dyitto wrote:And another one:
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6..|5..|...
.8.|4..|...
.9.|6..|...
---+---+---
1..|8..|5.3
...|..5|..2
...|...|...
---+---+---
..3|.6.|..7
..6|...|8..
...|...|15.
My solver needs 3 guessings but maybe a human player can come up with better ideas.
I need one ugly chain, perhaps someone can do better...
Not all steps below are necessary, I'll just write out whatever ways I can find eliminating candidates based on the new constraint.
After basic steps (singles, locked candidates, placing 1 in r5c5, eliminating 1 from all other cells opposite 1):
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*--------------------------------------------------------------------------------------*
| 6 2347 247 |*5 23789 123789 | 23479 24789 1489 |
|*2357 8 *1257 | 4 2379 12379 | 23679 2679 *159 |
|*23457 9 *12457 | 6 2378 12378 | 2347 2478 *1458 |
|----------------------------+----------------------------+----------------------------|
| 1 2467 2479 | 8 2479 24679 |*5 4679 3 |
| 34789 3467 4789 | 379 1 *5 | 4679 46789 2 |
|*2345789 *234567 *245789 | 2379 23479 234679 | 4679 1 489 |
|----------------------------+----------------------------+----------------------------|
|*4589 *145 3 | 19 6 489 | 249 249 7 |
| 2479 1247 6 | 1279 *5 2479 | 8 3 49 |
| 24789 247 24789 | 2379 234789 234789 | 1 *5 6 |
*--------------------------------------------------------------------------------------*
All possible locations for digit 5 marked with '*'. Only one of them, r7c1, has a opposite candidate one => r7c1=5 and r3c9=1.
This solves some singles, among other r2c3=1, which is opposite to 8, so we can remove 8 from all other cells opposite 1. Next we get stuck here:
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*-----------------------------------------------------------------------------*
| 6 2347 *247 | 5 2379 1 | 23479 2479 8 |
| 237 8 1 | 4 2379 *2379 | 23679 *2679 5 |
| 2347 9 5 | 6 8 *237 | 2347 *247 1 |
|-------------------------+-------------------------+-------------------------|
| 1 *2467 2479 | 8 2479 24679 | 5 479-6 3 |
| 3479 3467 479 | 379 1 5 | 4679 8 2 |
| 234789 5 24789 | 2379 23479 234679 | 4679 1 *49 |
|-------------------------+-------------------------+-------------------------|
| 5 14 3 | 19 6 8 | 249 249 7 |
| 2479 1247 6 | 1279 5 2479 | 8 3 49 |
| 24789 247 24789 |*2379 23479 2479-3 | 1 5 6 |
*-----------------------------------------------------------------------------*
Marked all unsolved cells that are opposite to a given or candidate 1. These cells must include the digits 234679, we may eliminate any candidate 234679 that can see every similar candidate in the cells marked above => r4c8<>6 and r9c6<>3. (solves r2c8=6)
Next we may eliminate 9 from r6c4, because it kills the candidates 9 in r6c9 and r9c4 and it solves r7c4=1, leaving no possible candidates 9 opposite 1.
Continuing with digit 9, we have a strong link in column 9:
If r6c9=9 => r9c4<>9 (both are opposite to 1).
If r8c9=9 => r7c4=9 => r9c4<>9.
=> Eliminate 9 from r9c4. Then we may also eliminate 9 from r6c6 as it can see the remaining 9s opposite to a possible 1.
Current state:
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*-----------------------------------------------------------------------------*
| 6 2347 *247 | 5 2379 1 | 23479 2479 8 |
| 237 8 1 | 4 2379 *2379 | 2379 *6 5 |
| 2347 9 5 | 6 8 *237 | 2347 *247 1 |
|-------------------------+-------------------------+-------------------------|
| 1 *2467 2479 | 8 2479 24679 | 5 479 3 |
| 3479 3467 479 | 379 1 5 | 4679 8 2 |
| 234789 5 24789 | 237 23479 23467 | 4679 1 *49 |
|-------------------------+-------------------------+-------------------------|
| 5 14 3 | 19 6 8 | 249 249 7 |
| 2479 1247 6 | 1279 5 2479 | 8 3 49 |
| 24789 247 24789 |*237 23479 2479 | 1 5 6 |
*-----------------------------------------------------------------------------*
Possible locations for 69 opposite 1 are r2c68, r4c2 and r6c9. Both cells r2c68 cannot be opposite 1 therefore at least one of r4c2=6 and r6c9=9 must be true.
Then comes the ugly chain, looking at the possibilities above, if we assume r6c9=4, then r4c2=6, r2c6=9 (and r8c4=1), r9c4=3 and r1c3&r3c8<>4. This leads to a contradiction using singles only (won't write out a long clumsy chain here) eliminating 4 from r6c9. From here on the puzzle is easy.
RW
