The New Sudoku Players' Forum

[udosuk]

Thanks Ron. I didn't realise a fin could have "indirect interaction" with the elimination cell. And I agree I didn't give a lot of thoughts on the naming of this move. I thought it's "sashimi" because without the fin (r5c5) the pattern reduces to a single (r4c4) and a grouped x-wing. The word "mutant" was used because it's not an ordinary row or column swordfish.

I originally thought about using r1c36 as the fins instead. Could you fish out something with that feature?

[Ruud]

On the other hand, I bet you can do better if you work on Windoku X or DG X...

Plain DG can also do better. I did a quick neighborhood search for the two 12-clue DG puzzles posted early 2006 by gsf.

Two 11-clue Sudoku-DG's popped out:

Code: Select all

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

046000003000001000003000000200000000000540000800000700100000000000000000000000000

Code: Select all

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

046000003000001000003000000200000800000940000000000700100000000000000000000000000

Two records broken in two days

@gsf:

Thanks for the comments on the canonicalization algorithm. Because the outer r/c swaps generate a total of 6 permutations, the total number of pattern permutations is 4 (Rot) * 2 (Mir) * 4 (r/c 46) * 6 (r/c 123/789) = 192. I updated the code and the 1167 still holds.

Using a second source of 17-clue puzzles, I was able to assemble an additional batch of 2030 12-clue puzzles. None of these were equivalent to the first batch. No elevens yet. I will add them to the online collection shortly.

Ruud

[ronk]

I originally thought about using r1c36 as the fins instead. Could you fish out something with that feature?

Code: Select all

*----------------------------------------------------------------*
| 6      35789 #379    | 1      4     #359    | 2      5789  -39 |
| 4      2     *379    |*5789  *3579  *359    | 35789  6      1  |
| 3589   35789  1      |#56789  2357   26     | 3579   5789   4  |
|----------------------+----------------------+------------------|
| 379    6     *379    |*59     8      4      | 1      2      57 |
| 789    789    2      | 3     *59     1      | 6      4      57 |
| 1      4      5      | 2      6      7      | 389    89     39 |
|----------------------+----------------------+------------------|
| 2      3579   8      | 579    13579  359    | 4      1579   6  |
| 579    1      6      | 4      579    8      | 579    3      2  |
| 3579   3579   4      | 5679   123579 26     | 59     1579   8  |
*----------------------------------------------------------------*

As in this case, it is frequently possible to "shuffle" the cover to come up with different fins. We have an r1c36 fin for ...

Code: Select all

sashimi mutant swordfish c3b25\r24d1 plus fins r1c36 and r3c4, implies r1c9<>9

As before, fin r3c4 indirectly sees r1c9 via the SL in b5. The "d1" in the cover is the diagonal of Sudoku-X, and I propose "a1" for the anti-diagonal. The '1' is superfluous, but it makes the syntax consistent with that of rows, columns and boxes (e.g., r2, c3 and b2).

I didn't realise a fin could have "indirect interaction" with the elimination cell.

I always try not to use an "indirect" or remote fin but sometimes, as here, there seems to be no choice with a single-digit pattern.

I thought it's "sashimi" because without the fin (r5c5) the pattern reduces to a single (r4c4) and a grouped x-wing. The word "mutant" was used because it's not an ordinary row or column swordfish.

You're correct in using "sashimi" here (my bad) and you may be correct about the "mutant" term too. The fish I presented earlier doesn't have both rows and columns in either the base or cover sets, so I called it "franken." But strictly speaking, fin r5c5 uses the diagonal as a cover sector too ... and that's definitely "mutant."

[udosuk]

Thanks for the alternative sashimi mutant swordfish, Ron. Great fishing!

Just FYI, in the killer community we use "d\" and "d/" to represent the 2 diagonals in walkthroughs. Self-explaining and you don't have to worry about the confusion of terms like "leading/non-leading" or "diagonal/anti-diagonal".

So for example this one can be marked as "[c3b2d\] \ [r24d/]".

If you have to label them with numbers I think using d1 for d\ and d2 for d/ is more intuitive.

Edited: minor typos fixed.

[ronk]

So for example this one can be marked as "[c3b2d\] \ [r24d/]".

If you have to labelled them with numbers I think using d1 for d\ and d2 for d/ is more intuitive.

