Opposites of 1

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Re: Opposites of 1

Postby RW » Wed Nov 10, 2010 2:26 pm

dyitto wrote:And another one:
Code: Select all
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):
Code: Select all
 *--------------------------------------------------------------------------------------*
 | 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:
Code: Select all
 *-----------------------------------------------------------------------------*
 | 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:
Code: Select all
 *-----------------------------------------------------------------------------*
 | 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
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Re: Opposites of 1

Postby dyitto » Fri Nov 12, 2010 9:04 pm

Hi RW thanks for your solution path :D
evert on the crashed forum
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