The New Sudoku Players' Forum

[mith]

Ah, good catch on box 9. I had made the other eliminations when checking in SE, but totally missed those! (Still 8.5, but I'll have to keep them in mind for future attempts.)

If you make the pm eliminations before placing the 6, the 6 is just a consequence of that. The shading is just another way to visualize the same eliminations.

[SpAce]

Ah, good catch on box 9. I had made the other eliminations when checking in SE, but totally missed those!

Glad to hear you agree they were valid. They're surprisingly helpful, too.

(Still 8.5, but I'll have to keep them in mind for future attempts.)

The SE score can be misleading because SE doesn't use ALSs in its chains. Some high 8s can be quite easy with relatively simple ALSs, like here.

If you make the pm eliminations before placing the 6, the 6 is just a consequence of that.

Good point. I missed that.

[mith]

Yeah, I can follow the logic of the chains using ALS, I'm just no good at spotting them. Should have explored a bit more with YZF's solver. (It gives the same eliminations as an ALS XY-Wing and a Skyscraper.)

[SpAce]

Yeah, I can follow the logic of the chains using ALS, I'm just no good at spotting them.

I don't think big ALS nodes are easy to spot and use in chains for anyone. That's why I avoid them as much as possible. In most cases there are simpler options available using the corresponding AHS nodes, like here. I usually try to find the option that uses the least resources, such as digits, cells, or candidates. I think it makes the logic easier to follow, too.

Should have explored a bit more with YZF's solver. (It gives the same eliminations as an ALS XY-Wing and a Skyscraper.)

The first one doesn't surprise me, but there's no simple Skyscraper available here. There's a Grouped Skyscraper (aka Finned X-Wing), though. It should be marked with the prefix, and I think it should be after the simple Kite in the hierarchy.

Hodoku also offers the ALS-XY-Wing for the first elimination, but it's an example of where AHS logic is much simpler. It's very clear if you compare the matrices. The first one is the ALS-XY-Wing and the second is my AHS-chain:

8x8 TM: Show

Code: Select all

 3r4c7 6r4c7
 . . . 6r1c7 8r1c7
 . . . . . . 8r1c4 2r1c4
 . . . . . . 8r1c6 . . . 4r1c6
 . . . . . . . . . 2r1c8 4r1c8 5r1c8
 3r2c8 . . . . . . . . . . . . 5r2c8 1r2c8
 3r8c8 . . . . . . . . . . . . 5r8c8 1r8c8 7r8c8
 3r7c8 . . . . . . . . . . . . . . . . . . 7r7c8
================================================
-3r5c8

(3=6)r4c7 - (6=8245)r1c7468 - (5=173)r278c8 => -3 r5c8

5x5 TM: Show

Code: Select all

 3r4c7 6r4c7
 . . . 6r1c7 6r1c2
 . . . . . . 5r1c2 5r1c8
 2r5c8 . . . . . . 2r1c8 2r3c8
 4r5c8 . . . . . . 4r1c8 4r3c8
==============================
-3r5c8

(3=6)r4c7 - r1c7 = (6-5)r1c2 = (524)r135c8 => -3 r5c8

(In Denis' system the first one is a braid[8] and the second one is a whip[5], I think, so the latter is simpler in both type and length in that point of view as well.)

[mith]

The first one doesn't surprise me, but there's no simple Skyscraper available here. There's a Grouped Skyscraper (aka Finned X-Wing), though. It should be marked with the prefix, and I think it should be after the simple Kite in the hierarchy.

Yes, there is another step in between that gets it to the Skyscraper. (It finds the Kite, but uses an Almost Locked Pair first, and then the Skyscraper is available.)

I suspect looking manually I would still find the Finned X-Wing first? But that's just because I am clearly obsessed with fish patterns...

Your chain was very clear and easy to follow, I agree that it's much clearer than the ALS XY-Wing.

[SpAce]

Yes, there is another step in between that gets it to the Skyscraper. (It finds the Kite, but uses an Almost Locked Pair first, and then the Skyscraper is available.)

Ok!

I suspect looking manually I would still find the Finned X-Wing first? But that's just because I am clearly obsessed with fish patterns...

Well, a Kite is a fish (Finned Mutant X-Wing) too But yeah, I understand. That's why all hierarchies are more or less subjective. I tend to see simple X-Chains first because I'm more of a chain-person, and bilocation strong links catch my eye before grouped ones. That said, Finned X-Wings are sometimes an exception for me too.

Your chain was very clear and easy to follow, I agree that it's much clearer than the ALS XY-Wing.

Glad we agree

[StrmCkr]

Agreeded space had them in my first attenpt noting 3 cells for 2 =8 in the bottom corner r7c9
and placing 2 in that cell left not eough digits for cells for red which is how i attained r3c9 =8 and something similar for the other but coukdnt explain it solidly. Subset counting is roughly my answer for it.

