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[mith]

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+-------+-------+-------+
| . 1 . | . 2 . | 3 . . |
| 4 . . | . . 1 | . . . |
| . . . | . . . | 2 . 5 |
+-------+-------+-------+
| . . . | 4 . . | . 6 . |
| 5 . . | . 7 . | . . 2 |
| . 6 . | . . 8 | . . . |
+-------+-------+-------+
| 3 . 9 | . . . | . . . |
| . . . | 6 . . | . . 8 |
| . . 7 | . 5 . | . 4 . |
+-------+-------+-------+
.1..2.3..4....1.........2.5...4...6.5...7...2.6...8...3.9.........6....8..7.5..4.

[Ajò Dimonios]

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+-----------------+----------------+------------------+
| 789   1    6    | 5789  2   579  | 3     789   4    |
| 4     25   25   | 3789  389 1    | 6789  789   679  |
| 789   379  38   | 789   6   4    | 2     1     5    |
+-----------------+----------------+------------------+
| 12789 379  1238 | 4     139 25   | 15789 6     1379 |
| 5     39   1348 | 139   7   6    | 1489  389   2    |
| 1279  6    1234 | 25    139 8    | 14579 3579  1379 |
+-----------------+----------------+------------------+
| 3     2458 9    | 1278  148 27   | 1567  257   167  |
| 12    245  125  | 6     49  2379 | 579   23579 8    |
| 6     28   7    | 1289  5   239  | 19    4     139  |
+-----------------+----------------+------------------+


4r7c2=(4-8)r7c5=r2c5-8r2c78=8r1c8-r5c8=(39)r5c28-(39=1)r5c4-1r79c4=1r7c5=>-4r7c5;btte

[SpAce]

Code: Select all

.-------------------.-------------------.----------------------.
| 789    1     6    | 5789   2     579  |  3       789    4    |
| 4      25    25   | 3789  a389   1    | d679-8   789    679  |
| 789    379   38   | 789    6     4    |  2       1      5    |
:-------------------+-------------------+----------------------:
| 12789  379   1238 | 4      139   25   |  15789   6      1379 |
| 5      39    1348 | 139    7     6    |  1489    389    2    |
| 1279   6     1234 | 25     139   8    |  14579   3579   1379 |
:-------------------+-------------------+----------------------:
| 3      2458  9    | 1278  a148   27   | c1567   c257    167  |
| 12     245   125  | 6     b49   b2379 | b579    b23579  8    |
| 6      28    7    | 1289   5     239  |  19      4      139  |
'-------------------'-------------------'----------------------'

(84)r27c5 = (4379-2|5)r8c5678 = (25-6)r7c87 = (6)r2c7 => -8 r2c7; btte

8x8 PM: Show

Code: Select all

      8r2
      2n7   7n5   8n5   8n6   8n7   8n8   7n8   7n7
   .------------------------------------------------
8C5| 8r2c5 8r7c5
4C5|       4r7c5 4r8c5
9R8|             9r8c5 9r8c6 9r8c7 9r8c8
7R8|                   7r8c6 7r8c7 7r8c8
3R8|                   3r8c6       3r8c8
2B9|                               2r8c8 2r7c8
5B9|                         5r8c7 5r8c8 5r7c8 5r7c7
6C7| 6r2c7                                     6r7c7
   '================================================
    -8r2c7

8x9 (Rank 1): {379R8 48C5 6C7 25B9 \ 8r2 78n5 8n6 278n7 78n8} => -8 r2c7

--
Edit: Added the matrix.

[mith]

There's a solution that doesn't use chains, but I'll give it a few days...

[mith]

My solution:

As discussed in Place a Digit, the cells r13579c13579 must contain exactly the digits in r2468c2468 plus one extra set of 1-9. There are 6 digits 1468 in the "even" partition, so we need 10 such digits in the "odd" partition. There are 14 empty cells in the odd partition... but in both boxes 1 and 9, at most two digits 1468 can be placed in the odd cells (since there are already two givens in these boxes not in the odd cells). So:

1. All the empty cells in r13579c13579 that aren't in b1 or b9 must be from 1468 (in fact three can be placed as singles from the start).
2. All the empty cells in r2468c2468 must be from 23579.
3. All the empty cells in b1 and b9 that aren't from r13c13 or r79c79 must be from 23579 as well.

And btte.

[yzfwsf]

Same this one?

MSLS.png (82.79 KiB) Viewed 899 times

[mith]

Hadn't updated your software recently... having done so, the 25 cell one is equivalent to the pattern I was looking at.

MSLS:25 Cells r2468c13579+r79c79,r3c13,r1c1,25 Links 68r2,18r4,14r6,14r8,279c1,235c3,39c5,579c7,379c9,8b1,16b9
6 Eliminations:r5c3<>3,r7c5,r8c2<>4,r2c48<>8,r5c7<>9

Interesting that there is another option using box 4 (though not surprising). The 25 cell version has the advantage of being available at the start (well, 26 cell at that point, including r1c3), whereas the 21 cell depends on the hidden triple.

[StrmCkr]

Code: Select all

+--------------------+--------------------+----------------------+
| 789    1     6     | 5789   2      579  | 3       79(8)   4    |
| 4      25    25    | 379-8  (389)  1    | 679(8)  79(-8)  679  |
| 789    379   38    | 789    6      4    | 2       1       5    |
+--------------------+--------------------+----------------------+
| 12789  379   1238  | 4      (139)  25   | 15789   6       1379 |
| 5      (39)  148-3 | (139)  7      6    | 148-9   (389)   2    |
| 1279   6     1234  | 25     (139)  8    | 14579   3579    1379 |
+--------------------+--------------------+----------------------+
| 3      2458  9     | 1278   148    27   | 1567    257     167  |
| 12     245   125   | 6      4-9    2379 | 579     23579   8    |
| 6      28    7     | 1289   5      239  | 19      4       139  |
+--------------------+--------------------+----------------------+

als A) 1389 @ R246C5
als B) 1389 @ R5C248
RC ) 1
ERI Digit 8 @ Box 3 {Transport}
-> double RC rule since eri sees both of the als it acts as a 2nd RC
R2C48 <> 8
R5C3 <>3
R5C7 <>9
R8C5 <> 9

pretty much singles from here out.... didn't use a "chain"