1 ==> r12c124, r4c124789, r789c4<>X

... for r4c9<>X. It also causes r9c4<>X creating locked candidates r9\b9 for r78c9<>X. As with the jellyfish, these cascading steps leave r1c9 as a hidden single.

[Mauricio]

Here is a real world example for the previous fish, though the fish eliminations don't solve the puzzle:

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

[ronk]

Here is a real world example for the previous fish, though the fish eliminations don't solve the puzzle

Mauricio, I didn't know you were a fisherman.

I don't see your fish, so would you please post the pencilmarks

[Mauricio]

The fish I talk about is the fish that daj and you talk about in the previous 2 posts, on 9's, or am i mistaken?

Code: Select all

 *  *  X |  *  .  . |  .  . +X
 *  *  X |  *  .  . |  .  .  /
 X  X  / |  X  /  / |  /  /  /
---------+----------+----------
 *  *  X | *X  X  X |  *  *  *
 .  .  / |  X  /  / |  .  .  /
 .  .  / |  X  /  / |  .  .  /
---------+----------+----------
 .  .  / |  *  .  . |  *  *  *
 .  .  / |  *  .  . |  *  *  *
 /  /  / |  X  /  / |  X  X  /
 mutant jellyfish r39c3b5\r4c4b19 ==> r12c124, r4c124789, r78c4789<>X

And one might first spot this swordfish ...

Code: Select all

 *  *  X |  *  .  . |  .  . +X
 *  *  X |  *  .  . |  .  .  /
 X  X  / |  X  /  / |  /  /  /
---------+----------+----------
 *  *  X | *X  X  X |  *  *  *
 .  .  / |  X  /  / |  .  .  /
 .  .  / |  X  /  / |  .  .  /
---------+----------+----------
 .  .  / |  *  .  . |  .  .  .
 .  .  / |  *  .  . |  .  .  .
 /  /  / |  *  /  / |  X  X  /
 mutant swordfish r3c3b5\r4c4b1 ==> r12c124, r4c124789, r789c4<>X

My puzzle has givens in all '/' cells, and in 2 more '.' cells, and has no 9's as a given, so

Code: Select all

.---------------------------.---------------------------.---------------------------.
| 134578-9 135678-9 *489    | 25678-9  2589     679     | 34789    34789    389     |
| 34578-9  35678-9  *489    | 5678-9   1        679     | 34789    34789    2       |
| *789     *789     2       | *789     3        4       | 1        5        6       |
:---------------------------+---------------------------+---------------------------:
| 13478-9  12378-9  *489    | *1356-9  *59      *1369   | 23568-9  12368-9  358-9   |
| 139      1239     5       | *1369    7        8       | 2369     12369    4       |
| 1389     1389     6       | 1359     4        2       | 3589     1389     7       |
:---------------------------+---------------------------+---------------------------:
| 589      589      1       | 23478-9  289      379     | 23456789 2346789  3589    |
| 6        589      7       | 12348-9  289      139     | 234589   23489    3589    |
| 2        4        3       | *78-9    6        5       | *789     *789     1       |
'---------------------------'---------------------------'---------------------------'

[ronk]

The fish I talk about is the fish that daj and you talk about in the previous 2 posts, on 9's, or am i mistaken?
My puzzle has givens in all '/' cells, and in 2 more '.' cells, and has no 9's as a given, so

Code: Select all

.---------------------------.---------------------------.---------------------------.
| 134578-9 135678-9 *489    | 25678-9  2589     679     | 34789    34789    389     |
| 34578-9  35678-9  *489    | 5678-9   1        679     | 34789    34789    2       |
| *789     *789     2       | *789     3        4       | 1        5        6       |
:---------------------------+---------------------------+---------------------------:
| 13478-9  12378-9  *489    | *1356-9  *59      *1369   | 23568-9  12368-9  358-9   |
| 139      1239     5       | *1369    7        8       | 2369     12369    4       |
| 1389     1389     6       | 1359     4        2       | 3589     1389     7       |
:---------------------------+---------------------------+---------------------------:
| 589      589      1       | 23478-9  289      379     | 23456789 2346789  3589    |
| 6        589      7       | 12348-9  289      139     | 234589   23489    3589    |
| 2        4        3       | *78-9    6        5       | *789     *789     1       |
'---------------------------'---------------------------'---------------------------'

Sorry, I think I was looking for a 5-fish as the smallest fish.

Mauricio, that's a very clever way to construct a test case for a theoretical pattern. It may not be the smallest fish on the "grid", but it is certainly valid.

[Mauricio]

I think the purpose of this thread is not to give puzzles that can be solved with fishes, but to give the fishy patterns.
Anyway, the following puzzle is very interesting (I've been toying around with this pattern since a few days ago):

Code: Select all

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


It is a difficult puzzle, but

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Franken JellyFish r3467\c159b5    [r1289c159],[r46c5],[r5c14569]<>9
Franken JellyFish c3467\r159b5    [c1289r159],[c46r5],[c5r14569]<>9

Note that the pencilmarks of the 9's is fully symmetric, so if you spot one of those Frankes Jellyfish, then you should spot the other. Those eliminations reduce the puzzle to singles, and I think there is no easier way to do that.

[daj95376]

In the PM below, the elimination [r2c3]<>7 appears to be Sashimi because of the fin cell in [c1]. In fact, several fish patterns are degenerate for this elimination with [r3c1] as a fin cell. However, there are two fish patterns that aren't degenerate. Suddenly, the definition of Sashimi has become very grey for me. Is Sashimi based on the candidate grid or is it based on the fish/hidden pattern grid used?

