The New Sudoku Players' Forum

[daj95376]

_

This is a puzzle posted by David P. Bird. I'm attempting to make sense of the (possible ?) multi-fish present in this puzzle.

Code: Select all

 (Example 1) MS-NS: r35679c1678 (20 cells)
 +--------------------------------------------------------------------------------+
 |  1       24579   2379    |  246     245     24567   |  3467    8       369     |
 |  34578   4578    378     |  1468    1458    9       |  2       3467    136     |
 |  4789    24789   6       |  1248    3       1247    |  147     479     5       |
 |--------------------------+--------------------------+--------------------------|
 |  2       1479    1379    |  13469   149     8       |  13567   35679   1369    |
 |  3489    1489    5       |  123469  7       12346   |  1368    2369    123689  |
 |  3789    6       13789   |  5       129     123     |  1378    2379    4       |
 |--------------------------+--------------------------+--------------------------|
 |  5689    12589   4       |  7       12589   1235    |  3568    2356    2368    |
 |  5678    2578    278     |  2348    2458    2345    |  9       1       2368    |
 |  589     3       1289    |  1289    6       125     |  458     245     7       |
 +--------------------------------------------------------------------------------+
 # 180 eliminations remain


Code: Select all

                               [r3c24,r5c249,r6c35,r7c259,r9c34]   -- 12 cells
<1> in r35679[c6],r356 [c7] or      *    ***    **    ***    **
<2> in r35679[c6],r5679[c8] or     **     **     *    ***    **
<8> in r35679[c1],r5679[c7] or     **    * *    *     ***    **
<9> in r35679[c1],r356 [c8] or     *     ***    **    **     **


All candiates for <1289> in base set r35679 are indicated in the above table. Also, each value can be considered to be covered by two columns and a subset of the 12 cells listed. This means that the 12 cells must contain the three remaining truths for each of the four values. This accounts for the following eliminations:

Code: Select all

<>3  r5c49,r6c3,r7c9
<>4  r35c24
<>5  r7c25
<>6  r5c49,r7c9
<>7  r3c2,r6c3


This leaves the eliminations for <1289> outside the base set but in the respective cover columns:

Code: Select all

<>1  r4c7
<>2  r18c6
<>8  r28c1   (missing r5c1 found by Templates)
<>9  r4c8


Note: I am not certain about my comment in dark-red being true in the general case. I just know that it's true in this instance.

Any help would be appreciated!

[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
| 1      *24579  *2379     |*246    *245     4567-2   | 3467    8      *369      |
| 3457-8 *4578   *378      |*1468   *1458    9        | 2       3467   *136      |
| 4789    289-47  6        | 128-4   3       1247     | 147     479     5        |
|--------------------------+--------------------------+--------------------------|
| 2      *1479   *1379     |*13469  *149     8        | 3567-1  3567-9 *1369     |
| 3489    189-4   5        | 129-346 7       12346    | 1368    2369    1289-36  |
| 3789    6       189-37   | 5       129     123      | 1378    2379    4        |
|--------------------------+--------------------------+--------------------------|
| 5689    1289-5  4        | 7       1289-5  1235     | 3568    2356    28-36    |
| 567-8  *2578   *278      |*2348   *2458    345-2    | 9       1      *2368     |
| 589     3       1289     | 1289    6       125      | 458     245     7        |
*--------------------------------------------------------------------------------*

The PM shows the following MSLS I found for this puzzle: MSLS 1 : Base 1289; r1248 c23459 : 20 Links; 29r1 18r2 19r4 28r8 ; 457c2 37c3 346c4 45c5 36c9 ;

The Base (or Home or Row) digits are 1289 and the Roof (or Away or Column) digits are the complement of the Base ie 34567.

The * cells form a 4 row x 5 column pattern and the 20 cell truths are matched by the 8 row links in digits 1289 and the 12 column links in digits 34567.

This means that you can eliminate all 1289's in Rows 124 and 8 but not in columns 2345 and 9.

Similarly you can eliminate all 34567's in columns 2345 and 9 but not in rows 124 and 8.

This leads to the 21 eliminations as marked.

A second structure MSLS 2 : Base 1289; c1678 r35679 : 20 Links; 89c1 12c6 18c7 29c8 ; 47r3 346r5 37r6 356r7 45r9 ; can also be found leading to (presumably) the same 21 eliminations.

