The New Sudoku Players' Forum

[Mauriès Robert]

Hi all,
Here's my christmas grid
I'm interested in your solving this puzzle, what will it be ?
2....1..5..3..6.....9.5.38......8.57..5...4..68........26.9.8.....8..5..3..2....1
Sincerely
Robert

my resolution with TDP: Show

After reduction of the grid by the basic techniques, the solution can be found quickly by tracing on the grid the conjugate tracks P(2r2c5) and P(2r3c6) which places the 2r3c6, then P(6r4c4) and P(6r5c4), one of which is invalid and the other gives the solution. But here is another step-by-step resolution that does not use direct contradiction.
1) P'(2r3c6) : -2r3c6->2r3c9->6r8c9->[9r6c9->9r5c6, 2r8c8]->2r5c5 => -2r2c5 => r3c6=2.

Hidden Text: Show

2) P'(6r1c2) : -6r1c2->6r3c2->4r3c9->4r4c4-4r6c3->7r1c3 =>-7r1c2.

Hidden Text: Show

3) P'(6r1c2) : -6r1c2->6r3c2->---->4r9c2 (see diagram) => -4r1c2 => r1c2=6 and r3c9=6.

Code: Select all

                     - - - - - - - - - - - - - -                 
                   /     /                        \
-6r1c2->6r3c2->4r3c9->2r2c9- - - - - - - - ->1r2c7->7r2c8->7r7c6->4r8c6->4r9c2
                   \                      /                     /
                    \         >6r4c7>79r19c7                   /
                     \      /                                 /
                       >4r4c4- - - - - - - - - - - - - - - - -


Hidden Text: Show

4) P'(6r9c7) : -6r9c7->6r4c7->4r4c4->4r2c5->2r2c9->2r8c8 => -6r8c8 => r8c5=6.

Hidden Text: Show

5) P'(4r3c4) : -4r3c4->4r2c5->------>7r5c4 (see diagram) => -7r3c4 => r3c4=4, stte.

Code: Select all

   
-4r3c4->4r2c5->2r2c9->17r2c78->9r1c7->6r9c7->6r5c8->7r5c4
           \                        /
            ->7r9c6- - - - - - - - -


Hidden Text: Show

Hidden Text: Show

[Leren]

The puzzle was solvable with basics and linear AIC's but a lot of them. My solver used 23 with one setup and HoDoku used 25. Leren

[eleven]

Hi Robert,

the first i found in your puzzle was this Sue de Coq.

Code: Select all

+-------------------------+-------------------------+-------------------------+
| 2       467     47      | 3       8       1       | 679     4679    5       |
| 8       5       3       | 9       247     6       | 127     1247    24      |
| 147     1467    9       | 47      5       247     | 3       8       246     |
+-------------------------+-------------------------+-------------------------+
| 149     1349    124     |*46      1234    8       | 1269    5       7       |
| 179     1379    5       |*67      1237    2379    | 4       12369   8       |
| 6       8      *1247    | 5       12347   23479   | 129     1239    239     |
+-------------------------+-------------------------+-------------------------+
| 5       2       6       | 1       9       347     | 8       347     34      |
| 1479    1479    147     | 8       3467    347     | 5       234679  23469   |
| 3       479     8       | 2       467     5       | 679     4679    1       |
+-------------------------+-------------------------+-------------------------+

Exactly one of 47 must be in r45c4, and r6c3 then (remaining in row 6). So you can eliminate 12 from r6c3 and 47 from r4c5, r5c56.
This didn't help much.

I also found 2r3c6, similar to your net, with the plan to solve box 2 to get a short solution.
But when trying to eliminate 4r2c5, i realised, that it could be solved with only 2 contradicting cells:

Code: Select all

+-------------+-------------+-------------+
| 2   6   7   | 3   8   1   | 9   4   5   |
| 8   5   3   | 9   4   6   | 1   7   2   |
| 4   1   9   | 7   5   2   | 3   8   6   |
+-------------+-------------+-------------+
| 9   3   2   | 4   1   8   | 6   5   7   |
| 1   7   5   | 6   2   3   | 4   9   8   |
| 6   8   4   | 5   7   9   | 2   1   3   |
+-------------+-------------+-------------+
| 5   2   6   | 1   9   7   | 8   3   4   |
| 7   9   1   | 8   3   4   | 5   2   69  |
| 3   4   8   | 2   6   5   | 7   69  1   |
+-------------+-------------+-------------+

So my plan was bad and i gave up.

With some effort I can follow your solution (where both nets and diagrams are incomplete). But it does not give me any hint, how i could find this solution manually.
Apart from the many options you have for the starting cells (you already choose a 3-digit cell, though there are at least 15 2-digit options), using nets give so many ways to continue, that i am totally lost, which one i should follow.
This is very different from AIC chains, where you only have one chain and a target, which you try to reach (and if reached, often can be shortened, cause you just didn't spot the shortcut - or you see, that the chain you have, leads to another elimination).

[Mauriès Robert]

Hi Eleven,

But when trying to eliminate 4r2c5, i realised, that it could be solved with only 2 contradicting cells

Can you elaborate on that?

