The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |7..|5.8|..3|
 |.42|3.6|78.|
 |.8.|.4.|.2.|
 |---+---+---|
 |85.|...|.79|
 |..7|...|5..|
 |41.|...|.32|
 |---+---+---|
 |.3.|.5.|.9.|
 |.24|8.9|36.|
 |9..|6.2|..4|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
| 7       69      69       | 5       2       8        | 14      14      3        |
| 1       4       2        | 3       9       6        | 7       8       5        |
| 3       8       5        | 17      4       17       | 9       2       6        |
|--------------------------+--------------------------+--------------------------|
| 8       5       3        | 2       16      14       | 146     7       9        |
| 2       6-9     7        |c149     168     3        | 5      c14     c18       |
| 4       1      a69       | 7-9     678     5        |b68      3       2        |
|--------------------------+--------------------------+--------------------------|
| 6       3       18       | 147     5       147      | 2       9       178      |
| 5       2       4        | 8       17      9        | 3       6       17       |
| 9       7       18       | 6       3       2        | 18      5       4        |
*--------------------------------------------------------------------------------*

ANS XY Wing: (9=6) r6c3 - (6=8) r6c7 - (8=1=4=9)[ANS:r5c489] => r5c2, r6c4 <> 9; stte

Leren

[ArkieTech]

Code: Select all

 *--------------------------------------------------*
 | 7    69   69   | 5    2    8    | 14   14   3    |
 | 1    4    2    | 3    9    6    | 7    8    5    |
 | 3    8    5    | 17   4    17   | 9    2    6    |
 |----------------+----------------+----------------|
 | 8    5    3    | 2    16   14   | 146  7    9    |
 | 2   d69   7    | 149 c168  3    | 5    14  b18   |
 | 4    1    9-6  | 79   678  5    |a68   3    2    |
 |----------------+----------------+----------------|
 | 6    3    18   | 147  5    147  | 2    9    178  |
 | 5    2    4    | 8    17   9    | 3    6    17   |
 | 9    7    18   | 6    3    2    | 18   5    4    |
 *--------------------------------------------------*
m-wing
(6=8)r6c7-r5c9=(8-6)r5c5=6r5c2 => -6r6c3; stte

[tlanglet]

A fruitless Type 2 UR(17) bears fruit as a AUR(17).

6r6c7=6r4c7-(6=1)r4c5-AUR(17)r37c46[1r8c5=(7-8)r7c9]=8r5c9 => r6c7<>8

Ted

[tlanglet]

If you want to go a little crazy with this puzzle, consider a

8-cell AUR(14)r1c78,r4c67,r5c48,r7c46 internal SIS 6r4c7,9r5c4,7r7c46
6r4c7-(6=8)r6c7-(8=1)r5c9-ALS(149)r5c48[1r5c48=9r5c4];
9r5c4;
7r7c46-(7=1)r8c5-(1=6)r4c5-r5c5=(6-9)r5c2=9r5c4 => r5c4=9

Ted

[RW]

A fruitless Type 2 UR(17) bears fruit as a AUR(17).

6r6c7=6r4c7-(6=1)r4c5-AUR(17)r37c46[1r8c5=(7-8)r7c9]=8r5c9 => r6c7<>8

Ted

AUR seems unnecessary complicated... Same elimination can be made as

6r6c7=6r4c7-(6=1)r4c5-(1=7)r8c5-(7=1)r8c9-(1=8)r5c9 => r6c7<>8

If you want to go a little crazy with this puzzle, consider a

8-cell AUR(14)r1c78,r4c67,r5c48,r7c46 internal SIS 6r4c7,9r5c4,7r7c46
6r4c7-(6=8)r6c7-(8=1)r5c9-ALS(149)r5c48[1r5c48=9r5c4];
9r5c4;
7r7c46-(7=1)r8c5-(1=6)r4c5-r5c5=(6-9)r5c2=9r5c4 => r5c4=9

What you really have there is a 10-cell BUG-lite with only 2 extra candidates:

Code: Select all

 *--------------------------------------------------*
 | 7    69   69   | 5    2    8    |*14  *14   3    |
 | 1    4    2    | 3    9    6    | 7    8    5    |
 | 3    8    5    |*17   4   *17   | 9    2    6    |
 |----------------+----------------+----------------|
 | 8    5    3    | 2    16  *14   |*14+6 7    9    |
 | 2    69   7    |*14+9 168  3    | 5   *14   18   |
 | 4    1    69   | 79   678  5    | 68   3    2    |
 |----------------+----------------+----------------|
 | 6    3    18   |*147  5   *147  | 2    9    178  |
 | 5    2    4    | 8    17   9    | 3    6    17   |
 | 9    7    18   | 6    3    2    | 18   5    4    |
 *--------------------------------------------------*

and you only need your first chain to show that r5c4=9.

RW

[Marty R.]

