The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |.4.|...|17.|
 |...|.2.|...|
 |..1|.49|..3|
 |---+---+---|
 |3..|...|..7|
 |...|6..|.14|
 |.89|..2|...|
 |---+---+---|
 |..3|25.|.8.|
 |...|...|...|
 |2..|.83|.6.|
 *-----------*


Play/Print this puzzle online

[SpAce]

Code: Select all

.-------------------.----------------.---------------.
| 89     4     2    | 3     6   5    | 1    7    89  |
| 5789   3     578  | 178   2   17   | 46   49   689 |
| 678    67    1    | 78    4   9    | 2    5    3   |
:-------------------+----------------+---------------:
| 3      16   *46   | 5     9  *14   | 8    2    7   |
| 57     2     57   | 6     3   8    | 9    1    4   |
|*14     8     9    | 147   17  2    | 56   3    56  |
:-------------------+----------------+---------------:
|*1467   1679  3    | 2     5  *1467 |#47   8    19  |
|#14678  5     4678 | 1479  17 #1467 | 3    9-4  2   |
| 2      179   47   | 1479  8   3    | 457  6    159 |
'-------------------'----------------'---------------'

5-link Oddagon (4s) with 3 guardians:

(4)r7c7 == (4)r8c16 => -4 r8c8; stte

PS. Could that also be called a Broken Wing, as the guardians see the victim directly? I haven't seen that name used here much, but I thought it might be because most of the Oddagons seen here use chains to prove their eliminations. Thus my theory is that all Broken Wings are Oddagons but not all Oddagons are Broken Wings. Is there any real distinction though?

[Cenoman]

Code: Select all

 +------------------------+---------------------+-------------------+
 |  89      4      2      |  3      6    5      |  1     7    89    |
 |  5789    3      578    | B178    2    17     |  46    49   689   |
 |  678     67     1      | B78     4    9      |  2     5    3     |
 +------------------------+---------------------+-------------------+
 |  3      b16    z46#    |  5      9   z14#    |  8     2    7     |
 |  57      2      57     |  6      3    8      |  9     1    4     |
 | c1-4     8      9      | B147    17   2      |  56    3    56    |
 +------------------------+---------------------+-------------------+
 | z1467#   1679   3      |  2      5   z1467#  | y47    8    19    |
 |  14678   5      4678   |  1479   17   1467   |  3     49   2     |
 |  2      a179    47     | A1479   8    3      | x457   6   x159   |
 +------------------------+---------------------+-------------------+

Kraken row (1)r9c249
(1)r9c2 - r4c2 = (1)r6c1 (a, b, c)
(1)r9c4 - (178=4)r236c4 (A, B)
(15-7)r9c79 = (7-4)r7c7 = [Skyscraper(4)r7c1=*r7c6-r4c6=r4c3] (x, y, z#)
=> -4 r6c1; ste

[SpAce]

Withdrawn.

[SpAce]

Originally I tried to find a UR solution but didn't (would love to see one, though!). However, I found a somewhat interesting move using two intertwined URs. I haven't tried something like that before. Does anyone see anything wrong with my logic or notation? (There are simpler ways to do this, but I'm mostly interested in the validity of the method.)

Code: Select all

.-------------------------.----------------.--------------------.
|  89*      4     2       | 3     6   5    | 1    7    89*      |
|b#57%#89*  3    c57%(#8) | 178   2   17   | 46   49  a9-8*(#6) |
|  678      67    1       | 78    4   9    | 2    5    3        |
:-------------------------+----------------+--------------------:
|  3        16    46      | 5     9   14   | 8    2   7         |
|  57%      2     57%     | 6     3   8    | 9    1   4         |
|  14       8     9       | 147   17  2    | 56   3   56        |
:-------------------------+----------------+--------------------:
|  1467     1679  3       | 2     5   1467 | 47   8   19        |
|  14678    5     4678    | 1479  17  1467 | 3    49  2         |
|  2        179   47      | 1479  8   3    | 457  6   159       |
'-------------------------'----------------'--------------------'

We have two URs connected at r2c13, with their corresponding derived strong links:

A(*): UR(89)r12c19 -> (6)r2c9 == (5|7)r2c1
B(%): UR(57)r25c13 -> (9)r2c1 == (8)r2c13

A chain using both URs, with one derived strong link and one derived weak link:

1) (6)r2c9 =[UR-A]= (5|7)r2c1 -[UR-B]- (5|7=8)r2c3 => -8 r2c9

Or the same with more detailed inlined explanations:

2) (6)r2c9 =[UR(89)r12c19]= (5|7)r2c1 -[UR(57)r25c13]- (5|7=8)r2c3 => -8 r2c9

Or with just the link markers (but I don't think it's informative enough in this case, though):

3) (6)r2c9 == (5|7)r2c1 -- (5|7=8)r2c3 => -8 r2c9

Is this valid logic and acceptable notation style?

PS. I guess this would be one simpler way to do it:

(6)r2c9 =[UR(89)r12c19 Type 3]= (1578)r2c1346 => -8 r2c9

How would you write that as a more complete chain, though? I only came up with this weirdo:

(6)r2c9 =[UR(89)r12c19]= ((5|7)-(8|9))r2c1 = (1578)r2c1346 => -8 r2c9

Another, even simpler, would be using the externals:

(8)r2c34 == (9)r2c8 - (9=8)r1c9 => -8 r2c9

[eleven]

Broken wings have been found (named) earlier than oddagons, which can have also more than 5, odd links.
The combined UR's are a MUG, with the externals you arrived at in the last line.

Code: Select all

 *------------------------------------------------------------------*
 |  89      4      2      |  3      6    5      |  1     7    89    |
 |  5789    3      578    |  178    2    17     |  46    49   689   |
 |  678     67     1      |  78     4    9      |  2     5    3     |
 |------------------------+---------------------+-------------------|
 |  3       16     46     |  5      9   a14     |  8     2    7     |
 |  57      2      57     |  6      3    8      |  9     1    4     |
 | a14      8      9      | a147    17   2      |  56    3    56    |
 |------------------------+---------------------+-------------------|
 | b467-1  f1679   3      |  2      5   b1467   | c47    8   e19    |
 |  4678-1  5      4678   |  1479   17   1467   |  3    d49   2     |
 |  2      g179    47     |  1479   8    3      | D457   6    159   |
 *------------------------------------------------------------------*
1r6c1 = 4r6c1&r4c6 - r7c16 = 4r7c7 - (4=9)r8c8 - r7c9 = 9r7c2 - (7|9=1)r9c2 => -1r78c1
                                   \ 7r7c7 = 7r9c7            /

[SpAce]

Broken wings have been found (named) earlier than oddagons, which can have also more than 5, odd links.
The combined UR's are a MUG, with the externals you arrived at in the last line.

Thanks, eleven!