The New Sudoku Players' Forum

[Mauriès Robert]

Hi all,
Here is the puzzle I suggest you solve.
Good resolution.
Robert
.6.53..8...7.1.........9.419......6...6.2.7...8......551.6.........5.3...3..87.5.

puzzle: Show

solution: Show

[Cenoman]

In four steps:

Code: Select all

 +-------------------------+------------------------+-------------------------+
 |  124     6      1249    |  5       3      24     |  2-9     8      7       |
 |  248     2459   7       |  248     1      2468   |  2569    239    2369    |
 |  238     25     2358    |  278     67     9      |  256     4      1       |
 +-------------------------+------------------------+-------------------------+
 |  9       2457   12345   |  13478   47     1458   |  1248    6      2348    |
 |  134     45     6       |  13489   2      458-1  |  7       139    3489    |
 |  12347   8      1234    |  13479   4679   146    |  1249    1239   5       |
 +-------------------------+------------------------+-------------------------+
 |  5       1      2489    |  6       49     3      |  2489    7      2489    |
 |  24678   2479   2489    |  1249    5      124    |  3       129    24689   |
 |  246     3      249     |  1249    8      7      |  1249-6  5      2469    |
 +-------------------------+------------------------+-------------------------+

1. (5)r5c6 = r5c2 - r4c3 = r3c3 - (5=26)r3c27 - r3c5 = r6c5 - (6=1)r6c6 => -1 r5c6

2. Double Kraken column (9)r12679c7, row (4)r6c134567, using almost skyscraper (1)r9c47,r5c48
As a net:

Code: Select all

(9)r1c7 *
 ||
(9 - 56)r23c7 = r9c7 - r8c9 = (6-79)r8c12 =(9)r2c2 *
 ||
 || (4)r6c1 - (72)b4p27 = r46c3 - (2=489)r789c3 *
 ||  ||
 || (4)r6c3 - (4=289)r789c3 *
 ||  ||
(9 - 4)r6c7
 ||  ||
 || (4)r6c45 - (4=7)r4c5 - (79)r48c2 = (9)r2c2 *
 ||  ||
 || (4)r6c6 - (4=29)r1c67
 ||
(9)r7c7 - (9=47)r47c5 - r4c2 = (7-9)r8c2 = (9)r2c2 *
 ||
(9 - 1)r9c7 = r8c8 - [r9c7 = r9c4 - r5c4 = r5c8] = r5c1 - r1c1 = (1)r1c3 *
---------------
=> -9 r1c3

3. Double Kraken column (3)r356c1, row (8)r3c134, using almost skyscraper (1)r9c47,r5c48
As a net:

Code: Select all

(3 - 1)r5c1 = [r5c8 = r5c4 - r9c4 = r9c7] - r8c8 = (1)r9c7
 ||
 || (8-7)r3c4 = (7-6)r3c5 = (6)r3c7 *
 ||  ||
(3 - 8)r3c1
 ||  ||
 || (8)r3c3 =  - r23c1 = (8-6)r8c1 = (6)r8c9 *
 ||
(3 - 7)r6c1 = (7-6)r8c1 = (6)r8c9 *
---------------
=>-6r9c7; 10 placements & basics

Code: Select all

 +-----------------------+------------------+----------------------+
 |  124     6     124    |  5     3   b24   |  9     8     7       |
 |  48      9     7      |  48    1    6    |  5     23    23      |
 |  238    d25    2358   | c28    7    9    |  6     4     1       |
 +-----------------------+------------------+----------------------+
 |  9       257   1235   |  37    4    58   |  128   6     238     |
 |  134    d45    6      |  39    2    58   |  7     139   3489    |
 |  237     8     234    |  379   6    1    |  24    239   5       |
 +-----------------------+------------------+----------------------+
 |  5       1     248    |  6     9    3    |  248   7     248     |
 |  24678   27-4  2489   |  124   5   a24   |  3     129   24689   |
 |  246     3     249    |  124   8    7    |  124   5     2469    |
 +-----------------------+------------------+----------------------+

4. (4=2)r8c6 - r1c6 = r3c4 - (2=54)r35c2 => -4 r8c2; lclste

[Mauriès Robert]

Hi Cenoman,
Bravo for this resolution based on double Krakens.
Here is my resolution, but with rather short chains which, in some respects, are in your Krakens.

After reduction by the basic techniques, the puzzle is as follows.

puzzle1: Show

Here is one of my resolutions (I have made several) with antitracks of no more than 7 candidates or groups of candidates.
I remind you that the expression B->C means here that if B is placed on the puzzle then the basic techniques allow us to deduce that C is also placed.
On the other hand, an anti-track P'(A,n) limited to n elements is the set of n candidates or groups of candidates placed on the puzzle if A is eliminated.
Property: if a candidate K sees both a candidate A and a candidate of P'(A,n), K can be eliminated.

P'(5L5C6, 5) : (-5r5c6) => [5r4c6->(5r3c3->3r3c1)->8r3c4]->8r5C6 => -1r5c6, -4r5c6.
P'(1r9c7, 5) : (-1r9c7) => (1r8c8 and 1r9c4)->1r5c1->1r1c3->9r1c7 => -9r9c7.
P'(9r7c5, 5) : (-9r7c5) => 4r7c5->7r4c5->7r8c2->9r2c2->9r1c7 => -9r7c7.
P'(9r1c7, 5) : (-9r1c7) => 9r1c3->9r8c2->7r8c1->6r8c9->56r23c7 => -9r2c7.
P'(4r125c1, 4) : (-4r125c1) => 1238r1235c1->2r123c1->5r3c2->4r5c2 => -4r6c1.
P'(9r1c7, 6) : (-9r1c7) => 9r1c3->9r8c2->[248r789c3 and (7r4c2->4r4c5)]->4r6c7 =>-9r6c7.
Finally, r1c7=9 => r2c2=9 et r2c7=5.

P'(4r4c5, 3) : (-4r4c5) => 7r4c5->6r3c5->6r6c6 => -4r6c6.
P'(4r4c5, 5) : (-4r4c5) => 7r4c5->6r3c5->2r3c7->5r3c2->4r5c2 => -4r5c4 and -4r4c23.
P'(4r5c2, 7) : (-4r5c2) => 5r5c2->2r3c2->[2r1c6 and (6r3c7->6r2c6->1r6c6)]->4r8c6 => -4r8c2.
Finally, r5c2=4 => r5c6=5.

P'(1r5c1, 3) : (-1r5c1) => 3r5c1->3r3c3->5r4c3 => -1r4c3.
P'(1r6c6, 6) : (-1r6c6) => 6r6c6->6r2c9->6r9c7->(1r9c4 and 1r8c8)->1r5c1 => -1r6c13.
Finally, r5c1=1 => r1c3=1 and -4r89c1.

P'(6r3c7) : (-6r3c7) => 6r9c7->2r9c1->2r3c23 => -2r3c7
Finally, r3c7=6 and stte.

Cordialy
Robert