Sashimi conjecture

Advanced methods and approaches for solving Sudoku puzzles

Sashimi conjecture

Postby Bob Hanson » Fri Jan 02, 2009 3:06 am

Happy 2009. Here is a challenge for you:

Conjecture: All Sashimi in rows have complementary almost-locked set eliminations in columns. These alternative eliminations always involve the complementary set of columns of the original Sashimi and may not be the same elimination.

Conjecture: All Sashimi in columns have complementary almost-locked set eliminations in rows. These alternative eliminations always involve the complementary set of rows of the original Sashimi and may not be the same elimination.

For each of these conjectures, the converse is not necessarily true.

Prove or disprove?

for discussion, see:

http://www.stolaf.edu/people/hansonr/sudoku/explain.htm#sashimi

Bob Hanson
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Joined: 04 December 2005

Re: Sashimi conjecture

Postby ronk » Fri Jan 02, 2009 3:57 am

Bob Hanson wrote:Conjecture: All Sashimi in rows have complementary almost-locked set eliminations in columns. These alternative eliminations always involve the complementary set of columns of the original Sashimi and may not be the same elimination.

Conjecture: All Sashimi in columns have complementary almost-locked set eliminations in rows. These alternative eliminations always involve the complementary set of rows of the original Sashimi and may not be the same elimination.

Bob, complementary fish have the same fin(s) and the same elimination(s), for example ...
Code: Select all
a6  .  . | a6  .  . |  .  .  .
 .  . b6 |  . b6  . |  . b6  .
 .  .  6 |  .  6  . | a6  . a6
---------+----------+----------
 .  .  . |  .  .  . |  .  .  .
 . b6  . |  .  .  . | #6  .  .
a6  6  . |  .  .  . | a6 -6 a6
---------+----------+----------
 .  .  . | a6  .  . |  .  6 a6
 . b6 b6 |  .  .  . |  . b6  .
 . b6  . |  . b6  . |  .  .  .

a: (6)c1479\r1367 + fin r5c7 ==> r6c8<>6
b: (6)r2589\c2358 + fin r5c7 ==> r6c8<>6
ronk
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Postby Bob Hanson » Fri Jan 02, 2009 6:59 am

Excellent! I've got that going now in the Sudoku Assistant.

Thanks again for your help.

Bob
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Posts: 75
Joined: 04 December 2005


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