## BUG1 or BUG4 or not at all?

Advanced methods and approaches for solving Sudoku puzzles

### BUG1 or BUG4 or not at all?

Code: Select all
*-----------*
|937|128|546|
|.2.|436|7.9|
|..4|759|.32|
|---+---+---|
|851|947|..3|
|396|215|478|
|472|683|951|
|---+---+---|
|.19|.74|..5|
|.43|.61|.97|
|7..|.92|..4|
*-----------*

*--------------------------------------------------*
| 9    3    7    | 1    2    8    | 5    4    6    |
| 15   2    58   | 4    3    6    | 7    18   9    |
| 16   68   4    | 7    5    9    | 18   3    2    |
|----------------+----------------+----------------|
| 8    5    1    | 9    4    7    | 26   26   3    |
| 3    9    6    | 2    1    5    | 4    7    8    |
| 4    7    2    | 6    8    3    | 9    5    1    |
|----------------+----------------+----------------|
| 26   1    9    | 38   7    4    |#36+8 #28+6 5   |
| 25   4    3    | 58   6    1    | 28   9    7    |
| 7    68   58   | 35   9    2    | 13   16   4    |
*--------------------------------------------------*

When I insert 8 in r7c7 and 6 in r7c8 the solution is correct. Both candidates 6 and 8 fulfill the conditions of BUG Typ 1 but there are two and usually BUG1 has only 1 threefold extra-candidate in the whole grid.

Bug 4 has two threefold extra-candidates in the grid but their cells are connected with a number showing up twice only in the respective region. Thus this number together with the two threefold candidates would expell the third candidate out of their two cells.

But this is neither the case here. SE solves it with a simple forcing chain but I hesitate to do so.

Is this a BUG or just a solution working just by chance I did?

With best wishes

Claudia
claudiarabia

Posts: 288
Joined: 14 May 2006

### Re: BUG1 or BUG4 or not at all?

claudiarabia wrote:Is this a BUG or just a solution working just by chance I did?

It is a valid BUG+2 with the strong inference BUG2:(r7c7 =8|6= r7c8), hence ...

r7c8 -8- BUG2:(r7c7 =8|6= r7c8) ==> r7c8<>8 and

BUG2:(r7c7 =8|6= r7c8) -6- r7c7 ==> r7c7<>6

ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: BUG1 or BUG4 or not at all?

claudiarabia wrote:SE solves it with a simple forcing chain but I hesitate to do so.

Code: Select all
*--------------------------------------------------*
| 9    3    7    | 1    2    8    | 5    4    6    |
| 15   2    58   | 4    3    6    | 7    18   9    |
| 16   68   4    | 7    5    9    | 18   3    2    |
|----------------+----------------+----------------|
| 8    5    1    | 9    4    7    |#26   26   3    |
| 3    9    6    | 2    1    5    | 4    7    8    |
| 4    7    2    | 6    8    3    | 9    5    1    |
|----------------+----------------+----------------|
|#26   1    9    | 38   7    4    | 38-6  268  5   |
|*25   4    3    | 58   6    1    |*28   9    7    |
| 7    68   58   | 35   9    2    | 13   16   4    |
*--------------------------------------------------*

You could use a W-wing. One of the marked 26 duos must be a six because of the strong link on 2s in row 8.
wintder

Posts: 297
Joined: 24 April 2007

### Re: BUG1 or BUG4 or not at all?

ronk"][quote="claudiarabia wrote:It is a valid BUG+2 with the strong inference BUG2:(r7c7 =8|6= r7c8

Thank you. You are always so fast in your replies.

Then in the SE-Language this is a BUG Typ 1 too but with 2 BUG-Cells.

I found an example for BUG Typ 4 where you have three candidates in two cells (r9c5 and r9c8) showing up thrice in its respective column, row and box. Both cells are connected with the value 1 in the two BUG-cells showing up there in the BUG-Region, the line 9, only. Thus you can eliminate the 5 in r9c5 and the 6 in r9c8. Other examples of BUG4 show only two candidates showing up thrice, each in every of the two BUG-Cells
Code: Select all

*-----------------------------------------------------------*
| 17    17    9     | 6     4     3     | 2     58    58    |
| 6     4     8     | 2     9     5     | 3     7     1     |
| 2     3     5     | 18    18    7     | 6     4     9     |
|-------------------+-------------------+-------------------|
| 58    58    4     | 9     3     1     | 7     26    26    |
| 17    2     3     | 47    6     48    | 15    9     58    |
| 9     17    6     | 5     78    2     | 4     18    3     |
|-------------------+-------------------+-------------------|
| 4     6     1     | 3     57    9     | 8     25    27    |
| 58    9     7     | 18    2     6     | 15    3     4     |
| 3     58    2     | 47   #15+78 48    | 9    #16+5  67    |
*-----------------------------------------------------------*.
So I conclude there will be a BUG Typ 1 with two BUG-Cells too.
claudiarabia

Posts: 288
Joined: 14 May 2006

### Re: BUG1 or BUG4 or not at all?

claudiarabia wrote:Then in the SE-Language this is a BUG Typ 1 too but with 2 BUG-Cells.
[...]
So I conclude there will be a BUG Typ 1 with two BUG-Cells too.

