The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|...|9..|
 |.8.|..6|.7.|
 |..5|.2.|..4|
 |---+---+---|
 |...|3..|.8.|
 |..2|.8.|1..|
 |.5.|..9|...|
 |---+---+---|
 |1..|.9.|6..|
 |.7.|8..|.4.|
 |..4|...|..2|
 *-----------*


Play/Print this puzzle online

[pjb]

Code: Select all

 23467   12346   1367   | 1457   13457  134578 | 9      12356 b13568 
 2349    8       139    | 1459   1345   6      | 25-3   7      135   
 3679    1369    5      | 179    2      1378   |a38     136    4     
------------------------+----------------------+---------------------
 4679    1469    1679   | 3      14567  12457  | 2457   8      5679   
 34679   3469    2      | 4567   8      457    | 1      3569   35679 
 34678   5       13678  | 12467  1467   9      | 247-3  236    367   
------------------------+----------------------+---------------------
 1       2-3    d38     | 2457   9      2457-3 | 6     e35    c78     
 23569   7       369    | 8      1356   1235   |f35     4      19     
 35689   369     4      | 1567   13567  1357   | 78     19     2     


(3=8)r3c7 - r1c9 = r7c9 - (8=3)r7c3 - (3=5)r7c8 - (5=3)r8c7 -loop => -3 r7c26, r26c7; stte

Phil

[Ngisa]

Code: Select all

+-----------------------+------------------------+-----------------------+
| 23467   12346   1367  | 1457    13457   134578 | 9      12356   e13568 |
| 2349    8       139   | 1459    1345    6      | 235    7        135   |
| 3679    1369    5     | 179     2       1378   | d38    136      4     |
+-----------------------+------------------------+-----------------------+
| 4679    1469    1679  | 3       14567   12457  | 2457   8        5679  |
| 34679   3469    2     | 4567    8       457    | 1      3569     35679 |
| 34678   5       13678 | 12467   1467    9      | 2347   236      367   |
+-----------------------+------------------------+-----------------------+
| 1      a2-3    g38    | 2457    9       23457  | 6     b35      f78    |
| 23569   7       369   | 8       1356    1235   |c35     4        19    |
| 35689   369     4     | 1567    13567   1357   | 78     19       2     |
+-----------------------+------------------------+-----------------------+


Almost like Phil
3r7c2 - r7c8 = r8c7 - (3=8)r3c7 - r1c9 = r7c9 - (8=3)r7c3 => - 3r7c2; stte

Clement

[Cenoman]

Other presentations of Phil's and Clement's logic, using node r9c7 instead of r1c9:

Code: Select all

 +--------------------------+---------------------------+-------------------------+
 |  23467   12346   1367    |  1457    13457   134578   |  9      12356   13568   |
 |  2349    8       139     |  1459    1345    6        |  25-3   7       135     |
 |  3679    1369    5       |  179     2       1378     | b38     136     4       |
 +--------------------------+---------------------------+-------------------------+
 |  4679    1469    1679    |  3       14567   12457    |  2457   8       5679    |
 |  34679   3469    2       |  4567    8       457      |  1      3569    35679   |
 |  34678   5       13678   |  12467   1467    9        |  247-3  236     367     |
 +--------------------------+---------------------------+-------------------------+
 |  1       2-3    a38      |  2457    9       2457-3   |  6     a35     a78      |
 |  23569   7       369     |  8       1356    1235     | b35     4       19      |
 |  35689   369     4       |  1567    13567   1357     | b78     19      2       |
 +--------------------------+---------------------------+-------------------------+

Doubly linked ALS-XZ rule (3578)r7c389 -57- (3578)r389c7 => -3 r7c26,r26c7; ste
or Loop (7=385)r7c389 - (5=357)r389c7@ => -3 r7c26,r26c7; ste

[SpAce]

Mine has a name, so it must be different! Lol. (No need for a diagram.)