But itsnin the air atm, ill look back at after i finish my coding updates finally figured out how to do aic for my solver got x chains to work awsum under 100 lines of code woot woot.

[yzfwsf]

Hi mith:Tks.
Using this puzzle, I fixed a bug in the MSLS code, and now my solver can find MSLS.

MSLS.png (43.67 KiB) Viewed 605 times

[SpAce]

Thanks for that, yzfwsf. I had a hard time seeing the MSLS, but your image made it clear as a day. So the sets are:

grid: Show

Code: Select all

          \46                \28[6]           \48               \24
.--------------------------.--------------------------.-----------------------.
| 7       *456      1      | *28      3       *48     |  68     *245     9    | \5
| 245      8        249    |  7       1249     6      |  2345    135-24  123  |
| 246     *469      3      | *1289    5       *1489   |  7      *124     68   | \19
:--------------------------+--------------------------+-----------------------:
| 3568     1357-6   678    |  4       18-6     2      |  36      9       367  |
| 248-36  *349-6    248-69 | *3689    7       *389    |  1      *234     5    | \39[6] \b5:[6]
| 2346     1379-46  24679  |  139-6   19-6     5      |  2346    8       2367 |
:--------------------------+--------------------------+-----------------------:
| 1       *3467     468-7  |  5       2468-9  *34789  | *2389   *37-2   *238  | \379
| 368      2        678    |  139-68  1689     1379-8 |  359-8   1357    4    |        \b9:28
| 9       *347      5      | *1238    248-1   *13478  | *238     6      *1238 | \137
'--------------------------'--------------------------'-----------------------'

22x22 {135N2468 7N26789 9N24679 \ 5r1 19r3 39r5 6[r5|c4|b5] 379r7 137r9 46c2 28c4 48c6 24c8 28b9} => 21 elims (incl. 2 x Rank 1)

Right? Note that I've added the Rank 1 cannibal elimination -6r5c2 because it's hit by r5 (one of the three alternate covers for 6r5c4) and c2. Wouldn't you agree?

Btw, once again Multifish is the simpler POV (at least for me):

Code: Select all

                              \[5n]
  \35n    \46       \57n      \28[6]   \79n    \48             \24
.---------------------------.--------------------------.---------------------.
|  7       456       1      |  28       3       48     | 68     245     9    | *2468
|  245     8^        249    |  7        1249    6^     | 2345   135-24  123  |        \b3:68
| \246     469       3      |  1289     5       1489   | 7      124     68   | *2468
:---------------------------+--------------------------+---------------------:
|  3568    1357-6    678    |  4^       18-6    2^     | 36     9       367  |
| \2468-3  3469     \2468-9 | \6-389    7       389    | 1      234     5    | *2468  \b5:[6]
|  2346    1379-46   24679  |  139-6    19-6    5      | 2346   8^      2367 |
:---------------------------+--------------------------+---------------------:
|  1       3467     \468-7  |  5       \2468-9  34789  | 2389   37-2    238  | *2468
|  368     2^        678    |  139-68   1689    1379-8 | 359-8  1357    4^   |        \b9:28
|  9       347       5      |  1238    \248-1   13478  | 238    6^      1238 | *248
'---------------------------'--------------------------'---------------------'

MF (2468 R): 19x19 {2468R1357 248R9 \ 46c2 28c4 6[c4|b5]|5n4 48c6 24c8 68b3 28b9 35n1 57n3 79n5} => 21 elims

the same in columns: Show

Code: Select all

  *2468             *2468             *2468            *2468          *268
.---------------------------.-------------------------.---------------------.
|  7       456       1      | 28       3       48     | 68     245     9    |
|  245     8^        249    | 7        1249    6^     | 2345   135-24  123  | \24   \b3:68
| \246     469       3      | 1289     5       1489   | 7      124     68   | \n1
:---------------------------+-------------------------+---------------------:
|  3568    1357-6    678    | 4^       168     2^     | 36     9       367  | \68
| \2468-3  3469     \2468-9 | 3689     7       389    | 1      234     5    | \n13
|  2346    1379-46   24679  | 139-6    169     5      | 2346   8^      2367 | \246
:---------------------------+-------------------------+---------------------:
|  1       3467     \468-7  | 5       \2468-9  34789  | 2389   37-2    238  | \n35
|  368     2^        678    | 139-68   1689    1379-8 | 359-8  1357    4^   | \68   \b9:28
|  9       347       5      | 1238    \248-1   13478  | 238    6^      1238 | \n5
'---------------------------'-------------------------'---------------------'

MF (2468 C): 19x19 {2468C1357 248C9 \ 24r2 68r4 246r6 68r8 68b3 28b9 3n1 5n13 7n35 9n5} => 16 elims

[yzfwsf]

Wouldn't you agree?