Bypassing the MSLS routine I found the following "conventional" Multifish for this puzzle:

Multifish 1.1: 20 Truths = { 1289R3 1289R5 1289R6 1289R7 1289R9 } 20 Links = { 1c67 2c68 8c17 9c18 3n24 5n249 6n35 7n259 9n34 }
Multifish 1.2: 20 Truths = { 34567R1 34567R2 34567R4 34567R8 } 20 Links = { 3c349 4c245 5c25 6c49 7c23 1n67 2n18 4n78 8n16 }
Multifish 2.1: 20 Truths = { 1289C2 1289C3 1289C4 1289C5 1289C9 } 20 Links = { 1r24 2r18 8r28 9r14 3n24 5n249 6n35 7n259 9n34 }
Multifish 2.2: 20 Truths = { 34567C1 34567C6 34567C7 34567C8 } 20 Links = { 3r567 4r359 5r79 6r57 7r36 1n67 2n18 4n78 8n16 }

The first of these leads to the same 21 eliminations as the MSLS and the others presumably lead to the same (or a subset of) the same 21 eliminations.

<Edit> Improved presentation of Multifish details and removed redundant logic sets.

Leren

[daj95376]

_

Bypassing the MSLS routine I found the following "conventional" Multifish for this puzzle:

Multifish 1.1: 20 Truths = { 1R35679 2R35679 8R35679 9R35679 } 20 Links = { 1c67 2c68 8c17 9c18 3n24 5n249 6n35 7n259 9n34 }
Multifish 2.1: 20 Truths = { 1C23459 2C23459 8C23459 9C23459 } 20 Links = { 1r24 2r18 8r28 9r14 3n24 5n249 6n35 7n259 9n34 }

These two results match my Template analyzer's findings. Now, I need to reconsider my objective.

[daj95376]

_

It appears that my objective was to track down an inconsistency in my Templates analyzer program.

Here's DPB's second puzzle with the correct (I hope) Multi-Fish markings from the analyzer.

Code: Select all

 +--------------------------------------------------------------------------------+
 |  3       148     14568   |  2457    24568   2478    |  9       267     12678   |
 |  689     7       468     |  249     234689  1       |  368     5       268     |
 |  15689   189     2       |  579     35689   3789    |  13678   367     4       |
 |--------------------------+--------------------------+--------------------------|
 |  2589    23489   3458    |  249     7       6       |  3458    1       2589    |
 |  12789   12489   1478    |  3       249     5       |  4678    24679   26789   |
 |  2579    6       3457    |  8       1       249     |  3457    23479   2579    |
 |--------------------------+--------------------------+--------------------------|
 |  4       138     13678   |  1579    3589    3789    |  2       679     15679   |
 |  127     5       137     |  6       2349    23479   |  147     8       179     |
 |  12678   128     9       |  12457   2458    2478    |  14567   467     3       |
 +--------------------------------------------------------------------------------+
 # 176 eliminations remain


Code: Select all

(19) Truths = ( 2349R24568 - 3R5 )
(19) Links  = ( 29c19 34c37 2n45 4n24 5n258 6n68 8n56 )

<>2  r9c1,r1c9   +   r5c19 from Templates
<>3  r3c7,r7c3
<>4  r1c3,r9c7   +   r5c37 from Templates
<>9  r3c1,r7c9   +   r5c19 from Templates

<>1  r5c2
<>6  r2c5,r5c8
<>7  r8c6,r56c8
<>8  r45c2,r2c5


There are 17 eliminations from the Multi-Fish, and six additional eliminations found by Templates.

Unfortunately, the analyzer is restricted to finding a small subset -- row/column sectors -- of the Multi-Fish present in most puzzles.

[David P Bird]

DAJ, the combination of row and column cover sets ensures that every candidate in the 4x5 array of Naked Set cells is covered once (so no uncovered candidate can exist in these cells). As the 20 digit covers match the number of cells, every assignment will reduce both counts equally, so there is a one-to-one relationship between them. That relationship would be lost if one of the eliminations was considered true because it would then leave 19 digits to occupy 20 cells.

[Obi-Wahn]

@daj95376:
In the second puzzle there's a simpler Multifish with 16 truths, if you remove 249r5 from the set and 5n258 from the link set. This one gives the 6 missing eliminations of your template analyzer but misses the 4 eliminations in the removed cells 5n28, therefor yielding 19 eliminations in total.

