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3D Medusa does account for all X/Y cycles + more

 
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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: Mon Oct 24, 2005 6:51 am    Post subject: 3D Medusa does account for all X/Y cycles + more Reply with quote

All X- and Y- cycles do indeed fall into a much more general category, as evidenced by the Sudoku Assistant.

http:www.stolaf.edu/people/hansonr/sudoku

Using top95 as a benchmark, the full Medusa strategy solves 54/95. This is up from 47/95 last week when I was only considering "in-the-plane-of-the-board" or "standard" weak edges.

The lesson here is simple and, I think could provide the basis for many more relatively simple usable constructs for human solving.

1) If you commonly look for XY pairs, i.e. only two possibilities in a certain cell, look also for X-----X pairs, where there are exactly two Xs in a row, column, or block, but any other candidates in those two cells as well.

2) You can do anything with these that you might do with an XY pair and vice-versa. Just mix-and-match. Consider the XY pair to be two "ends" of a "strong edge."

3) The simplest way to think about this is that by connecting the dots, you get a set of "strong chains" that can be drawn not just from one cell to another but from one MARK in a cell (where a cell can have 9 marks) to another MARK.

Certain patterns, like X-wings and XY-wings, are just salient manifestations of these connected chains.
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Bob Hanson
Professor of Chemistry
St. Olaf College
Northfield, MN
http://www.stolaf.edu/people/hansonr
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