W-Wing with transport loop (or "W-Ring with transport", perhaps?):

(3=8)r7c3 - r9c1 = r9c7 - (8=3) - r8c8 = (3)r7c8 - loop => -3 r7c26, r26c7; stte

[Sudtyro2]

Code: Select all

+---------------------+---------------------+-------------------+
| 23467 #12346 1367   | 1457  13457 134578  | 9    12356 13568b |
| 2349   8     139    | 1459  1345  6       |#235  7     135    |
|#3679  *1369  5      | 179   2    #1378    |*38a #136   4      |
+---------------------+---------------------+-------------------+
| 4679   1469  1679   | 3     14567 12457   | 2457 8     5679   |
| 34679 #3469  2      | 4567  8     457     | 1    3569  35679  |
| 34678  5     13678  | 12467 1467  9       |#2347 236   367    |
+---------------------+---------------------+-------------------+
| 1     *2-3  #38d    | 2457  9    #23457   | 6   *35    78c    |
| 23569  7     369    | 8     1356  1235    |*35   4     19     |
| 35689 #369   4      | 1567  13567 1357    | 78   19    2      |
+---------------------+---------------------+-------------------+

Here's a late entry for the week's "Best Obfuscation Award"...
In 3s, a 5-link oddagon(*) with ten guardians(#):
3r159c2,r7c36 == 3r26c7,r3c168 - 3r3c7 == 3r7c3 => - 3r7c2; stte
Hint: See Phil's first four nodes.

SteveC

[Cenoman]

Here's a late entry for the week's "Best Obfuscation Award"...
In 3s, a 5-link oddagon(*) with ten guardians(#):
3r159c2,r7c36 == 3r26c7,r3c168 - 3r3c7 == 3r7c3 => - 3r7c2; stte
Hint: See Phil's first four nodes.
SteveC

...late but not least !
I admire your sustained effort to unearth this well protected treasure.

(Added) Suggestion, why not write:
3r159c2,r7c36 == 3r26c7,r3c168 => -3 r7c2|-3 r3c7; stte
since each of 3r7c2 or 3r3c7 is enough for the ste finish, and since you demonstrate that at least one is eliminated ?

[SpAce]

Here's a late entry for the week's "Best Obfuscation Award"...
In 3s, a 5-link oddagon(*) with ten guardians(#):
3r159c2,r7c36 == 3r26c7,r3c168 - 3r3c7 == 3r7c3 => - 3r7c2; stte
Hint: See Phil's first four nodes.
SteveC

...late but not least !
I admire your sustained effort to unearth this well protected treasure.

(Added) Suggestion, why not write:
3r159c2,r7c36 == 3r26c7,r3c168 => -3 r7c2|-3 r3c7; stte
since each of 3r7c2 or 3r3c7 is enough for the ste finish, and since you demonstrate that at least one is eliminated ?

Great job, both of you! I think Cenoman's suggestion makes it even more elegant as no chains (not even implicit ones) need to be considered -- just the derived weak link between those two cells (i.e. both can't be true) which can be easily seen by looking at the two ORed guardian patterns. Then again, I guess the same deduction could be written as a really short chain:

(3)r7c8 = (3)r8c7 => -3 r7c2 | -3 r3c7; stte

Added: Something in this alternate logic bothers me, though (not Steve's original, which seems perfectly valid). It has a strong taste of circular reasoning. We've only proved that those two 3s have a derived weak link between them, i.e. at least one must be false, but that doesn't yet let us eliminate either one. It seems to help anyway because we happen to know that they're both stte-cells and thus either one would work-- but that piece of knowledge (obtained through a backdoor search or something) shouldn't play any part in our proof, right? If it did, we could just as well reduce the solution to: -3 r7c2, r3c7 (+ any other known stte-cell); stte. That makes no sense, of course, as our job is to prove one or more of those stte-eliminations. I don't think Cenoman's suggestion or my alternate chain do that.