## What's This Called?

Post the puzzle or solving technique that's causing you trouble and someone will help

### What's This Called?

Here's another one of those Near The End situations.
Is this an X Chain, a Bug + 1 or something else?
I thought I could load an image but it looks like it has to be a Code.
*--------------------------------------------------*
| 1 4 6 | 9 2 8 | 3 7 5 |
| 5 | 6 1 7 | 8 4 2 |
| 8 7 2 | 4 3 5 | 9 1 6 |
|----------------+----------------+----------------|
| 7 2 1 | 3 5 9 | 6 8 4 |
| 6 8 | 2 7 4 | 5 1 |
| 4 5 | 1 8 6 | |
|----------------+----------------+----------------|
| 2 5 | 8 9 1 | 4 6 |
| 8 4 | 7 6 2 | 1 5 |
| 6 1 | 5 4 3 | 8 |
*--------------------------------------------------*
r6c9 has candidates 379, and it can see both ends of a 4-link 3,9 bi-value chain running from r6c2 to r8c9.
If r6c9 = 3, the chain predicts that r8c9 also is a 3, so that is not possible.
Similarly, when r6c9 = 9 the chain forces a 9 at r8c9, which is also not possible.
Therefore r6c9 can only be 7, and the puzzle is quickly solved from there.

What drew my eye to this key move was that I already had a lot of 3,9 cells, and r6c9 had (I thought) 3,9 and 7.
OK it turned out that a Pointing Pair in Box 9 eliminated 3 from r6c9 anyway, but that didn't change the logic.
It worked a treat! But was that an X Chain I was using?
Yogi
2017 Supporter

Posts: 181
Joined: 05 December 2015
Location: New Zealand

### Re: What's This Called?

To display the diagram correctly select it and click on the Code button (4th from the left at the top of the reply box).

Also, you might have to indicate unsolved cells by . For example, in the first 3 cells in Row 2 I can't tell whether you mean 5.. .5. or ..5 so I can't help you yet.

Code: Select all
`*--------------------------------------------------*| 1 4 6 | 9 2 8 | 3 7 5 || 5 | 6 1 7 | 8 4 2 || 8 7 2 | 4 3 5 | 9 1 6 ||----------------+----------------+----------------|| 7 2 1 | 3 5 9 | 6 8 4 || 6 8 | 2 7 4 | 5 1 || 4 5 | 1 8 6 | ||----------------+----------------+----------------|| 2 5 | 8 9 1 | 4 6 || 8 4 | 7 6 2 | 1 5 || 6 1 | 5 4 3 | 8 |*--------------------------------------------------*`

PS this is what I get when I put your diagram in Code format. Looks like you will have to put the dots in like I said and shorten the band lines. When you do this click on the Preview button at the bottom of the reply box, and adjust your diagram until it displays OK, then click on the Submit button.

Leren
Leren

Posts: 3961
Joined: 03 June 2012

Yogi wrote:
Code: Select all
` *--------------------------------------------------* | 1    4      6   | 9    2    8    | 3    7    5    | | 5                 | 6    1    7    | 8    4    2    | | 8    7    2     | 4    3    5    | 9    1    6    | |----------------+----------------+----------------| | 7    2    1    | 3    5    9    | 6     8    4    | |       6    8    | 2    7    4    | 5           1    | | 4          5    | 1    8    6    |                    | |----------------+----------------+----------------| | 2    5          | 8    9    1    | 4     6          | |       8    4    | 7    6    2    | 1     5          | | 6    1          | 5    4    3    |              8    | *--------------------------------------------------*`

would indeed be better with a dot for empty cell
Code: Select all
`1 4 6   9 2 8   3 7 55 . .   6 1 7   8 4 28 7 2   4 3 5   9 1 67 2 1   3 5 9   6 8 4. 6 8   2 7 4   5 . 14 . 5   1 8 6   . . .2 5 .   8 9 1   4 6 .. 8 4   7 6 2   1 5 .6 1 .   5 4 3   . . 8`

1469283755..617842872435916721359684.682745.14.5186...25.89146..8476215.61.543..8

Pat

Posts: 3882
Joined: 18 July 2005

### Re: What's This Called?

Many thanks to Pat for figuring out what the puzzle status was, and providing a . based line format, the most civilized way to go ( I recently posted a rant about the 0 based line format, which is dangerous in Excel) !.

Code: Select all
`*--------------------------------------------------------------*| 1     4     6      | 9     2     8      | 3     7     5      || 5     39    39     | 6     1     7      | 8     4     2      || 8     7     2      | 4     3     5      | 9     1     6      ||--------------------+--------------------+--------------------|| 7     2     1      | 3     5     9      | 6     8     4      || 39    6     8      | 2     7     4      | 5     39    1      || 4     39    5      | 1     8     6      | 27   *9-23  79     ||--------------------+--------------------+--------------------|| 2     5     37     | 8     9     1      | 4     6     37     || 39    8     4      | 7     6     2      | 1     5     39     || 6     1     79     | 5     4     3      | 27    29    8      |*--------------------------------------------------------------*`

The solution to the puzzle is called BUG+1, where BUG stands for Bi-value Universal Grave.

If you look at r6c8, if it were not 9 (2 or 3), then every unsolved cell would have 2 digits, and there would be exactly 2 instances of each remaining candidate in each row, column and box in which they appear.

It can be shown that this situation would lead to either 0 or 2 solutions, so r6c8 must be 9, which solves the puzzle.

Here is a link to some external sites which discuss the BUG principle : http://hodoku.sourceforge.net/en/tech_ur.php#bug1 and http://www.sudokuwiki.org/BUG

I vaguely remember that there is a proof of the BUG principle on this site somewhere but I can't find it at the moment.

Nevertheless, here is a link to a thread on this site that discusses the BUG principle: http://forum.enjoysudoku.com/post14899.html?hilit=BUG%20proof#p14899

Leren
Leren

Posts: 3961
Joined: 03 June 2012

### Re: What's This Called?

OK Thanx. I will put this one down as a Near Miss, in that I was right to be interested in what I thought was a 3-candidate cell (r6c9) when most of the others were bi-value. My logic seemed to work anyway, but it seems that I should have seen that it had only 2 candidates left as well. That would have left r6c8 as the only 3-candidate cell.
Yogi
2017 Supporter

Posts: 181
Joined: 05 December 2015
Location: New Zealand