The New Sudoku Players' Forum

[eleven]

unsure what youd call it exactly, but i imagine it as a bivalue oddagon on 8 and 9 with grouped links thru b7
guardians 7r1c1 = 7r9c9 => -7r9c1

That's exactly, how i would call it.
Other bivalue oddagons have 2 cells for a node (with a third digit to guarantee the digit change), here it is the empty rectangle for both digits.
(Without the guardians you would always have one of 89 in r78c1 and the other in r9c23 - a 5 digit bivalue oddagon is a remote pair seeing a cell with the 2 digits, here r1c1,r9c9 sees 89 in r1c9)

[Added:]However that step is not needed for a loop eliminating all 3 7's.
To simplify it, replace 89 by xy (whatever which is which), and set r1c9 to x (-> 7y in r1c1 and r9c9).
Then you get
Either 7r1c1 and 7r9c23,
or yr1c1 and r9c23 and 7r9c9 and 7r78c1

[shye]

However that step is not needed for a loop eliminating all 3 7's.
To simplify it, replace 89 by xy (whatever which is which), and set r1c9 to x (-> 7y in r1c1 and r9c9).
Then you get
Either 7r1c1 and 7r9c23,
or yr1c1 and r9c23 and 7r9c9 and 7r78c1

thats a gorgeous way to simplify it, thanks! nice to know i wasnt completely off with the oddagon idea too

edit:
in fact, you could call it an ERI pair on 7 and "y", maybe this does have a name after all

[Cenoman]

Code: Select all

 +-------------------------+-------------------------+-----------------------+
 | #789     4       1      |  789      5      2      |  3      6      #89    |
 |  23      5789    5789   |  34789    347    6      |  129    12589   589   |
 |  23      589     6      |  389      1      89     |  7      2589    4     |
 +-------------------------+-------------------------+-----------------------+
 |  4       56789   5789   |  5678     27     578    |  29     3       1     |
 |  5-7     2       3      |  1457     9      1457   |  8      457     6     |
 |  1       56789   5789   |  345678   2347   4578   |  249    24579   579   |
 +-------------------------+-------------------------+-----------------------+
 | #78      1       2      |  479      6      479    |  5      478     3     |
 | #679     3       4      |  15       8      15     |  69     79      2     |
 | #5689-7 #5789   #5789   |  2        4-7    3      |  1469   14789  #789   |
 +-------------------------+-------------------------+-----------------------+

56789 in 8 cells marked #: r1c19, r9c9, b7p14789
Any digit can be True at most twice. 5, 6 True at most once => 7, 8, 9 must be twice.
7 must be True in c1 AND r9 => -7 r5c1, r9c15; ste