Yes you are right.
Because of a bug in the code, the solver did not find the autophagy deletion number. Thanks for providing it. Now I am correcting the code.

MSLS.png (87.67 KiB) Viewed 587 times

[SpAce]

Because of a bug in the code, the solver did not find the autophagy deletion number. Thanks for providing it. Now I am correcting the code.

Great! Btw, I like the term 'autophagy'. I haven't seen it used in this context, but it makes much more sense than cannibalism. (It used to be autocannibalism, which actually made sense, but I guess it was dropped because it's a long word.)

[Cenoman]

Last night, I had found another MSLS manually. I am neither boasting, nor claiming anteriority.
Note that, by chance, the MSLS I found was the dual of yzfwsf's. The post is aimed to convice those who are not yet, that MSLS is also a resolution tool for manual solvers.

The likeness of the pattern with MSLS has been noticed by mith "This sort of argument is equivalent to MSLS".
It seems normal to try with the even digits as the "base" in the even rows:

Code: Select all

 +---------------------------+--------------------------+------------------------+
 |  7       456      1       |  28      3       48      |  68     245     9      |
 | <245     8       <249     |  7      <1249    6       | <2345   12345  <123    | 24
 |  246     469      3       |  1289    5       1489    |  7      124     68     |
 +---------------------------+--------------------------+------------------------+
 | <3568    13567   <678     |  4      <168     2       | <36     9      <367    | 68
 |  23468   3469     24689   |  3689    7       389     |  1      234     5      |
 | <2346    134679  <24679   |  1369   <169     5       | <2346   8      <2367   | 246
 +---------------------------+--------------------------+------------------------+
 |  1       3467     4678    |  5       24689   34789   |  2389   237     238    |
 | <368     2       <678     |  13689  <1689    13789   | <3589   1357    4      | 68
 |  9       347      5       |  1238    1248    13478   |  238    6       1238   |
 +---------------------------+--------------------------+------------------------+
    35               79                 19                 35(9)          (1)37

19 cells, 19 certain links, but two troublesome cells: r2c9 & r8c7. The issue is: 1r2c9 and 9r8c7 are not linked (two more links needed)
In such case, try to add cells. Here the four purple cells seem to be useful items.

Code: Select all

 +---------------------------+--------------------------+------------------------+
 |  7       456      1       |  28      3       48      |  68     245     9      |
 | <245     8       <249     |  7      <1249    6       | <2345   135-24 <123    | 24
 |  246     469      3       |  1289    5       1489    |  7      124     68     |
 +---------------------------+--------------------------+------------------------+
 | <3568    1357-6  <678     |  4      <168     2       | <36     9      <367    | 68
 |  2468-3  3469     2468-9  |  3689    7       389     |  1      234     5      |
 | <2346    1379-46 <24679   |  139-6  <169     5       | <2346   8      <2367   | 246
 +---------------------------+--------------------------+------------------------+
 |  1       3467     468-7   |  5       2468-9  34789   | <2389   37-2   <238    |
 | <368     2       <678     |  139-68 <1689    1379-8  | <359-8  1357    4      | 68
 |  9       347      5       |  1238    248-1   13478   | <238    6      <1238   |
 +---------------------------+--------------------------+------------------------+
    35               79                 19                 359            137
                                                                   28b9

Digits 1,3,9 in cells r79c79 are linked by the column links 39c7, 13 c9
Provisional count: 23 cells, 21 links. Digits added in cells r79c79 and missing links are 2,8. They are linked by box links 2b9, 8b9
Hence, the ultimate balance: 23 cells, 23 links.

MSLS:
23 cell truths: r246c13579, r8c1357, b9p1379
23 links: 24r2, 68r4, 246r6, 68r8, 35c1, 79c3, 19c5, 359c7, 137c9, 28b9
16 eliminations: -24 r2c8, -6 r4c2, -46 r6c2, -6 r6c4, -68 r8c4, -8 r8c6, -3 r5c1, -9 r5c3, -7 r7c3, -9 r7c5, -1 r9c5, -2 r7c8, -8r8c7

After running basics, the PM is the same as after the other MSLS (26 given or solved cells, 181 candidates). End of the solution already given by SpAce.

[SpAce]

Very nice, Cenoman! That corresponds with the column-based MF (2468 C). So, we now have four variants of the pattern. I guess that should be enough, but since this is such a nice example and a good practice case, I yearn for more. Can someone write a Multifish with the odd digit set? I briefly tried, but it seemed more challenging so I gave up.

[yzfwsf]

Hi Cenoman:
In fact, my solver will find these 2 equivalent MSLS.

MSLS.png (69.33 KiB) Viewed 557 times

[Cenoman]

In fact, my solver will find these 2 equivalent MSLS.

I have never doubted that it would
I was just proud to have found mine without help of any solver.