The New Sudoku Players' Forum

[tarek]

Code: Select all

+-------+-------+-------+
| . . 4 | . 2 . | 3 . . |
| 2 . . | 7 . 6 | . . . |
| 5 6 . | 3 . 1 | . . . |
+-------+-------+-------+
| . 1 5 | . . 7 | . . . |
| . . 8 | . . . | 4 . . |
| . . . | 1 . . | 5 7 . |
+-------+-------+-------+
| . . . | 5 . 2 | . 4 8 |
| . . . | 8 . 3 | . . 6 |
| . . 2 | . 1 . | 7 . . |
+-------+-------+-------+
..4.2.3..2..7.6...56.3.1....15..7.....8...4.....1..57....5.2.48...8.3..6..2.1.7..


Play this puzzle online at the Daily Sudoku site

[StrmCkr]

Code: Select all

+---------------------+----------------+-------------------+
| 17(8)  78     4     | 9   2     (58) | 3    6      157   |
| 2      389    139   | 7   458   6    | 189  159    1459  |
| 5      6      79    | 3   48    1    | 289  29     2479  |
+---------------------+----------------+-------------------+
| 349    1      5     | 24  39    7    | 6    8      239   |
| 3679   2379   8     | 26  3569  (59) | 4    1239   1239  |
| 3469   2349   369   | 1   3689  489  | 5    7      239   |
+---------------------+----------------+-------------------+
| 13679  379    13679 | 5   679   2    | 19   4      8     |
| 1479   4579   179   | 8   79    3    | 129  1259   6     |
| 69(8)  (589)  2     | 46  1     4-9  | 7    (359)  (359) |
+---------------------+----------------+-------------------+

Almost Locked Set W-Wing: A=r9c289 {3589}, B=r15c6 {589}, connect by 8r19c1 => r9c6<>9
singles and 2- blr to finish.

[tarek]

I couldn't find a straightforward move to reduce it to stte … It can be SStte

Although the ER=7.1. The Backdoor targeting moves are 8.0+

[SpAce]

I'll just take the easy way out.

Code: Select all

.----------------------.-------------------.-----------------.
|  c178    78    4     |   9    2     b58  | 3    6     157  |
|   2      389   139   |   7    458    6   | 189  159   1459 |
|   5      6     79    |   3    48     1   | 289  29    2479 |
:----------------------+-------------------+-----------------:
|   349    1     5     |   24   39     7   | 6    8     239  |
|   3679   2379  8     |   26   3569  b59  | 4    1239  1239 |
|   3469   2349  369   |   1    3689   489 | 5    7     239  |
:----------------------+-------------------+-----------------:
|   13679  379   13679 |   5    679    2   | 19   4     8    |
|   1479   4579  179   |   8    79     3   | 129  1259  6    |
| d(8)9-6  589   2     | a[6]4  1     a49  | 7    359   359  |
'----------------------'-------------------'-----------------'


ALS-H-Wing:

(6=49)r9c46 - (9=58)r51c6 - r1c1 = (8)r9c1 => -6 r9c1; btte

--
Added. Simpler:

Code: Select all

.------------------------.-------------------.------------------.
|  178     78      4     |  9     2      58  | 3    6      157  |
|  2       389     139   |  7     458    6   | 189  159    1459 |
|  5       6       79    |  3     48     1   | 289  29     2479 |
:------------------------+-------------------+------------------:
| a39[4]   1       5     | a[42]  39     7   | 6    8     b239  |
|  3679    2379    8     |  26    3569   59  | 4    1239   1239 |
|  3469  d(2)39-4  369   |  1     3689   489 | 5    7     c239  |
:------------------------+-------------------+------------------:
|  13679   379     13679 |  5     679    2   | 19   4      8    |
|  1479    4579    179   |  8     79     3   | 129  1259   6    |
|  689     589     2     |  46    1      49  | 7    359    359  |
'------------------------'-------------------'------------------'

L2-Wing (aka "Purple Cow" ):

(42)r4c14 = r4c9 - r6c9 = (2)r6c2 => -4 r6c2; btte

[Mauriès Robert]

Hi,
Unsatisfactory resolution!
P(8r1c6) invalide (see diagram and puzzle) => -8r1c6 => r1c6 =5, stte.

