The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |986|..7|...|
 |.1.|...|..8|
 |..7|.85|.9.|
 |---+---+---|
 |.5.|..8|3..|
 |.2.|716|.5.|
 |..1|3..|.2.|
 |---+---+---|
 |.7.|84.|9..|
 |1..|...|.8.|
 |...|9..|217|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*----------------------------------------*
| 9   8  6    | 1   23  7  | 5   4   23  |
| 245 1  245  | 246 239 49 |b67 c367 8   |
| 24  3  7    | 246 8   5  | 1   9   26  |
|-------------+------------+-------------|
| 67  5  49   | 24  29  8  | 3   67  1   |
| 348 2  3489 | 7   1   6  | 48  5   49  |
| 78  69 1    | 3   5   49 | 78  2   469 |
|-------------+------------+-------------|
| 236 7  23   | 8   4   1  | 9  d3-6 5   |
| 1   69 39   | 5   7   2  |a46  8   346 |
| 58  4  58   | 9   6   3  | 2   1   7   |
*----------------------------------------*

L3 Wing : (6) r8c7 = (6-7) r2c7 = (7-3)r2c8 = 3 r7c8 => - 6 r7c8; stte

Leren

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 | 9     8     6     | 1     23    7     | 5     4     23    |
 | 245   1     245   | 246   239   49    |b67    367   8     |
 | 24    3     7     | 246   8     5     | 1     9     2-6   |
 *-------------------+-------------------+-------------------|
 | 67    5     49    | 24    29    8     | 3     67    1     |
 | 348   2     3489  | 7     1     6     |a48    5    a49    |
 | 78    69    1     | 3     5     49    |a78    2    a469   |
 *-------------------+-------------------+-------------------|
 | 236   7     23    | 8     4     1     | 9     36    5     |
 | 1     69    39    | 5     7     2     | 46    8     346   |
 | 58    4     58    | 9     6     3     | 2     1     7     |
 *-----------------------------------------------------------*


(6=4789)b6p4679 - (7=6)r2c7 => -6 r3c9 ; stte

[SpAce]

Code: Select all

.---------------.--------------.---------------------.
| 9    8   6    | 1    23   7  |   5      4      23  |
| 245  1   245  | 246  239  49 | a(67)  a(67)-3  8   |
| 24   3   7    | 246  8    5  |   1      9      26  |
:---------------+--------------+---------------------:
| 67   5   49   | 24   29   8  |   3      67     1   |
| 348  2   3489 | 7    1    6  |   48     5      49  |
| 78   69  1    | 3    5    49 |   78     2      469 |
:---------------+--------------+---------------------:
| 236  7   23   | 8    4    1  |   9    b(3)6    5   |
| 1    69  39   | 5    7    2  |  b4(6)   8      346 |
| 58   4   58   | 9    6    3  |   2      1      7   |
'---------------'--------------'---------------------'

H2-Wing: (76)r2c78 = (63)b9p42 => -3 r2c8; stte

[Ngisa]

Code: Select all

+----------------------+--------------------+----------------------+
| 9        8      6    | 1       23      7  | 5        34      234 |
| 245      1      245  | 246     239     49 | 67       367     8   |
| 24       3      7    | 246     8       5  | 1        9       26  |
+----------------------+--------------------+----------------------+
|b467      5      49   | 24      29      8  | 3       a467     1   |
| 348      2      3489 | 7       1       6  |e48       5       49  |
|c4678     69     1    | 3       5       49 |d478-6    2       469 |
+----------------------+--------------------+----------------------+
| 236      7      23   | 8       4       1  | 9        3-6     5   |
| 1        69     39   | 5       7       2  |e46       8       346 |
| 58       4      58   | 9       6       3  | 2        1       7   |
+----------------------+--------------------+----------------------+


(6)r4c8 = (6-7)r4c1 = (7-8)r6c1 = r6c7 - (8=46)r58c7 => - 6r6c7, r7c8; stte

Clement

[Sudtyro2]

Code: Select all

+--------------------+--------------+--------------+
|  9     8     6     | 1   23  7    | 5   4   23   |
| *245   1    *245   | 246 239 49   | 67  367 8    |
|  24    3     7     | 246 8   5    | 1   9   26   |
+--------------------+--------------+--------------+
|  67    5     49    | 24  29  8    | 3   67  1    |
| *348   2    *348+9 | 7   1   6    | 48  5   49   |
|  78    6-9   1     | 3   5   49   | 78  2   469  |
+--------------------+--------------+--------------+
| *23+6  7    *23    | 8   4   1    | 9   36  5    |
|  1     69    39    | 5   7   2    | 46  8   346  |
| *58    4    *58    | 9   6   3    | 2   1   7    |
+--------------------+--------------+--------------+

A MUG (maybe) from DP(458)r259c13 + DP(234)r257c13, using internals.
9r5c3 == 6r7c1 - (6=9)r8c2 => - 9r6c2; stte

SteveC

[eleven]

It's not a MUG.
There is no simple way to determine, if a pattern is a MUG.