Code: Select all

PM sdaj_09_20a:

 *-----------------------------------------------------------*
 | 5     1     4     | 6     378   2     | 78    9     378   |
 | 9     6     78    | 58    1     37    | 2578  2358  4     |
 | 37    378   2     | 9     578   4     | 6     58    1     |
 |-------------------+-------------------+-------------------|
 | 37    4     6     | 1     9     378   | 2578  28    578   |
 | 1     5     9     | 2     6     78    | 3     4     78    |
 | 2     378   378   | 37    4     5     | 9     1     6     |
 |-------------------+-------------------+-------------------|
 | 8     2     5     | 37    37    1     | 4     6     9     |
 | 4     9     13    | 58    2     6     | 158   7     358   |
 | 6     37    137   | 4     58    9     | 158   358   2     |
 *-----------------------------------------------------------*

+-----------------------------------+
|  .  .  .  |  .  7  .  |  7  .  7  |
|  .  . -7  |  .  .  7  |  7  .  .  |
| #7  7  .  |  .  7  .  |  .  .  .  |
|-----------+-----------+-----------|
|  7  .  .  |  .  .  7  |  7  .  7  |
|  .  .  .  |  .  .  7  |  .  .  7  |
|  .  7  7  |  7  .  .  |  .  .  .  |
|-----------+-----------+-----------|
|  .  .  .  |  7  7  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  7  .  |
|  .  7  7  |  .  .  .  |  .  .  .  |
+-----------------------------------+


Code: Select all

(non-Sashimi) Franken Swordfish c16b6\r245   -or- equivalent
(non-Sashimi) mutant  Swordfish r6c16\r2b45
+-----------------------------------+
|  /  .  .  |  .  .  /  |  .  .  .  |
|  .  *  *  |  *  *  .  |  *  *  *  |
|  /  .  .  |  .  .  /  |  .  .  .  |
|-----------+-----------+-----------|
|  .  *  *  |  *  *  .  |  .  .  .  |
|  .  *  *  |  *  *  .  |  .  .  .  |
|  /  .  .  |  .  .  /  |  /  /  /  |
|-----------+-----------+-----------|
|  /  .  .  |  .  .  /  |  .  .  .  |
|  /  .  .  |  .  .  /  |  .  .  .  |
|  /  .  .  |  .  .  /  |  .  .  .  |
+-----------------------------------+


Yes, there is also a Sashimi(?) Jellyfish c1679\r1245 for this elimination. In fact, I was investigating it when I ran across the Franken and mutant Swordfish.

[Edit: removed fin cell and elimination cell from fish pattern because it was misleading.]

[ronk]

Suddenly, the definition of Sashimi has become very grey for me. Is Sashimi based on the candidate grid or is it based on the fish/hidden pattern grid used?

Code: Select all

+-----------------------------------+
|  .  .  .  |  .  7  .  |  7  .  7  |
|  .  . -7  |  .  .  7  |  7  .  .  |
| #7  7  .  |  .  7  .  |  .  .  .  |
|-----------+-----------+-----------|
|  7  .  .  |  .  .  7  |  7  .  7  |
|  .  .  .  |  .  .  7  |  .  .  7  |
|  .  7  7  |  7  .  .  |  .  .  .  |
|-----------+-----------+-----------|
|  .  .  .  |  7  7  .  |  .  .  .  |
|  .  .  .  |  .  .  .  |  .  7  .  |
|  .  7  7  |  .  .  .  |  .  .  .  |
+-----------------------------------+


Code: Select all

(non-Sashimi) Franken Swordfish c16b6\r245   -or- equivalent
(non-Sashimi) mutant  Swordfish r6c16\r2b45
+-----------------------------------+
|  /  .  .  |  .  .  /  |  .  .  .  |
|  .  *  *  |  *  *  .  |  *  *  *  |
|  /  .  .  |  .  .  /  |  .  .  .  |
|-----------+-----------+-----------|
|  .  *  *  |  *  *  .  |  .  .  .  |
|  .  *  *  |  *  *  .  |  .  .  .  |
|  /  .  .  |  .  .  /  |  /  /  /  |
|-----------+-----------+-----------|
|  /  .  .  |  .  .  /  |  .  .  .  |
|  /  .  .  |  .  .  /  |  .  .  .  |
|  /  .  .  |  .  .  /  |  .  .  .  |
+-----------------------------------+


A fish is or is not sashimi based on the result of a fish pattern applied to an actual candidate grid. In this case, although the exemplar is non-sashimi, the actual fish is sashimi.

[ronk]

ronk's GFF (the Z method in my solver) labels these finned

Code: Select all

fish 7 3 1/-  1X  finned franken sword       c16b6\r2345 ==> r2c3<>7
fish 7 3 1/-  1X  finned mutant sword        r6c16\r2b145 ==> r2c3<>7


from the output using these options

Code: Select all

-v2 -q-XYKO+Z

As those fish are both sashimi (as my current GFF reports), the code I supplied to gsf obviously has a bug. I will correct the bug ASAP.

My GFF uses the same definition that ...

If, after all the fin cells of a fish are removed,

either 1) all the candidates of one base unit (aka sector, house) are entirely within one cover unit,

or 2) all the candidates of one cover unit are entirely within one base unit,

then the finned fish is sashimi.