Code: Select all

                                    ->79r78c5->3r4c5 - - - - -
                                  /                           \
P(8r1c6) : 8r1c6->8r2c2->8r9c1->6r9c4->2r5c4->2r6c2->4r6c1*    \
              \                           \        /            \
                ->7r1c2->7r5c1*             ->4r4c4 - - - - - - ->9r4c1*
                \    \
                  - - - - ->1r1c1* 
(*) => contradiction in r8c1             


It sounds complicated, but by marking the anti-track on the puzzle, it's very easy!

puzzle: Show

Robert

[Mauriès Robert]

Hi SpAce,
Bravo for your resolution and I regret not having seen this shorter path!
In my own way (TDP) I will write :
P'(6r9c9) : -6r9c4 -> 4r9c4 -> 9r9c6 -> 5r5c6 -> 8r1c6 -> 8r2c2 -> 8r9c1 => -6r9c1 => r9c4=6, btte.
We also note that this anti-track leading to a contradiction is invalid.
Robert

[SpAce]

Hi Robert,

Hi SpAce,
Bravo for your resolution and I regret not having seen this shorter path!

Thanks. StrmCkr's ALS-W-Wing is just as simple, though I'd rather present it as an AIC:

(9=58)r51c6 - r1c1 = r9c1 - (8=539)r9c289 => -9 r9c6; btte

In fact, I'd shorten it a bit:

(9=58)r51c6 - r1c1 = (864)r9c146 => -9 r9c6; btte

That's no longer an ALS-W-Wing, though. (Perhaps ALS-AHS-M-Wing, if one really wants a name). See also my new simpler solution.

Note that both StrmCkr's and my (both) solutions are "btte" (basics to the end). While acceptable, what we really seek is "stte" (singles to the end). That's much harder with this puzzle (like tarek said), and probably requires a net-based solution like yours (which is stte).

I recommend you also mark this distinction (stte vs btte) when you present your solutions. Both kinds are acceptable but 'stte' is appreciated more because it's sometimes much more difficult to achieve (like here). For that very reason you might have seen me complain when someone presents a btte-solution and falsely marks it as stte. (It annoys me to no end, especially if it's never corrected.)

So, your solution is in fact superior in that regard. However, its value is lowered because it's presented as a contradiction. To make it more interesting, you should present it as a verity even if it's found as a contradiction. In other words, you could convert it into a (TDP equivalent of a) kraken net with the cell r8c1 as the main SIS (strong inference set). Otherwise I'm afraid no one really cares, because (as you said yourself) contradictions are easy to find. Making them presentable is often harder.

Added. Here's one way to express your solution as a verity:

Code: Select all

Double Kraken

(1)r8c1 - (1=78)r1c12
||
(4)r8c1 - r46c1 = (4-2)r6c2 = r5c2 - (2=6)r5c4 - r9c4 = (6-8)r9c1 = (8)r1c1
||
(7)r8c1 - r5c1 = r5c2 - (7=8)r1c2
||
(9)r8c1 - (9)r4c1
          ||
          (3)r4c1 - (3=9)r4c5 - (97=6)r78c5 - r9c4 = (6-8)r9c1 = (8)r1c1
          ||
          (4)r4c1 - (4=2)r4c4 - (2=6)r5c4 - r9c4 = (6-8)r9c1 = (8)r1c1


=> -8 r1c6; stte

...or without the redundancy:

Code: Select all

(1)r8c1 - (1=78)r1c12
||
(7)r8c1 - r5c1 = r5c2 - (7=8)r1c2
||
(4)r8c1 - r46c1 = (4-2)r6c2 = r5c2 - (2=6)r5c4 - r9c4 = (6-8)r9c1 = (8)r1c1
||                                 /           /
||        (4)r4c1 - (4=2)r4c4 ----            /
||        ||                                 /
||        (3)r4c1 - (3=9)r4c5 - (97=6)r78c5 -
||        ||
(9)r8c1 - (9)r4c1


