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Medusa 2: "blade drop" -- a new pattern?

 
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Bob Hanson

Joined: 05 Oct 2005
Posts: 187
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Location: St. Olaf College

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PostPosted: Tue Nov 08, 2005 3:11 pm    Post subject: Medusa 2: "blade drop" -- a new pattern? Reply with quote

I suspect these are all well known. They are so simple. Nonetheless, here is another very simple pattern that should be quite useful (and probably is by some other name). I do apologize in advance if this is just old news.

"blade drop" (?)

Code:

------1------------1------
      .            .
      .            .
      .            .
      .            .
      1            .
       2           .
        .          .
          .        1
           .(*2)....2



Here we have one row, column or block that has just two
occurances of a 1 in it. Weakly connected to that "blade"
we have two cells that only have 1 and some other number in
them, say, "2". Any occurance of this other number that is weakly
connected to BOTH of those cells may be eliminated.

Note that the two"dropped" cells don't have to be in the same row,
column, or block, but the 2 that can be eliminated has to
be in the same row, column, or block of one of them AND
in the same row, column, or block of the other as well.
(Same row as one, same column as the other, for example.)

Theory:

We have three weakly linked strong edges for which, F-->T and T<--F
overall. This analysis begins with assigning a FALSE to each end in
turn, and following the implications of this at the other end.

Code:

   2---1...1---1...1---2
   F-->T-->F-->T-->F-->T
and
   T<--F<--T<--F<--T<--F


Thus, the weak links are transmitting "True implies False" in both
directions. No matter what else, one end of the weakly linked chains
must be 2, allowing the elimination of any 2 that forms a "weak corner"
between them.
_________________
Bob Hanson
Professor of Chemistry
St. Olaf College
Northfield, MN
http://www.stolaf.edu/people/hansonr
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