[pjb]

In the second puzzle there's also a classic SK loop (often present where there's a 16T rank zero multifish) which gives the same 19 eliminations followed by 6 with a naked triple.

Phil

[daj95376]

@daj95376:
In the second puzzle there's a simpler Multifish with 16 truths, if you remove 249r5 from the set and 5n258 from the link set. This one gives the 6 missing eliminations of your template analyzer but misses the 4 eliminations in the removed cells 5n28, therefor yielding 19 eliminations in total.

Okay, I lose four (non-primary value) eliminations in r5c258, but I gain six (primary value) eliminations in r5c1379. I should have noticed the significance of all the missing eliminations being in [r5].

Hidden Text: Show

Code: Select all

(16) Truths = ( 2349R2468 )
(16) Links  = ( 29c19 34c37 2n45 4n24 6n68 8n56 )

<>2  r9c1,r1c9   +   r5c19
<>3  r3c7,r7c3
<>4  r1c3,r9c7   +   r5c37
<>9  r3c1,r7c9   +   r5c19

<>6  r2c5
<>7  r6c8,r8c6
<>8  r2c5,r4c2

 +-----------------------------------+
 |  .  .  .  |  2  2  2  |  .  2 -2  |
 |  .  .  .  | *2 *2  .  |  .  . #2  |
 |  .  .  2  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 | #2 *2  .  | *2  .  .  |  .  . #2  |
 | -2  2  .  |  .  2  .  |  .  2 -2  |
 | #2  .  .  |  .  . *2  |  . *2 #2  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  2  .  .  |
 | #2  .  .  |  . *2 *2  |  .  .  .  |
 | -2  2  .  |  2  2  2  |  .  .  .  |
 +-----------------------------------+

 +-----------------------------------+
 |  3  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  . *3  .  | #3  .  .  |
 |  .  .  .  |  .  3  3  | -3  3  .  |
 |-----------+-----------+-----------|
 |  . *3 #3  |  .  .  .  | #3  .  .  |
 |  .  .  .  |  3  .  .  |  .  .  .  |
 |  .  . #3  |  .  .  .  | #3 *3  .  |
 |-----------+-----------+-----------|
 |  .  3 -3  |  .  3  3  |  .  .  .  |
 |  .  . #3  |  . *3 *3  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  3  |
 +-----------------------------------+

 +-----------------------------------+
 |  .  4 -4  |  4  4  4  |  .  .  .  |
 |  .  . #4  | *4 *4  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  4  |
 |-----------+-----------+-----------|
 |  . *4 #4  | *4  .  .  | #4  .  .  |
 |  .  4 -4  |  .  4  .  | -4  4  .  |
 |  .  . #4  |  .  . *4  | #4 *4  .  |
 |-----------+-----------+-----------|
 |  4  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  . *4 *4  | #4  .  .  |
 |  .  .  .  |  4  4  4  | -4  4  .  |
 +-----------------------------------+

 +-----------------------------------+
 |  .  .  .  |  .  .  .  |  9  .  .  |
 | #9  .  .  | *9 *9  .  |  .  .  .  |
 | -9  9  .  |  9  9  9  |  .  .  .  |
 |-----------+-----------+-----------|
 | #9 *9  .  | *9  .  .  |  .  . #9  |
 | -9  9  .  |  .  9  .  |  .  9 -9  |
 | #9  .  .  |  .  . *9  |  . *9 #9  |
 |-----------+-----------+-----------|
 |  .  .  .  |  9  9  9  |  .  9 -9  |
 |  .  .  .  |  . *9 *9  |  .  . #9  |
 |  .  .  9  |  .  .  .  |  .  .  .  |
 +-----------------------------------+


[daj95376]

In the second puzzle there's also a classic SK loop (often present where there's a 16T rank zero multifish) which gives the same 17 eliminations followed by 6 with a naked triple.

It's also a V-Loop. (I corrected what I believe to be a typo in your elimination count.)