=> -8 r1c6; stte

13x13 TM: Show

Code: Select all

  8r1c1 8r9c1
        6r9c1 6r9c4
              6r5c4 2r5c4
                    2r5c2 2r6c2
                    2r4c4       4r4c4
                          4r6c2 4r4c1 4r6c1
              6r7c5                         79cr78c5
                                             9r4c5   3r4c5
                                4r4c1                3r4c1 9r4c1
  8r1c2                                                          7r1c2
                                                                 7r5c1 7r5c1                             
                                      4r8c1                9r8c1       7r8c1 1r8c1
 78r1c12                                                                     1r1c1
----------------------------------------------------------------------------------
-8r1c6

[tarek]

In Dan's absence I've generated 31 puzzles which should cover the 31 days from 19 December onwards. The puzzles will average at ER = 7.2 but like today the singles backdoor could be at a higher rating. Also there will be very few puzzles in the 7.5 - 7.8 range which were vetted to have very few forcing chains but I will get your feedback on them as we go forward.

I would like to still enjoy solving / analyzing them too after the puzzle is posted just like when Dan posted them so I'm not solving them step by step completely before posting!

tarek

[Ngisa]

Code: Select all

+-------------------------+--------------------+---------------------+
| 17-8      78      4     | 9     2       a58  | 3      6       157  |
| 2        389      139   | 7     458      6   | 189    159     1459 |
| 5        6        79    | 3     48       1   | 289    29      2479 |
+-------------------------+--------------------+---------------------+
| 349      1        5     | 24    39       7   | 6      8       239  |
| 3679    c2379     8     |b26    3569    a59  | 4      1239    1239 |
| 3469    d2349     369   | 1     3689     489 | 5      7       239  |
+-------------------------+--------------------+---------------------+
| 13679    379      13679 | 5     679      2   | 19     4       8    |
| 1479    e4579     179   | 8     79       3   | 129    1259    6    |
|g689     f589      2     |b46    1       a49  | 7      359     359  |
+-------------------------+--------------------+---------------------+


(8=594)r159c6 - (4=62)r95c4 - (2)r5c2 = (2-4)r6c2 = (4-5)r8c2 = (5-8)r9c2 = (8)r9c1 => - 8r1c1; btte

Clement

[Mauriès Robert]

Hi SpAce,
Thank you for your comments and advice. I corrected.
With TDP one can also solve without contradiction by interaction of two conjugated tracks, like this :
P(8r1c6) : 8r1c6->8r2c2->8r9c1 and P(5r1c6) : 5r1c6 --- ->8r9c1 (see diagram)
=> r9c1=8, btte.

Code: Select all

                   - - - - - - - - - - - - ->8r9c1
                 /       /              /
5r1c6->9r5c6->4r9c6->6r9c4->4r4c4      /
         \                     \      /
           ->3r4c5 - - - - - - - >9r4c1


But we can also find a path that leads to the elimination of 8r1c6 like this:
P'(8r1c1):-8r1c1->8r9c1->- - - ->8r1c2 => -8r1c6 (see diagram), stte.

Code: Select all

                                ->79r78c5->3r4c5 - - -
                              /                        \
                             /       - - ->4r4c4 - - - - ->9r4c1- - - - - - - - 
                            /      /           \                                \
P'(8r1c1):-8r1c1->8r9c1->6r9c4->2r5c4->2r6c2->4r6c1- - - - - - - - - - - - - - - \ 
                          /                   /                                   \
                         /                   /                                     \
                         ->4r9c6 - - - - - -                                        \
                                  /                                                  \
                                  ->4r8c2->5r8c8->39r9c89->239r469c9->1r5c9->1r1c1->7r8c1->7r5c2->8r1c2 
=> -8r1c6, stte                     


Robert