The New Sudoku Players' Forum

[Mauriès Robert]

Hi all,
I have this puzzle for you to solve.
.1..9.52....2.5...5.23.6..1....8......1...4..4..6.1..5..9...6....67.28...2.9.8.7.

puzzle: Show

Good resolution
Robert

[eleven]

Eliminate 4r1c3 with a singles net (too boring to write that down), then the rest solves with a pair.

[Cenoman]

Solution in two steps, with a net as a first step (triple kraken):

Code: Select all

 +-------------------------+-------------------+--------------------------+
 |  67      1       347    |  8    9     47    |  5       2       367     |
 |  6789    36789   3478   |  2    1     5     |  379     34689   36789   |
 |  5       789     2      |  3    47    6     |  79      49-8    1       |
 +-------------------------+-------------------+--------------------------+
 |  2679    5       37     |  4    8     379   |  12379   1369    3679    |
 |  26789   36789   1      |  5    237   379   |  4       3689    36789   |
 |  4       3789    378    |  6    237   1     |  2379    389     5       |
 +-------------------------+-------------------+--------------------------+
 |  78      78      9      |  1    345   34    |  6       35      2       |
 |  13      4       6      |  7    35    2     |  8       1359    39      |
 |  13      2       5      |  9    6     8     |  13      7       4       |
 +-------------------------+-------------------+--------------------------+

Triple kraken (7) row 5, cell r3c2, (6) row 4

Code: Select all

(7-8)r5c9 = (8)r2c9 *
 ||
(7)r5c6 - r1c6 = (7-4)r3c5 = (4)r3c8 *
 ||
 ||     r46c3 = r12c3 - (7)r3c2
 ||    /                 ||
(7)r5c12                (8)r3c2 *
 ||    \                 ||
 ||     (7=389)b4p389 - (9)r3c2
 ||
(7-2)r5c5 = r5c1 - (2=3796)r4c1369 - (6)r4c8
                                      ||
                                     (6)r4c1 - (6=74)r1c16 - r3c5 = (4)r3c8 *
                                      ||
                                     (6)r4c9 - r12c9 = (6-4)r2c8 = (4)r3c8 *
-----------------
=> -8 r3c8; 4 placements & basics

End with X-wing(7)r26c57 => -7 r5c5, r24c7; ste

Code: Select all

 +---------------------+-------------------+-------------------------+
 |  67     1     347   |  8    9     47    |  5       2      367     |
 |  679    369   347   |  2    1     5     |  3-7     3468   3678    |
 |  5      8     2     |  3    47*   6     |  79*     49     1       |
 +---------------------+-------------------+-------------------------+
 |  2679   5     37    |  4    8     379   |  1239-7  1369   3679    |
 |  2679   369   1     |  5    23-7  379   |  4       3689   36789   |
 |  4      39    8     |  6    27*   1     |  27*     39     5       |
 +---------------------+-------------------+-------------------------+
 |  8      7     9     |  1    345   34    |  6       35     2       |
 |  13     4     6     |  7    35    2     |  8       1359   39      |
 |  13     2     5     |  9    6     8     |  13      7      4       |
 +---------------------+-------------------+-------------------------+

[Mauriès Robert]

Hi all,
The fastest resolution is obtained, as Eleven indicates, by eliminating the 4r1c3 (or 7r1c6) but the P(4r1c3) track is very long to develop before falling on a contradiction. This supposes to be worth the trouble to be tempted to have noticed beforehand that the 4r1c6 is a backdoor. It is a T&E resolution.
Cenomam's resolution, which is more constructive, is very interesting.
It is possible to solve the puzzle with relatively short anti-tracks (length<9), some of which are derived from known models. Here's how.

1) P'(8r1c3) : -8r6c3->8r1c3->8r5c9 => -8r6c8 , -8r5c12

puzzle1: Show

2) P'(9r3c7) : -9r3c7->[7r3c7->7r1c6->4r1c3->3r1c9]->9r2c7 => -9b3c89, -9r46c7

puzzle2: Show

3) P'(8r5c9) : -8r5c9->8r2c9->[(8r3c2 & 4r3c8->7r3c5)->(7r7c2 & 8r6c3)]->7r6c7 => -7r5c9

puzzle3: Show

4) P'(7r4c3) : -7r4c3->3r4c3->3r1c9->79r23c7->7r4c9 => -7r4c167

puzzle4: Show

5) P'(7r4c3) : -7r4c3->3r4c3->3r1c9->6r1c1->6r5c2 => -7r5c2

puzzle5: Show

6) P'(7r6c237) : -7r6c237->7r4c9--> ... ->7r3c5 => -7r6c5 => -7r5c1 (see diagram)

Code: Select all

[-7r6c237->7r4c9->3r4c3->9r4c6]->7r5c2->7r7c2------->7r3c5
                           \        \             /
                            ---------->9r56c2->9r3c7


puzzle6: Show

7) P'(9r4c6) : -9r4c6->3r4c6->7r4c3->(7r6c7->9r3c7)->3r2c7->3r1c3->4r1c6->7r5c6 => -9r5c6 => r4c6=9

puzzle7: Show

8) P'(7r3c5) : -7r3c5->4r3c5->4r1c3->3r1c9->6r1c1->2r4c1->2r6c7->3r6c5->7r5c6 => -7r1c6, -7r5c5 => r3c5=7, stte.

puzzle8: Show