The New Sudoku Players' Forum

[daj95376]

pseudo-Triple Implication Chain on [b7] for <3> results in (four cells) [r46c46]<>3 through X-Wings!

Code: Select all

# original from Eioru
1..4..5...8..5..9...5..7..34.....2...6.....8...7.....98..2..3...1..7..6...6..9..4

# reduced to
 *-----------------------------------------------------------------------------*
 | 1       279     3       | 4       2689    268     | 5       27      268     |
 | 67      8       24      | 136     5       1236    | 1467    9       1267    |
 | 269     249     5       | 1689    12689   7       | 1468    124     3       |
 |-------------------------+-------------------------+-------------------------|
 | 4       359     8       | 135679- 1369    1356-   | 2       137     167     |
 | 239     6       1       | 379     234     234     | 47      8       5       |
 | 235     235     7       | 13568-  12348   12358-  | 146     134     9       |
 |-------------------------+-------------------------+-------------------------|
 | 8       457     9       | 2       146     1456    | 3       157     17      |
 | 235*    1       24      | 358     7       3458    | 9       6       28      |
 | 2357*   2357*    6      | 1358    138     9       | 178     125     4       |
 *-----------------------------------------------------------------------------*


[ronk]

pseudo-Triple Implication Chain on [b7] for <3> results in (four cells) [r46c46]<>3 through X-Wings!

Nice, but at least one of r8c1<>3 and r9c2<>3 must be true, so you don't really need r9c1<>3. Depending upon what you mean by 'pseudo', that might make it a pseudo-double implication chain.

[daj95376]

ronk, Thanks for the feedback and alternate viewpoint. Your logic based on the two inequalities seems cleaner!!!

I was under the impression that Implication Chains must consider all cells in a unit containing a value ... and assert each assignment of that value ... and check for overlapping effects. Since the key unit for <3> seemed to be [b7], that's why I called it a Triple Implication Chain. I used the prefix pseudo- because I didn't know if the proper use of an Implication Chain would also include eliminations from sub-patterns like X-Wings.

[Myth Jellies]

Similar logic using colored box-box (or x-wing) interactions

Code: Select all

 *-----------------------------------------------------------------------------*
 | 1       279     3       | 4       2689    268     | 5       27      268     |
 | 67      8       24      |A136     5      A1236    | 1467    9       1267    |
 | 269     249     5       | 1689    12689   7       | 1468    124     3       |
 |-------------------------+-------------------------+-------------------------|
 | 4      B359     8       |-135679  1369   -1356    | 2      B137     167     |
 | 239     6       1       | 379     234     234     | 47      8       5       |
 | 235    B235     7       |-13568   12348  -12358   | 146    B134     9       |
 |-------------------------+-------------------------+-------------------------|
 | 8       457     9       | 2       146     1456    | 3       157     17      |
 |a235     1       24      |A358     7      A3458    | 9       6       28      |
 | 2357   b2357     6      | 1358    138     9       | 178     125     4       |
 *-----------------------------------------------------------------------------*


A = a - b = B => color A or color B or both is true. Either the colored box-box interaction A or the colored box-box interaction B will eliminate the threes in r46c46. These also work as colored x-wings.

Also have the finned swordfish shown below

Code: Select all

 *-----------------------------------------------------------------------------*
 | 1       279     3       | 4       2689    268     | 5       27      268     |
 | 67      8       24      | 136     5       1236    | 1467    9       1267    |
 | 269     249     5       | 1689    12689   7       | 1468    124     3       |
 |-------------------------+-------------------------+-------------------------|
 | 4      *359     8       |-135679 *1369   -1356    | 2      *137     167     |
 | 239     6       1       | 379    #234     234     | 47      8       5       |
 | 235    *235     7       |-13568  *12348  -12358   | 146    *134     9       |
 |-------------------------+-------------------------+-------------------------|
 | 8       457     9       | 2       146     1456    | 3       157     17      |
 | 235     1       24      | 358     7       3458    | 9       6       28      |
 | 2357   *2357     6      | 1358   *138     9       | 178    *125     4       |
 *-----------------------------------------------------------------------------*


[ronk]

daj95376, this is a very old thread, but do you know how the original puzzle was -- or might be -- "reduced" to the pencilmarks shown?

TIA, Ron

[daj95376]

daj95376, this is a very old thread, but do you know how the original puzzle was -- or might be -- "reduced" to the pencilmarks shown?

ronk, I'm at a loss to explain how the original puzzle was reduced to the posted PM. When I tried to re-create the results, there was nothing in my solver's output to explain the additional eliminations after SSTS and fish. In fact, there is no way that I could have handled the fish eliminations at that time without using Templates. Sorry!

[ronk]

daj95376, thanks for looking. This PM is of interest to me because the elimination cells r46c46 are "covered" by three different fish, a swordfish and two almost x-wings. I was thinking of using it as an example in another forum but, as you know, I like PMs that can be reached with simple steps, preferably just with SSTS.

Code: Select all

 .  .  . |  .  .  . |  .  .  .        .  .  . |  .  .  . |  .  .  .
 .  .  . |  3  .  3 |  .  .  .        .  .  . | A3  . A3 |  .  .  .
 .  .  . |  .  .  . |  .  .  .        .  .  . |  .  .  . |  .  .  .
---------+----------+----------      ---------+----------+----------
 .  3  . | *3 X3 *3 |  .  3  .        . B3  . | *3  3 *3 |  . B3  .
X3  .  . | X3 @3 X3 |  .  .  .        3  .  . |  3  3  3 |  .  .  .
 3  3  . | *3 X3 *3 |  .  3  .        3 B3  . | *3  3 *3 |  . B3  .
---------+----------+----------      ---------+----------+----------
 .  .  . |  .  .  . |  .  .  .        .  .  . |  .  .  . |  .  .  .
X3  .  . |  3  .  3 |  .  .  .       a3  .  . | A3  . A3 |  .  .  .
X3 X3  . |  3 X3  . |  .  .  .        3 b3  . |  3  3  . |  .  .  .

r5c5b7\r9c1b5 plus endo-fin r5c5      r28\c46 plus fin r8c1 and
                                      c28\r46 plus fin r8c9 where
                                      the fins are weakly linked