The New Sudoku Players' Forum

[Wecoc]

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+-------+-------+-------+
| . . 4 | . 6 . | 7 . . |
| . 8 . | . . . | . 9 . |
| 1 . . | 4 . 7 | . . 6 |
+-------+-------+-------+
| . . 6 | . 8 . | 5 . . |
| 7 . . | 6 . 3 | . . 8 |
| . . 9 | . 2 . | 6 . . |
+-------+-------+-------+
| 3 . . | 9 . 2 | . . 7 |
| . 7 . | . . . | . 8 . |
| . . 1 | . 7 . | 3 . . |
+-------+-------+-------+
..4.6.7...8.....9.1..4.7..6..6.8.5..7..6.3..8..9.2.6..3..9.2..7.7.....8...1.7.3..

[Ajò Dimonios]

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+---------------+-----------------+------------------+
| 259  259   4  | 12358 6    1589 | 7    1235  1235  |
| 6    8     7  | 1235  135  15   | 124  9     12345 |
| 1    259   3  | 4     59   7    | 8    25    6     |
+---------------+-----------------+------------------+
| 24   1234  6  | 17    8    149  | 5    12347 12349 |
| 7    1245  25 | 6     1459 3    | 1249 124   8     |
| 8    1345  9  | 157   2    145  | 6    1347  134   |
+---------------+-----------------+------------------+
| 3    456   8  | 9     145  2    | 14   1456  7     |
| 2459 7     25 | 135   1345 6    | 1249 8     12459 |
| 2459 24569 1  | 58    7    458  | 3    2456  2459  |
+---------------+-----------------+------------------+


Easily resolved with TDP
P(2r2c7)=>backdoor
P(2r5c7)=>contradiction=>-2r5c7
P(2r8c7)=>contradiction=>-2r8c7=>stte

Or if you do not want to use contradictions, you can eliminate the common candidates that are eliminated from the development of the three tracks {P (2r2c7, P (2r5c7 and P (2r8c7}) using only the basic technique, which are those shown in the figure. the solution is obtained (stte).
http://www.sitohd.com/siti/23142/portfolio/#i1

The gray cells are the backdoors, those with other colors are candidates which, if assumed to be true, lead to a contradiction using only (Singles and Intersections).

http://www.sitohd.com/siti/23142/foto/414595.jpg

[Mauriès Robert]

Hi,
Another way of using TDP, equivalent to that of Ajo Dimonios, is to construct a network of two conjugated tracks from the 2r3 pair.

- Step 1 development of P(2r3c2) (see puzzle1)
P(2r3c2) : 2r3c2->5r2c8->9r3c5->9r4c6->9r5c7-> ---
P(2r3c2).P'(2r8c3) = P(2r3c2).{-2r8c3-> --- ->2r8c1} => P(2r3c2) does not contain 2r8c7, therefore contains 2r2c7 .

puzzle1: Show

- Step 2 development of P(2r3c8) (see puzzle2)
P(2r3c8) : 2r3c8->2r2c4-> ---
P(2r3c8).P'(2r5c7) = P(2r3c8).{-2r5c7->2r4c9->9r4c6->9r3c5->5r3c2->5r5c3->2r8c3} => P(2r3c2) does not contain 2r8c7, therefore contains 2r5c7 .

puzzle2: Show

- Step 3 development and intersection of the two tracks (see puzzle3).
From then on, both tracks are easily developed, with only the basic techniques, as on the puzzle3.
This allows the elimination of all candidates who see both colors, and validations r1c1=5, r9c1=9 and r7c7=1.

puzzle3: Show

- Step4 end of resolution
After these eliminations, the puzzle is the next one on which the two tracks can be extended to complete the solution, with the 6r9c2 common to both tracks being validated.

puzzle4: Show

Robert

[Cenoman]

In six steps

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 +----------------------+------------------------+-------------------------+
 |  259    259     4    |  12358   6      1589   |  7      1235    1235    |
 |  6      8       7    |  1235    135    15     |  124    9       12345   |
 |  1      29-5    3    |  4       59     7      |  8      25      6       |
 +----------------------+------------------------+-------------------------+
 |  24     1234    6    |  17      8      49-1   |  5      12347   12349   |
 |  7      1245    25   |  6       1459   3      |  1249   124     8       |
 |  8      1345    9    |  157     2      145    |  6      1347    134     |
 +----------------------+------------------------+-------------------------+
 |  3      456     8    |  9       145    2      |  14     146-5   7       |
 |  2459   7       25   |  135     1345   6      |  1249   8       12459   |
 |  2459   4569-2  1    |  58      7      458    |  3      246-5   2459    |
 +----------------------+------------------------+-------------------------+

1. (1=5)r2c6 - (5=9)r3c5 - r1c6 = (9)r4c6 => -1 r4c6
2. (2)r13c2 = (2-594)r189c1 = (46)r79c2 => -2 r9c2

3. Kraken column (2)r258c7
(2)r2c7 - r3c8 = (2)r3c2
(2-9)r5c7 = r5c5 - r3c5 = (9)r3c2
(2)r8c7 - (2=5)r8c3 - r5c3 = (5)r56c2
=> -5 r3c2

4. (5=8)r9c4 - r1c4 = (8-9)r1c6 = (9-5)r3c5 = (5)r3c8 => -5 r9c8

5. Kraken cell (4569)r9c2
(4)r9c2 - r89c1 = r4c1 - (4=9)r4c6 - r1c6 = (9-5)r3c5 = (5)r3c8
(5)r9c2 - (5=84)r9c46 - r78c5 = (4-9)r5c5 = (9-5)r3c5 = (5)r3c8
(6)r9c2 - r7c2 = (6)r7c8
(9)r9c2 - (9=2)r3c2 - (2=5)r3c8
=> -5 r7c8; five placements

Code: Select all

 +---------------------+----------------------+-----------------------+
 |  59     59     4    |  1238   6      18    |  7     123     123    |
 |  6      8      7    |  1235   135    15    |  124   9       1234   |
 |  1      2      3    |  4      9      7     |  8     5       6      |
 +---------------------+----------------------+-----------------------+
 |  24*    134    6    |  17     8      9     |  5     12347*  1234*  |
 |  7      145    25   |  6      145    3     |  9     14-2    8      |
 |  8      1345   9    |  157    2      145   |  6     1347    134    |
 +---------------------+----------------------+-----------------------+
 |  3      456    8    |  9      145    2     |  14    146     7      |
 |  2459   7      25   |  135    1345   6     |  124   8       59     |
 |  2459*  4569   1    |  58     7      458   |  3     246*    59     |
 +---------------------+----------------------+-----------------------+

6. (2)r9c8 = r9c1 - r4c1 = r4c89 => -2 r5c8; ste