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Asellus
Joined: 05 Jun 2007 Posts: 865 Location: Sonoma County, CA, USA
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Posted: Tue Sep 25, 2007 10:15 pm Post subject: Medusa Coloring: A Special Bivalue Extension |
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In normal Medusa Coloring, the coloring is extended by exploiting overt "strong" (conjugate) links. However, there is a special case involving a bivalue cell in which two "hidden" conjugate links can be exploited. This occurs if the two digits of a bivalue cell can each "see" a colored instance of themselves, even if only weakly linked.
If the colors are opposite, then eliminations will occur via Medusa "Trap" as shown in this example:
Code: | +------------------+------------------+------------------+
| 2 5 1 | 9 8 3 | 7 6 4 |
| 4r7g 6g7r 8 | 5 1g6r 1r4g | 3 2 9 |
| 4g9r 6r9g 3 | 4r6g 2 7 | 58 1 58 |
+------------------+------------------+------------------+
| 3 4 6 | 1 9 8 | 2 5 7 |
| 1g79 a1279 279 | 346r7 5 4r6g | 148 38 138 |
| 8 #17 5 | 347 37 2 | 149 39 6 |
+------------------+------------------+------------------+
| 6 3 279 | 78 4 5 | 189 789 128 |
| 1r79 8 4 | 2 36g7 1g6r | 59 379 35 |
| 5 b1g27 27 | 378 1r37 9 | 6 4 238 |
+------------------+------------------+------------------+ |
The affected bivalue is marked #. It "sees" the red <7> in R2C2 and the green <1> in R9C2. Thus, it can be colored: 1r7g. This results in elimination of <1> from "a" and elimination of <7> from "a" and "b".
The logic is fairly evident: Either red is true or green is true. If red is true, the bivalue cell is <1>. If green is true, it is <7>. Since there is no other possibility for the cell, the colors can be placed.
I'm not sure if it's possible (I haven't encountered an example), but, in principal, if the colors "seen" by the bivalue cell are matching, then a "Medusa Wrap" would occur eliminating that color. For instance, if the {17} bivalue could "see" a green <1> and a green <7>, then all green digits would be eliminated and all red values placed. [This "Wrap" scenario may not be logically possible. I would welcome either an example showing that it is or a rigorous proof that it is not.] |
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