A property of a MUG is, that whatever outside candidates you set, there will be always multiple solutions of the pattern left - or none.

So one way to disprove it is to find outside numbers, which only leave a single pattern solution (it does not matter, if they are possible in a concrete candidates grid). Here a 5 in r2, and a 3 in r13c3, and 3 in r5 would only leave one pattern solution.

Code: Select all

 . . . . . . . . .
 2 . 4 . . . 5 . .
 . . 3 . . . . . .
 . . . . . . . . .
 4 . 8 . . . 3 . .
 . . . . . . . . .
 3 . 2 . . . . . .
 . . . . . . . . .
 8 . 5 . . . . . .


[Sudtyro2]

Hi eleven,
Thx for the feedback on the "maybe" MUG! I was definitely concerned because of the conjugate 5s on r2 and the conjugate 3s on r5 as maybe killing their respective joined DP patterns. Cenoman also had some feedback via PM, so I'm hoping for further continued discussions on this interesting pattern. I'm a newbie on most MUGs!

SteveC

[SpAce]

I'm hoping for further continued discussions on this interesting pattern. I'm a newbie on most MUGs!

Me too, on both accounts! My first reaction to your solution was "Very nice!" (especially since I'd been eyeballing those cells for a DP as well, but without success). However, I left it unsaid because I couldn't confirm myself that it was indeed a valid MUG (or not). I still can't. That's why I have to trust eleven's and Cenoman's judgment -- and I do -- but it's a bit frustrating because I'd like to understand it myself. I usually have no problem understanding URs, BUGs, or BUG-Lites, but some MUGs can get really hairy.

[Cenoman]

My first reaction was also "Very nice!" But the reasons why I thought Steve's pattern was a MUG are questionable and now, not even convincing myself.
I just stare at eleven's demonstration using digit 5, that is locked in cells r29c13 of the pattern...

[Sudtyro2]

With reference to Myth's seminal MUG thread, it seemed clear to me that one could quickly form MUGs from the union of two simple UR patterns. However, the discussions then moved on to more complicated cases that required special analysis to prove that they were true MUGs (or not). Below is a summary of quotes from three contributors in that thread regarding the tests needed.

Myth Jellies:
I am going to propose that a MUG candidate is really a deadly pattern if you cannot find a group and a candidate where if you got rid of that candidate in that group you would have a valid puzzle pattern that was not a BUG or a MUG.
vidarino:
And as far as I can tell, a *UG has to be "self-contained", as in no extra visible candidates outside the pattern.
So it suffices to have a pattern such that all possible results of discarding zero or more times a given digit from a given row or column or box leaves a pattern with more than one solution.
aeb:
The rule is always: find an involution and it will have orbits of sizes 1 and 2. Those of size 2 give an even number of solutions, so can be discarded.

So, bottom line for me is that I still have much work to do to fully understand MUG-testing procedures. In the meantime thanks again for the amazing post by eleven and also PM communications from Cenoman.

SteveC

[eleven]

It is relatively simple here to see, that it cannot be a MUG.
You have 5 digits in the pattern, but only 4 rows.
So any pattern solution with different digits in the columns, which are not in the same row, disproves the MUG, e.g.

Code: Select all

 .   . .       . . .
 245 . 245    2 . 5
 .   . 3      . . .
 .   . .      . . .
 348 . 348    8 . 4
 .   . .      . . .
 23  . 23     3 . 2
 4   . .      . . .
 58  . 58     5 . 8


With the single 3 in the first column and 4 in the second they are fixed to stay there in any full solution grid:
If you move them, the row or column would lose this number, and you would have to change outside numbers.
So the only chance for a second pattern solution with these digits would be to have 2 solutions for rows 29, but there are 3 digits in the 2 rows.

With a 5th row e.g. these would be a valid MUGs:

Code: Select all

 .   . .      .     . . 
 245 . 245    23458 . 23458
 34  . 34     23458 . 23458
 .   . .      .     . . 
 348 . 348    23458 . 23458
 .   . .      .     . . 
 234 . 234    23458 . 23458
 .   . .      .     . . 
 58  . 58     23458 . 23458

[Added:]All patterns, you can derive from the "full" pattern on the right side by placing digits somewhere, are either MUG's or deadly (have no solution).