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| daj95376
| | Joined: 05 Feb 2006 | | Posts: 349 | | : | |
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 Posted: Sat Aug 19, 2006 6:42 pm Post subject: Double Implication Chain and Templates/POMS |
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Part I ...
In Sudoku, many times techniques overlap. For those who object to Templates and POMs, maybe Double Implication Chains are acceptable as a counterpart to some basic Template/POM logic.
| Code: | Original
6..2.8...59.4..3..3.2.....6...7.28.........51....5..3.....7......15.3....859.....
After Singles and Locked Candidate resolved
*-----------------------------------------------------------------------------*
| 6 1 47 | 2 3 8 | 4579 479 4579 |
| 5 9 8 | 4 6 7 | 3 1 2 |
| 3 47 2 | 1 9 5 | 47 8 6 |
|-------------------------+-------------------------+-------------------------|
| 149 5 3 | 7 14 2 | 8 6 49 |
| 24789 2467 4679 | 3 48 469 | 2479 5 1 |
| 124789 2467 4679 | 68 5 1469 | 2479 3 479 |
|-------------------------+-------------------------+-------------------------|
| 249 3 469 | 68 7 146 | 14569 249 4589 |
| 2479 2467 1 | 5 248 3 | 4679 2479 4789 |
| 247 8 5 | 9 124 146 | 1467 247 3 |
*-----------------------------------------------------------------------------* |
| Code: | My solver suggests:
r6c2 <> 6 Templates -- Pass C
r6c1 <> 7 Templates -- Pass C
r6c2 <> 7 Templates -- Pass C
r7c9 <> 9 Templates -- Pass C |
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| daj95376
| | Joined: 05 Feb 2006 | | Posts: 349 | | : | |
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| Posted: Sat Aug 19, 2006 6:50 pm Post subject: |
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Part II ...
I'm sorry that I had to break this message into two parts, but the automatic formatting feature screws up my message unless I turn off HTML and BBcode for the following.
Now, Multi-Coloring will also produce the first elimination, but let's investigate these eliminations in terms of bilocation cells and Double Implication Chains.
I) <6> in [c4]
[r6c4]=6 => [r6c23]<>6
[r7c4]=6 => [r8c2]=6 => [r56c2]<>6
So, we can deduce [r6c2]<>6. (Double Implication Chain elimination)
II) <7> in [b1]
[r1c3]=7 => [r3c7]=7 => [r6c9]=7 => [r6c12]<>7
[r3c2]=7 => [r568c2]<>7 => (Locked Candidate for <7> in [b7]) => [r56c1]<>7
So, we can deduce [r6c12]<>7. (??? Double Implication Chain elimination)
III) <9> in [r4]
[r4c9]=9 => [r1678c9]<>9
[r4c1]=9 => [r7c3]=9 => [r7c789]<>9
So, we can deduce [r7c9]<>9. (Double Implication Chain elimination) |
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| rkral
| | Joined: 21 Oct 2005 | | Posts: 233 | | : | |
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| Posted: Sat Aug 19, 2006 9:36 pm Post subject: |
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| daj95376 wrote: | II) <7> in [b1]
[r1c3]=7 => [r3c7]=7 => [r6c9]=7 => [r6c12]<7> [r568c2]<7> (Locked Candidate for <7> in [b7]) => [r56c1]<>7
So, we can deduce [r6c12]<>7. (??? Double Implication Chain elimination) |
In nice loop notation: | Code: |
r6c12-7-r6c79=7=r5c7-r13c7=7=r1c89-7-r1c3=7=r3c2-7-r6c2
-7-r8c2=7=r89c1-7-r6c1
... implying r6c12<>7 |
Due to the multiple inference of r3c2=7, this is considered a triple implication chain. |
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| daj95376
| | Joined: 05 Feb 2006 | | Posts: 349 | | : | |
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| Posted: Sat Aug 19, 2006 10:07 pm Post subject: |
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| rkral ... Thanks for the clarification! I was pretty sure something wasn't right. That's why I included the '???'. |
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