## Triple Implication Chain Forces X-Wings

Everything about Sudoku that doesn't fit in one of the other sections

### Triple Implication Chain Forces X-Wings

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

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`# original from Eioru1..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       | *-----------------------------------------------------------------------------*`
daj95376
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### Re: Triple Implication Chain Forces X-Wings

daj95376 wrote: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.
ronk
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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.
daj95376
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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       |  *-----------------------------------------------------------------------------* `
Myth Jellies

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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
ronk
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ronk wrote: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!
daj95376
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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`
ronk
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