Cool, I see you spotted using d\ instead of b5 too. Considered using it, but then thought beginning with both d\ and d/ in one fish would cause a startup jolt.

Since d/ is the true diagonal, how about reversing your numbers ... for d1 for d/ and d2 for d\ -- as in "diagonal too?"

[gsf]

Thanks for the comments on the canonicalization algorithm. Because the outer r/c swaps generate a total of 6 permutations, the total number of pattern permutations is 4 (Rot) * 2 (Mir) * 4 (r/c 46) * 6 (r/c 123/789) = 192. I updated the code and the 1167 still holds.

could you post the canonicalized solution grids too
any bugs in your/my x-canon algorithm might be tickled by puzzle grids with higher and/or symmetric clue populations

[udosuk]

Since d/ is the true diagonal, how about reversing your numbers ... for d1 for d/ and d2 for d\ -- as in "diagonal too?"

There is a reason d\ always precedes d/. For you can see, the top cell of d\ is r1c1, while that of d/ is r1c9. When sorting 2 groups (e.g. lines, blocks, cages etc), the systematic way is to always sort them by the coordinates of the leftmost cell on the top row of each group. So in this case, d\ must be the 1st one, d/ the 2nd.

[Pat]

Since d/ is the true diagonal

no, d\ is the (main) diagonal (starts at r1c1);

d/ is the anti-diagonal.

[ronk]

Since d/ is the true diagonal

no, d\ is the (main) diagonal (starts at r1c1);

d/ is the anti-diagonal.

While I agree that's the way it should be, I'm sticking with the sudopedia definition until somebody officially changes it, whatever "official" means there. If the term is incorrectly defined there, perhaps usage per the definition will highlight the need for a change in the definition.

In any case, this illustrates the relative unambigousness of 'd\' and 'd/', even though I dislike using the '\' again in "base\cover" constraint-set (fish) notation.

[gsf]

Since d/ is the true diagonal

no, d\ is the (main) diagonal (starts at r1c1);

d/ is the anti-diagonal.

rats -- I got this backwards in my solver dihedral symmetry table
it a simple 2-line code fix, but reprogramming my brain is another story ...

[udosuk]

I can't believe so many people got this wrong.

If one has studied linear algebra in highschool or uni, one would know that the terms "main diagonal" or "anti-diagonal" are used for square matrices, as in this source.

The main diagonal is always from the 1st cell (r1c1) to the last cell (r[n]c[n]), and a matrix with non-zero entries only residing on the main diagonal is called a diagonal matrix, such as the identity matrix.

Obviously a sudoku grid is just a 9x9 square matrix. So there should be no ambiguity whatsoever. I wonder why Ruud has put in the incorrect definitions on the sudopedia pages in the first place.

[gsf]

I can't believe so many people got this wrong.

my problem was at least twofold:
/ slash vs \ backslash (back ~ anti)
and I (improperly) inverted a dihedral symmetry table when transcribing from gfroyle's sudoku symmetry note

[Ruud]

I wonder why Ruud has put in the incorrect definitions on the sudopedia pages in the first place.

I'm wondering about that myself, too.

Initially, I chose the main diagonal to run from top-left to right-bottom, but someone (cannot remember who) mailed me that I got it wrong, so I corrected it. The argument, if I remember it correctly, was that in Math, coordinates usually start at the bottom-left (like X & Y coordinates in a graph), so despite using different coordinates, the main diagonal still ran from LB to RT.

Glad you cleared this up, udosuk. I will have to correct multiple references to this subject (SudoCue program, solving guide, Sudopedia)...

Ruud.

[Ruud]

Came across a 13-clue Sudoku-X which starts with 41 consecutive empty cells:

Code: Select all

. . .|. . .|. . .
. . .|. . .|. . .
. . .|. . .|. . .
-----\-----/-----
. . .|. . .|. . .
. . .|. . 1|2 . .
3 . .|. 4 .|. 5 .
-----/-----\-----
. . 2|6 . 7|. . .
. . .|8 . .|. . 1
7 . .|. . .|3 4 .

000000000000000000000000000000000000000001200300040050002607000000800001700000340

Ruud

[ronk]

The argument, if I remember it correctly, was that in Math, coordinates usually start at the bottom-left (like X & Y coordinates in a graph), so despite using different coordinates, the main diagonal still ran from LB to RT.

While reference to a coordinate system may be helpful, IMO the definition should not depend on the coordinate system.