Hidden Text: Show

Code: Select all

 +--------------------------------------------------------------------------------+
 |  3       148     14568   |  2457    24568   2478    |  9       267     12678   |
 |  689     7       468     |  249     234689  1       |  368     5       268     |
 |  15689   189     2       |  579     35689   3789    |  13678   367     4       |
 |--------------------------+--------------------------+--------------------------|
 |  2589    23489   3458    |  249     7       6       |  3458    1       2589    |
 |  12789   12489   1478    |  3       249     5       |  4678    24679   26789   |
 |  2579    6       3457    |  8       1       249     |  3457    23479   2579    |
 |--------------------------+--------------------------+--------------------------|
 |  4       138     13678   |  1579    3589    3789    |  2       679     15679   |
 |  127     5       137     |  6       2349    23479   |  147     8       179     |
 |  12678   128     9       |  12457   2458    2478    |  14567   467     3       |
 +--------------------------------------------------------------------------------+
 # 176 eliminations remain

 (49=18)r13c2 - (18=23)r79c2 - (23=17)r8c13 - (17=49)r8c79 -
 (49=67)r79c8 - (67=23)r13c8 - (23=68)r2c79 - (68=49)r2c13 - V-Loop  =>

  r2c5<>68; r5c2<>18; r5c8<>67; r1c9,r9c1<>2; r3c7,r7c3<>3; r1c3,r9c7<>4;
  r6c8,r8c6<>7; r4c2<>8; r3c1,r7c9<>9


 r5      Naked  Triple                   <> 249  r5c1379


[pjb]

daj95376 wrote:
It's also a V-Loop.

Thanks for picking the typo
Could you please explain what is a V-Loop as opposed to an SK-Loop? Isn't this one much the same as the "easter monster" which is described as having an SK-Loop?

Phil

[daj95376]

Could you please explain what is a V-Loop as opposed to an SK-Loop? Isn't this one much the same as the "easter monster" which is described as having an SK-Loop?

I'm working from a discussion between ronk and champagne over the proper format of an SK-Loop. Champagne ended up calling his results a V-Loop.

For a "classic" SK-Loop, it's my understanding that you use six cells for every row/column spanned. For a V-Loop, you use four cells for every row/column spanned. My results above are for the V-Loop. Here's the SK-Loop.

Code: Select all

 (49)r13c2 = (49-23)r45c2 = (23)r79c2 -
 (23)r8c13 = (23-49)r8c56 = (49)r8c79 -
 (49)r79c8 = (49-23)r56c8 = (23)r13c8 -
 (23)r2c79 = (23-49)r2c45 = (49)r2c13 - loop


For reference, here's the SK-Loop for Easter Monster from my notes.

Code: Select all

Steve Kurzhal's original presentation w/ RonK's labels:

1.......2.9.4...5...6...7...5.9.3.......7.......85..4.7.....6...3...9.8...2.....1

     1      A478     34578   | 3567    3689    5678    | 3489   I369     2
    L238     9      L378     | 4      K12368  K12678   |J138     5      J368
     23458  A248     6       | 1235    12389   1258    | 7      I139     3489
    -------------------------+-------------------------+-----------------------
     2468    5       1478    | 9       1246    3       | 128    H1267    678
     234689 B12468   13489   | 126     7       1246    | 123589 H12369   35689
     2369   B1267    1379    | 8       5       126     | 1239    4       3679
    -------------------------+-------------------------+-----------------------
     7      C148     14589   | 1235    12348   12458   | 6      G239     3459
    D456     3      D145     |E12567  E1246    9       |F245     8      F457
     45689  C468     2       | 3567    3468    45678   | 3459   G379     1

    (27)r13c2=(27-16)r56c2=(16)r79c2-(16)r8c13=(16-27)r8c45=(27)r8c79-
    (27)r79c8=(27-16)r45c8=(16)r13c8-(16)r2c79=(16-27)r2c56=(27)r2c13-loop


Here's the V-Loop from my notes:

Code: Select all

 (48=27)r13c2 - (27=38)r2c13 - (38=16)r2c79 - (16=39)r13c8 -
 (39=27)r79c8 - (27=45)r8c79 - (45=16)r8c13 - (16=48)r79c2 - V-Loop  =>

  r2c5<>38; r5c2<>48; r5c8<>39;
  r7c3<>1; r3c1<>2; r8c5<>4; r8c4<>5; r9c1<>6; r1c3<>7; r2c6<>8


[pjb]

I''ve been using the V-Loop logic, although I've been calling them SK loops. Its all a bit confusing.
Thank you, Phil