Code: Select all

+---------+-------------+------------+
| 7 69 69 | 5   2   8   | 14  14 3   |
| 1 4  2  | 3   9   6   | 7   8  5   |
| 3 8  5  | 17  4   17  | 9   2  6   |
+---------+-------------+------------+
| 8 5  3  | 2   16  14  | 146 7  9   |
| 2 69 7  | 149 168 3   | 5   14 18  |
| 4 1  69 | 79  678 5   | 68  3  2   |
+---------+-------------+------------+
| 6 3  18 | 147 5   147 | 2   9  178 |
| 5 2  4  | 8   17  9   | 3   6  17  |
| 9 7  18 | 6   3   2   | 18  5  4   |
+---------+-------------+------------+


Play this puzzle online at the Daily Sudoku site

Some sort of chain.

(7=1)r8c5-(1=6)r4c5-r5c5=r5c2-(6=9)r6c3-(9=7)r6c4=>r6c5,r7c4<>7

[tlanglet]

RW,

I usually post a solution as I initially found it, realizing that it is not always the least complicated view, but it reflects what I was doing when I found the solution.

And yes, the 10-cell AUR is both more interesting and simple. I am not sure why I did not consider it since I had already posted the AUR(17) portion.

I appreciate your comments.

Ted

[RW]

RW,

I usually post a solution as I initially found it, realizing that it is not always the least complicated view, but it reflects what I was doing when I found the solution.

No problem. I haven't been around much lately and as I'm not used to the notation you guys use nowadays it took me a while to figure out what your AUR solution really meant, while the other chain through r8c59 was quite obvious. Perhaps the most elegant way to express that elimination would be with the XY-chain r4c5-r8c5-r8c9-r5c9-r6c7 (which of course technically doesn't make the exact same elimination, though it's essentially the same chain with the same consequences).

I find I often use AURs when there are easier ways to make the same eliminations as well. In manual solving I sometimes even use an UR to place a digit when I later notice it was actually already a naked single...

[Luke]

What you really have there is a 10-cell BUG-lite with only 2 extra candidates:

Code: Select all

 *--------------------------------------------------*
 | 7    69   69   | 5    2    8    |*14  *14   3    |
 | 1    4    2    | 3    9    6    | 7    8    5    |
 | 3    8    5    |*17   4   *17   | 9    2    6    |
 |----------------+----------------+----------------|
 | 8    5    3    | 2    16  *14   |*14+6 7    9    |
 | 2    69   7    |*14+9 168  3    | 5   *14   18   |
 | 4    1    69   | 79   678  5    | 68   3    2    |
 |----------------+----------------+----------------|
 | 6    3    18   |*147  5   *147  | 2    9    178  |
 | 5    2    4    | 8    17   9    | 3    6    17   |
 | 9    7    18   | 6    3    2    | 18   5    4    |
 *--------------------------------------------------*

Yes! This DP is seldom seen/pointed out. V cool.

I don't see why you would call it a BUG-Lite, though. Considering the (147)r7c46, wouldn't you say it falls under the MUG umbrella?

------------------

Adding a much more mundane solution:
(7)r6c4=(7-8)r6c5=(8-6)r5c5=(6-9)r5c2=(9)r5c4 ==>r6c4<>9

[eleven]

I don't see why you would call it a BUG-Lite, though. Considering the (147)r7c46, wouldn't you say it falls under the MUG umbrella?

If you have read about BUG-Lites and MUG's, you will know, that they like one another, and don't have notation problems

[Luke]

I don't see why you would call it a BUG-Lite, though. Considering the (147)r7c46, wouldn't you say it falls under the MUG umbrella?

If you have read about BUG-Lites and MUG's, you will know, that they like one another, and don't have notation problems

I've read enough to know they are not the same thing ... so just to humor me, which is it?

[RW]

I've read enough to know they are not the same thing ... so just to humor me, which is it?

To me they are the same thing.

Code: Select all

abc  abc  abc
-------------
abc  abc  abc

is no different from

Code: Select all

ab  bc  ac
----------
ab  bc  ac

from the solver's point of view. Both are deadly patterns and can be used in exactly the same way to make deductions. The latter is just a subset of the first with some of the candidates already eliminated. But as we know, it makes no difference if some candidates from a deadly pattern are already eliminated, the pattern still behaves in exactly the same way.

Technically it's probably wrong to call the 10-cell pattern a BUG-lite, because it uses some non-bivalue cells. You are correct there. But as I think of them all in the same way, I usually also refer to them by the same name. To me it makes no sense to label them as different patterns.

[Luke]

RW, thanks for your attention. I know you're one of the guys that wrote the book on this stuff, so I very much appreciate your perspective.

I found this pattern fascinating, as with all things buggy, muggy or otherwise deadly. It probably would be better described as a Layered BUG-Lite, or maybe "composite" in the usage of others. Either way, I know you've aren't a big fan of the MUG term to begin with.

I saw the pattern as equivalent to this, which is a MUG in the usage I have seen:

Code: Select all

17
--
14
--
147
--

Of course, the above is also the layering of two BUG-Lites, in this case the overlapping of (14) and (17) URs.

[RW]

Hehe, I completely had forgot that "Layered BUG-lite" term. You are right, "composite" would be a better word, though.

When I think about it, this pattern (which is essentially the same as in the puzzle, except the extension of 14 cells):

Code: Select all

17  17
14  14
147 147

would in fact be quite hard to describe as a MUG. Because, if we end up here, candidate 1 is automatically eliminated from the 147 cells and we are left with

Code: Select all

17  17
14  14
47  47

= a standard BUG-lite.