The famility of Chain Strategies/Techniques

Advanced methods and approaches for solving Sudoku puzzles

The famility of Chain Strategies/Techniques

Postby dino_hsu_1019 » Thu May 03, 2012 3:36 am

The way I am improving my sudoku power is whenever I am stuck I will use Andrew Stuart's solver to see what's the suggested next step with its associated technique, however, I have problem fully understanding those tecniques, possibly due to ambiguiety or contradiction (with other site for the same technique), at this moment, the family of chain techniques. I have Andrew Stuart's book (Extreme Sudoku for Dummies), but there are too few techniques in the book.

Let me try to develop those techniques in this way, in my own words: a link is composed of two nodes/cells in a unit (box/row/column) with a candidate appearing in both nodes/cells, a strong link means those two nodes/cells are the only nodes/cells that accomodate the candidate in the unit, and a weak link means there are one or more nodes/cells that accomodate the same candidate. A chain is composed of links connected by a shared node/cell between any two links, note that these links can be of the same candidate or be of different candidates, depending on the requirements of different techniques. There is a sub-family of techniques that requires a chain composed on only strong links, which can further be divided into same-candidate links and different-candidate links (the latter requires the two ending links should share the same candidate to serve the elimination rule), another sub-family allows strong links and weak links, but strong and weak links should be alternately connected. I will move on from here, but please advise whether I have exhausted the classifications from a high level, thanks in advance.
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Re: The famility of Chain Strategies/Techniques

Postby JasonLion » Thu May 03, 2012 11:44 am

You have the right general idea, but are missing some of the details/more complex cases. A link can occur inside a single cell, without involving a house. For example a single cell with only two pencil marks is both a strong and a weak link. Also, a strong link is a little more general than what you wrote. A strong link occurs when two premises cannot both be false. A weak link when two premises can not both be true. Most of the simple strong links are both strong and weak, one of the two must be true and the other must be false. However, it is possible to have strong links where one, the other, or both premises can be true. And finally (for now) a premise can be more complex than just a single pencil mark. A premise might say, for example, that one of these four cells contains 7, without specifying which of the four cells.
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Re: The famility of Chain Strategies/Techniques

Postby hobiwan » Sat May 05, 2012 12:18 pm

I tried to give an overview over chaining techniques including some examples here.
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