I don't follow Sudoku Explainer closely enough to know, but I hope that's not true.

BUG Type 1 should be analogous to UR Type 1 ... meaning there is only one cell with extra candidates.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: BUG1 or BUG4 or not at all?

wintder wrote:
claudiarabia wrote:SE solves it with a simple forcing chain but I hesitate to do so.

Code: Select all
*--------------------------------------------------*
| 9    3    7    | 1    2    8    | 5    4    6    |
| 15   2    58   | 4    3    6    | 7    18   9    |
| 16   68   4    | 7    5    9    | 18   3    2    |
|----------------+----------------+----------------|
| 8    5    1    | 9    4    7    |#26   26   3    |
| 3    9    6    | 2    1    5    | 4    7    8    |
| 4    7    2    | 6    8    3    | 9    5    1    |
|----------------+----------------+----------------|
|#26   1    9    | 38   7    4    | 38-6  268  5   |
|*25   4    3    | 58   6    1    |*28   9    7    |
| 7    68   58   | 35   9    2    | 13   16   4    |
*--------------------------------------------------*

You could use a W-wing. One of the marked 26 duos must be a six because of the strong link on 2s in row 8.

Hi Wintder,

thank you so much because of the hint at the phantastic W-Wing. It is easy to spot and to perceive. I hope I can use this W-wing-strategy in many more sudokus.
claudiarabia

Posts: 288
Joined: 14 May 2006

### Some more BUG+2 Sudokus

Code: Select all
8.......2
.........
..43.65..
..3.1.4..
...9.7...
..5.8.3..
..65.41..
.........
2.......7

*-----------*
|85.|.4.|632|
|36.|.5.|714|
|1.4|3.6|5..|
|---+---+---|
|..3|615|4..|
|41.|937|.65|
|6.5|482|3.1|
|---+---+---|
|..6|5.4|1.3|
|53.|.9.|.46|
|24.|.63|957|
*-----------*

*--------------------------------------------------*
| 8    5    79   | 17   4    19   | 6    3    2    |
| 3    6    29   | 28   5    89   | 7    1    4    |
| 1    27   4    | 3    27   6    | 5    89   89   |
|----------------+----------------+----------------|
| 79   28   3    | 6    1    5    | 4    27   89   |
| 4    1    28   | 9    3    7    | 28   6    5    |
| 6    79   5    | 4    8    2    | 3    79   1    |
|----------------+----------------+----------------|
| 79  89+7  6    | 5    27   4    | 1    28   3    |
| 5    3   17+8  | 27   9    18   | 28   4    6    |
| 2    4    18   | 18   6    3    | 9    5    7    |
*--------------------------------------------------*
Actually, SE solves this Sudoku with a forcing chain.
--------------------------------------------------------------------------

Code: Select all
*-----------*
|647|.1.|9.5|
|.51|649|.8.|
|8.9|..5|416|
|---+---+---|
|764|291|853|
|1.5|43.|.79|
|.9.|5.7|.41|
|---+---+---|
|4.2|1..|598|
|51.|9.4|.6.|
|9.6|.5.|1.4|
*-----------*

*--------------------------------------------------*
| 6    4    7    | 38   1    28   | 9    23   5    |
| 23   5    1    | 6    4    9    | 37   8    27   |
| 8    23   9    | 37   27   5    | 4    1    6    |
|----------------+----------------+----------------|
| 7    6    4    | 2    9    1    | 8    5    3    |
| 1    28   5    | 4    3    68   | 26   7    9    |
| 23   9    38   | 5    68   7    | 26   4    1    |
|----------------+----------------+----------------|
| 4    37   2    | 1    67   36   | 5    9    8    |
| 5    1    38   | 9    28   4    | 37   6    27   |
| 9   78+3  6    | 78   5   23+8  | 1    23   4    |
*--------------------------------------------------*

Actually this one can be solved by an xy-wing too, but I chose to eliminate the 3 in r1c6, r9c4 with a sky-scraper and then this picture appears.

Claudiarabia
claudiarabia

Posts: 288
Joined: 14 May 2006

Code: Select all
*--------------------------------------------------*
| 8    5    79   | 17   4    19   | 6    3    2    |
| 3    6    29   | 28   5    89   | 7    1    4    |
| 1    27   4    | 3    27   6    | 5    89   89   |
|----------------+----------------+----------------|
| 79   28   3    | 6    1    5    | 4    27   89   |
| 4    1    28   | 9    3    7    | 28   6    5    |
| 6    79   5    | 4    8    2    | 3    79   1    |
|----------------+----------------+----------------|
| 79  89+7  6    | 5    27   4    | 1    28   3    |
| 5    3   17+8  | 27   9    18   | 28   4    6    |
| 2    4    18   | 18   6    3    | 9    5    7    |
*--------------------------------------------------*

I don't see a specific question associated with this puzzle.

If [r7c2]<>7 and [r8c3]<>8, then a BUG results.

Code: Select all
BUG+2 => [r5c3]<>8
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006