The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |..9|1..|8.7|
 |...|.28|.5.|
 |1..|5..|...|
 |---+---+---|
 |.35|7..|91.|
 |8.2|3.1|...|
 |9..|...|2..|
 |---+---+---|
 |.2.|..9|1..|
 |...|21.|5.8|
 |..1|.43|.92|
 *-----------*


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[SpAce]

Code: Select all

.-----------------------.---------------.------------------.
| 2       5        9    |   1    3  46+ |   8     46+   7  |
| 3467    467      346  |   9    2  8   |  c46+3  5     1  |
| 1     ac46[+8]  b3468 |   5    7  46+ |  b346   2     9  |
:-----------------------+---------------+------------------:
| 46      3        5    |   7    8  2   |   9     1     46 |
| 8       46+      2    |   3    9  1   |  d46+7  467   5  |
| 9       1        7    |   4    6  5   |   2     8     3  |
:-----------------------+---------------+------------------:
| 3467    2        3468 |   68   5  9   |   1     3467  46 |
| 346     9        346  |   2    1  7   |   5     346   8  |
| 5       67-8     1    | e(68)  4  3   | e(6)7   9     2  |
'-----------------------'---------------'------------------'

7-link Bivalue Oddagon+3 (46)r135c267b3 (+3r2c7 +8r3c2 +7r5c7)

(8)r3c2 = (83)r3c37 - (8|3)r3c2,r2c7 == (7)r5c7 - (7=68)r9c74 => -8 r9c2; stte

--

Added. Actually, I think this would suffice:

Code: Select all

.---------------------.---------------.------------------.
| 2      5       9    |   1    3  46+ |  8      46+   7  |
| 3467   467     346  |   9    2  8   |  346+   5     1  |
| 1     a46[+8]  3468 |   5    7  46+ |  346+   2     9  |
:---------------------+---------------+------------------:
| 46     3       5    |   7    8  2   |  9      1     46 |
| 8      46+     2    |   3    9  1   |  46+7   467   5  |
| 9      1       7    |   4    6  5   |  2      8     3  |
:---------------------+---------------+------------------:
| 3467   2       3468 |   68   5  9   |  1      3467  46 |
| 346    9       346  |   2    1  7   |  5      346   8  |
| 5      67-8    1    | b(68)  4  3   | b7(#6)  9     2  |
'---------------------'---------------'------------------'

7-link Grouped Bivalue Oddagon+2 (46)r135c267b3 (+8r3c2 +7r5c7) using mixed +internal/#external:

(8)r3c2 == (68)r9c74 => -8 r9c2; stte

[SteveG48]

Code: Select all

 *------------------------------------------------------------*
 | 2     5     9     | 1     3    d46    |  8    d46    7     |
 | 3467  467   346   | 9     2     8     |  346   5     1     |
 | 1  acd468   3468  | 5     7    d46    |  346   2     9     |
 *-------------------+-------------------+--------------------|
 | 46    3     5     | 7     8     2     |  9     1    d46    |
 | 8    d46    2     | 3     9     1     |cd467   467   5     |
 | 9     1     7     | 4     6     5     |  2     8     3     |
 *-------------------+-------------------+--------------------|
 | 3467  2     3468  | 68    5     9     |  1    e3467 d46    |
 | 346   9     346   | 2     1     7     |  5    e346   8     |
 | 5    b67-8  1     |f68    4     3     |bf67    9     2     |
 *------------------------------------------------------------*


8r3c2 = (78)r9c27 - (7|8)r3c2,r5c7 = [46RP r1c68,r3c26,r4c9,r5c27,r7c9] - (4|6=37)r78c8 - (7=68)r9c47 => -8 r9c2 ; stte

Hmm. Essentially the same as SpAce.


Corrected typo. Thanks, SpAce..

[SpAce]

8r3c2 = (78)r9c27 - (7|8)r3c2,r5c7 = [46RP r1c68,r3c26,r4c9,r5c27,r7c9] - (4|6=37)r78c8 - (7=68)r9c47 => -8 r9c2 ; stte

Hmm. Essentially the same as SpAce.

Hi Steve! I think it's nice and not really the same at all. I think there's a fundamentally different POV between a DP and a non-DP solution, even if they use similar elements (I guess Bivalue Oddagon is the DP side of a Remote Pair). Inspired by your RP solution, I tried looking at mine from that POV as well, and found some new insights.

A slightly different RP solution (corresponding with my oddagon):

(8)r3c2 = (87)r9c27 - (8|7)r3c2,r5c7 = RP(4/6):[r1c8=r1c6-r3c6=r3c2-r5c2=r5c7] - (4|6=3)r2c7 - (3=46)r3c76 => -46 r3c2; stte

However, looking at that RP more closely it's obvious that it would produce a contradiction (forcing two 3s in r23c7), so we could see it like this as well:

(8)r3c2 = (87)r9c27 - (8|7)r3c2,r5c7 = RP(4/6):[r1c8=r1c6-r3c6=r3c2-r5c2=r5c7] - (4|6)r23c7 = (3)r2&3c7[!] => +8 r3c2; stte

In other words, that RP is in fact a DP itself (with two guardians: 8r3c2 & 7r5c7), and that realization resulted in my new simplified solution (edited above). So, thanks for that!

[SteveG48]

In other words, that RP is in fact a DP itself (with two guardians: 8r3c2 & 7r5c7), and that realization resulted in my new simplified solution (edited above). So, thanks for that!

Thanks, SpAce. I didn't think through it to the extent that you have, but it was the similarity between a 46 oddagon and a 46 almost RP that needed of couple of candidates removed that made the solutions quite similar to me.

[eleven]

Yet another 46 DP (5-link grouped bivalue oddagon)

Code: Select all

 *-----------------------------------------------------------*
 |  2      5     9      |  1    3  46   |  8     46     7    |
 | #346+7  467  #346    |  9    2  8    | #346   5      1    |
 |  1     #46+8  3468   |  5    7  46   |  346   2      9    |
 |----------------------+---------------+--------------------|
 |  46     3     5      |  7    8  2    |  9     1      46   |
 |  8     #46    2      |  3    9  1    | #46+7  467    5    |
 |  9      1     7      |  4    6  5    |  2     8      3    |
 |----------------------+---------------+--------------------|
 |  3467   2     3468   |  68   5  9    |  1     3467   46   |
 |  346    9     346    |  2    1  7    |  5     346    8    |
 |  5     b678   1      |  68   4  3    | a67    9      2    |
 *-----------------------------------------------------------*

DP 46(r2c137,r3c2,r5c27), guardians 7r2c1,r5c7, 8r3c2
the 7 guardians imply -7r2c2 (r6c7 via r9c7, r9c2), 46r25c2 and 8r3c2.
=> 8r3c2

[SpAce]

Yet another 46 DP (5-link grouped bivalue oddagon)

DP 46(r2c137,r3c2,r5c27), guardians 7r2c1,r5c7, 8r3c2
the 7 guardians imply -7r2c2 (r6c7 via r9c7, r9c2), 46r25c2 and 8r3c2.
=> 8r3c2

Neat! Don't you need to have also 3r2c7 as a guardian (easy), though? I don't see how the link in c7 works otherwise.

[eleven]

No, i think, the oddagon works with 3r2c7.
And that this way i found a bigger DP including cells r2c2,r9c247 and single guardian 8r3c2.