... by: Chuck Bruno
The "Avoidable Rectangles" stratagy is not one of the stratagies listed on the main page. Is this an oversite, or was this left out on purpose?Thanks,
Chuck Bruno
Andrew Stuart writes:
OK now in the side menu






Avoidable Rectangles Avoidable Rectangles are a most unusual strategy ‑ and, to this author’s knowledge, the only one that makes use of solved cells. We are used to the idea that a solution kills all the other numbers of the same value along the row, column and box, meaning that all information about that cell has been used up. Apparently, this is not so. To understand this strategy, we have to put ourselves in the shoes of the puzzle creator, not the puzzle solver.
There are millions of possible puzzles derivable from a completed Sudoku board. The top third of the puzzle above is just one example. Notice, however, that at least one of the four cells (C5) from our example is a clue  which avoids creating a double solution.
So the rule of Avoidable Rectangles is: We can remove a candidate that forms a potential interchangeable pair with three other cells spread over two boxes where the three other cells are solved cells (not clues). Extensions of this strategies are documented in my book The Logic of Sudoku. Note: This strategy does not exist in the solver because it relies on knowledge of what the original clues where. However, my solver is only given the state of the board as it currently exists and not an additional set of numbers saying what the clues where. Its a small overhead to add it but I've chosen not to do so. 
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