With some effort I can follow your solution (where both nets and diagrams are incomplete).

What do you mean incomplete?
Thank you.
Robert

[Cenoman]

Four steps, all present in the PMs below:

Code: Select all

 +-----------------------+-----------------------+--------------------------+
 |  2      467    47     |  3    8       1       |  679    4679     5       |
 |  8      5      3      |  9    247     6       |  127    1247     24      |
 |  147    1467   9      |  47   5       247     |  3      8        246     |
 +-----------------------+-----------------------+--------------------------+
 |  149    1349   124    |  46   1234    8       |  1269   5        7       |
 |  179    1379   5      |  67   1237    2379    |  4      12369    8       |
 |  6      8      1247   |  5    12347   23479   |  129    1239     239     |
 +-----------------------+-----------------------+--------------------------+
 |  5      2      6      |  1    9       347     |  8      347      34      |
 |  1479   1479   147    |  8    3467    347     |  5      234679   23469   |
 |  3      479    8      |  2    467     5       |  679    4679     1       |
 +-----------------------+-----------------------+--------------------------+

1. (2)r8c8 = r8c9 - r23c9 = (2-17)r2c78 = r2c5 - r3c4 = (7-6)r5c4 = (6)r5c8 =>-6r8c8

2. Kraken cell (179)r5c1
(1)r5c1 - r3c1 = (1-6)r3c2 = (6)r1c2
(7)r5c1 - (7=64)r45c4 - r4c12 = r46c3 - (4=7)r1c3
(9)r5c1 - r5c6 = r6c6 - r6c9 = (9-6)r8c9 = r3c9 - r3c2 = (6)r1c2
=>-7r1c2

3. Kraken row (7)r2c578
(7)r2c5 - r89c5 = (7)r78c6
(7-126)r246c7 = r4c4 - (6=7)r5c4
(7)r2c8 - r7c8 = (7)r7c6
=>-7r6c6

4. Double Kraken cell (479)r9c2 & column (7)r129c7
(4)r9c2
(7)r9c2 - r9c7 = [(7)r1c7 = (7-126)r246c7 = r4c4 - (6=7)r5c4 - r6c56 = (7)r6c3] - (7=4)r1c3
(9)r9c2 - r9c78 = (92)r8c89 - (6)r8c9 = r3c9 - r3c2 = (6)r1c2
=>-4r1c2; lclste

[Mauriès Robert]

Hi Cenoman,
Nice resolution too and there are many others possible.
We can even reduce to only two steps like this:
Step 1) P'(2r3c6) : -2r3c6->2r3c9->6r8c9->[9r6c9->9r5c6, 2r8c8]->2r5c5 => -2r2c5 => r3c6=2.
Step 2) P'(4r4c4) : -4r4c4->6r4c4----->4r4c2 (see diagram) => -4r4c4 =>r4c4=6, stte,
It is a long and complex chain to write, easier to see on the puzzle with a coloured marking.

puzzle: Show

Code: Select all

                              - - - - - - - - - -
                             |                   |
            >6r5c8 - - - ->6r9c7- - >7r1c7->9r1c8->9r8c9->9r9c2 - - -
           |            |              |      |      |               |
           |            |              |      |      |               |
-4r4c4->6r4c4->4r3c4->6r3c9            |       - - - - ->9r6c7->9r5c6->9r4c1->4r4c2
           |     |                     |                                    |
           |      >7r2c5- - - - - - - -                                     |
           |                                                                |
            >7r5c4->7r6c3->4r1c3 - - - - - - - - - - - - - - - - - - - - - -


Robert

[eleven]

Hi Eleven,

But when trying to eliminate 4r2c5, i realised, that it could be solved with only 2 contradicting cells

Can you elaborate on that?

In the 2-stepper above you made, what my plan was - you eliminated 4r4c4 or 4r2c5 resp.
But when i tried that, i could fill all but 2 cells in a valid way, i.e. i arrived at a contradiction at the very end. This is really boring, and it was too boring for me, to find a way for the elimination manually without a contradiction - with hundreds of options to change the order of setting singles or using pairs or UR's.

With some effort I can follow your solution (where both nets and diagrams are incomplete).

What do you mean incomplete?

2 points for step 3: 6r4c7 does not follow from 4r3c9, but from 4r4c4, and i am missing 4r4c4->4r2c5 together with 7r7c6 to get 4r8c6.

[Mauriès Robert]

Hi Eleven,
Indeed, I had drawn the diagram of stage 3 very badly, which made it incomprehensible. But the color marking on the puzzle was correct.
I redid the diagram.
Before, you also wrote:

Apart from the many options you have for the starting cells (you already choose a 3-digit cell, though there are at least 15 2-digit options), using nets give so many ways to continue, that i am totally lost, which one i should follow.
This is very different from AIC chains, where you only have one chain and a target, which you try to reach (and if reached, often can be shortened, cause you just didn't spot the shortcut - or you see, that the chain you have, leads to another elimination).

With TDP, as with AIC, the target is determined and the path to that target is searched to produce an elimination. On this puzzle, the role of 6, 4 and 9 is quite easy to see and that is what guided my choices.
Sincerely
Robert