The New Sudoku Players' Forum

[ncantoral]

hello, new to the forums and I love the site. I love sudoku and been hooked for about 3 years now.

anyhow, I was lookin at brainbashers oct 10th super hard for some time now and I need help seeing the "BUG" elimination. I am primarily a pencil and paper type of guy, but I use a couple of the online solvers to help eliminate candidates.

here is the original puzzle

x x 2 9 x 8 7 x x

x x x x 3 x x x x

5 x 3 7 x 1 9 x 2

3 x 5 x x x 8 x 7

x 9 x x x x x 1 x

6 x 1 x x x 2 x 5

2 x 9 8 x 3 1 x 6

x x x x 9 x x x x

x x 8 2 x 4 3 x x

enjoy,

Norm

[Ruud]

Hi Norm, welcome to the forum.

Here are some hints:

After the series with X-Wing and Swordfishes which I expect you to have caught, there is an XY-Wing that you may take, but if you ignore it, there is a BUG+3 that has the same result. (just for educational purposes)

Code: Select all

.---------------.---------------.---------------.
| 4    16   2   | 9    56   8   | 7    35   13  |
| 9    17   67  | 56   3    2   | 45   8    14  |
| 5    8    3   | 7    4    1   | 9    6    2   |
:---------------+---------------+---------------:
| 3    2    5   | 46   1    69  | 8    49   7   |
| 8    9    47  | 35   2    57  | 6    1    34  |
| 6    47   1   | 34   8    79  | 2    39+4 5   |
:---------------+---------------+---------------:
| 2    45   9   | 8    57   3   | 1    47+5 6   |
| 7    3    46  | 1    9    56  | 45   2    8   |
| 1    56   8   | 2    67+5 4   | 3    57   9   |
'---------------'---------------'---------------'

BUG+3:

Deadly pattern with 2 solutions remains when r6c8<>4 and r7c8<>5 and r9c5<>5. One of them must be true.

r6c8=4 => r6c4=3 => r5c4=5 => r2c4=6 => r1c5=5 => r7c5=7
r7c8=5 => r7c5=7
r9c5=5 => r7c5=7

After this move and the subsequent singles (or the XY-Wing):

Code: Select all

.---------------.---------------.---------------.
| 4    16   2   | 9    56   8   | 7    35   13  |
| 9    17   67  | 56   3    2   | 45   8    14  |
| 5    8    3   | 7    4    1   | 9    6    2   |
:---------------+---------------+---------------:
| 3    2    5   | 46   1    69  | 8    49   7   |
| 8    9    47  | 35   2    57  | 6    1    34  |
| 6    47   1   | 34   8    79  | 2    39+4 5   |
:---------------+---------------+---------------:
| 2    45   9   | 8    7    3   | 1    45   6   |
| 7    3    46  | 1    9    56  | 45   2    8   |
| 1    56   8   | 2    56   4   | 3    7    9   |
'---------------'---------------'---------------'

BUG+1: r6c8=4

There is an explanation of BUG in Sudopedia.

Ruud

[ncantoral]

Ruud,
thank you, but did you mean to type in r6 col 8??? by chance??

[RW]

I suppose it should have been r6c8, and I believe a step is missing in the chain: r6c4=2 => ??? => r2c4=6.

There is also a shorter chain for this cell if you look at hidden singles:
r6c8=4 => r8c7=4 => r8c6=5 => r7c5=7

RW

[udosuk]

Here is a solving process without any uniqueness assumption:

After singles and box-line interactions:

Code: Select all

 *-----------------------------------------------------------*
 | 4     16    2     | 9     56    8     | 7     356   13    |
 | 9     1678  67    | 56    3     2     | 456   4568  14    |
 | 5     68    3     | 7     4     1     | 9     68    2     |
 |-------------------+-------------------+-------------------|
 | 3     2     5     | 46    1     69    | 8     469   7     |
 | 8     9    #47    |-3456  2     567   | 46    1    @34    |
 | 6    #47    1     |@34    8     79    | 2    -349   5     |
 |-------------------+-------------------+-------------------|
 | 2     45    9     | 8     57    3     | 1     457   6     |
 | 7     3     46    | 1     9     56    | 45    2     8     |
 | 1     56    8     | 2     567   4     | 3     57    9     |
 *-----------------------------------------------------------*

Y-wing (aka W-wing/semi-remote-pair):
Strong link of 4 in r5c3+r6c2 with r5c9,r6c4=3|4 => r5c4,r6c8 can't be 3

The rest are singles.

[ncantoral]

thank you very much everyone.

ruud, thank you for the link, that made it a lot clearer.

just seeing the swordfish took quite a while, but that is when I finally gave up. I have no problem with the x wings and I think I got a handle on swordfish. I like those a lot better than the 5 or 6 cell chains. I actually prefer looking for finned wings before I start listing for a chain. I noticed that some of the harder puzzles will have finned x-wings as a solution path countering an xy chain path or some other chain.