The New Sudoku Players' Forum

[wapati]

This is the original puzzle.

Code: Select all

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

SE steps through it to this point and then wants a chain. (Which I don't want. )

Code: Select all

.------------.------------.------------.
| 37  9   6  | 18  14  48 | 37  5   2  |
| 8   2   5  | 37  79  379| 6   4   1  |
| 1   4   37 | 6   5   2  | 37  9   8  |
:------------+------------+------------:
| 2  *37  9  | 5   8   1  | 4   6  *37 |
| 47 *35  1  | 9   47  6  | 8   2  *35 |
| 467*567 8  | 2   3   47 | 9   1  *57 |
:------------+------------+------------:
| 9   1   37 | 4   2   37 | 5   8   6  |
| 5   67  2  | 78  679 789| 1   3   4  |
| 36  8   4  | 13  16  5  | 2   7   9  |
'------------'------------'------------'

The marked cells seem to require r6c2 to be 6, else unpleasantness.
Is this a BUG pattern?

[re'born]

wapati,

I don't think this is a BUG(-lite) pattern, as least how you've presented it. On the other hand, I do think that this is a BUG+5 grid.

Code: Select all

 *--------------------------------------------------*
 | 37   9    6    | 18   14   48   | 37   5    2    |
 | 8    2    5    | 37   79   39+7 | 6    4    1    |
 | 1    4    37   | 6    5    2    | 37   9    8    |
 |----------------+----------------+----------------|
 | 2    37   9    | 5    8    1    | 4    6    37   |
 | 47   35   1    | 9    47   6    | 8    2    35   |
 | 46+7 56+7 8    | 2    3    47   | 9    1    57   |
 |----------------+----------------+----------------|
 | 9    1    37   | 4    2    37   | 5    8    6    |
 | 5    67   2    | 78   69+7 89+7 | 1    3    4    |
 | 36   8    4    | 13   16   5    | 2    7    9    |
 *--------------------------------------------------*


It is easy to see from here that r2c5 <> 7, and the puzzle then solves with singles.

Edit: I take back the first thing I said. I found the following post in the BUG-lite thread:

Considering the third of the 6-cell patterns listed...the BUG-Lite rule would catch the following nicely...

Code: Select all

 .   .   ab  |  ab  .  .  |  .   .   .
 .   .   bc  |  bc  .  .  |  .   .   .
 .   .   ac  |  acx .  .  |  .   .   .


This is would seem to be your pattern.

On the other hand:

The fundamental rule for both BUG and BUG-Lite grids is the same, the deadly pattern has each candidate appearing exactly twice in each row, col, and box. While the BUG involves the entire grid, the BUG-Lite involves only a portion.

In your case, the 7's do not satisfy that criterion.

I'm inclined to believe that your pattern is thus not a BUG-lite, but I would appreciate an expert weighing in on this.

[udosuk]

Code: Select all

+------------+------------+------------+
| 37  9   6  | 18  14  48 | 37  5   2  |
| 8   2   5  | 37  79  379| 6   4   1  |
| 1   4   37 | 6   5   2  | 37  9   8  |
+------------+------------+------------+
| 2  *37  9  | 5   8   1  | 4   6  *37 |
| 47 *35  1  | 9   47  6  | 8   2  *35 |
| 467-567 8  | 2   3   47 | 9   1  *57 |
+------------+------------+------------+
| 9   1   37 | 4   2   37 | 5   8   6  |
| 5   67  2  | 78  679 789| 1   3   4  |
| 36  8   4  | 13  16  5  | 2   7   9  |
+------------+------------+------------+

I'm no expert on BUGs... But isn't this a 2x3 UR_1?

If r6c2<>6, then r456c29 form a deadly pattern ([357|735] or [735|357])...

Therefore r6c2=6 and the rest are all singles...

Is this valid uniqueness reasoning?

[ronk]

On the other hand:

The fundamental rule for both BUG and BUG-Lite grids is the same, the deadly pattern has each candidate appearing exactly twice in each row, col, and box. While the BUG involves the entire grid, the BUG-Lite involves only a portion.

For a BUG-Lite I meant that "each candidate appearing exactly twice in each row, col, and box" applied to only the cells of the BUG-Lite. IOW the other cells are ignored, and when in doubt just recall that's what we do with a UR Type 1.

So wapati's grid is indeed a BUG-Lite+1 and r6c2=6 is valid.

Code: Select all

 *----------------------------------*
 | .  .    .  | .  .  .  | .  .  .  |
 | .  .    .  | .  .  .  | .  .  .  |
 | .  .    .  | .  .  .  | .  .  .  |
 |------------+----------+----------|
 | .  37   .  | .  .  .  | .  .  37 |
 | .  35   .  | .  .  .  | .  .  35 |
 | .  57+6 .  | .  .  .  | .  .  57 |
 |------------+----------+----------|
 | .  .    .  | .  .  .  | .  .  .  |
 | .  .    .  | .  .  .  | .  .  .  |
 | .  .    .  | .  .  .  | .  .  .  |
 *----------------------------------*

[re'born]

Thanks ronk. This pattern hasn't shown up so often (at least as far I as I remember). So, good find wapati.