The New Sudoku Players' Forum

[ArkieTech]

Can anyone see a method to solve this puzzle?

Code: Select all

 
 *-----------*
 |.4.|...|...|
 |813|4..|...|
 |...|.1.|.2.|
 |---+---+---|
 |...|6.3|587|
 |58.|...|13.|
 |...|...|..2|
 |---+---+---|
 |...|..8|976|
 |...|1..|...|
 |.59|2.6|...|
 *-----------*
 *-----------------------------------------------------------*
 | 279   4     257   | 79    38    579   | 368   16    138   |
 | 8     1     3     | 4     6     2     | 7     59    59    |
 | 679   679   57    | 38    1     579   | 348   2     348   |
 |-------------------+-------------------+-------------------|
 | 1249  29    124   | 6     49    3     | 5     8     7     |
 | 5     8     6     | 79    2     479   | 1     3     49    |
 | 3479  379   47    | 58    58    1     | 46    469   2     |
 |-------------------+-------------------+-------------------|
 | 1234  23    124   | 35    345   8     | 9     7     6     |
 | 3467  367   8     | 1     3479  49    | 2     45    345   |
 | 347   5     9     | 2     347   6     | 348   14    1348  |
 *-----------------------------------------------------------*


dan

[daj95376]

All I can offer is a contradiction chain ...

Code: Select all

4=[r5c9]=9=[r6c8]-9-[r2c8]-5-[r8c8]-4-[r8c6]=4=[r5c6]-4-[r5c9] => [r5c9]<>4


Singles complete the puzzle.

[ArkieTech]

daj95376 said:

All I can offer is a contradiction chain ...

Thanks, I like your notation. I was hoping for a strange fish or an ALS.

dan

[daj95376]

Thanks, I like your notation. I was hoping for a strange fish or an ALS.

I know. No fish ... and I don't do ALS. I bet others find many ALS examples.

[ronk]

I was hoping for a strange fish or an ALS.

Here are two instances where the ALS xz-rule applies.

Code: Select all

 279  4    257  | 79   38    579  |A368  16   D18-3
 8    1    3    | 4    6     2    | 7    59   B59
 679  679  57   | 38   1     579  |A348  2   DB348
----------------+-----------------+----------------
 1249 29   124  | 6    49    3    | 5    8     7
 5    8    6    | 79   2     47-9 | 1    3   DB49
 3479 379  47   | 58   58    1    |A46   469   2
----------------+-----------------+----------------
 1234 23   124  | 35   345   8    | 9    7     6
 3467 367  8    | 1    3479 C49   | 2   C45  DB345
 347  5    9    | 2    347   6    | 348  14   D1348

 ALS 1: A = {r136c7} = {3468}
        B = {r2358c9} = {34589}
        x = 8, z = 3 implies r1c9<>3

 ALS 2: C = {r8c68} = {459}
        D = {r13589c9} = {134589}
        x = 5, z = 9 implies r5c6<>9

Neither exposes a "singles backdoor" like daj95376's chain, but the two bivalues created can then be used in a long (13-node) xy-chain for r1c7<>6.

[ArkieTech]

ronk said

Here are two instances where the ALZ xz-rule applies

Thanks, It is a rainy day here and I think I will investigate the implications of the three cells that are in both xls's (r358c9).

dan

[daj95376]

Neither exposes a "singles backdoor" like daj95376's chain, but the two bivalues created can then be used in a long (13-node) xy-chain for r1c7<>6.

Wow ronk, that's one impressive XY-Chain from [r1c8] to [r6c7] ... resulting in [r6c8]<>6 as well. Since it connects diagonal cells in an X-Wing, it also forcing the endpoints of the XY-Chain to be 6. Lots of action in your XY-Chain