Relaxed Rules Sudoku

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Relaxed Rules Sudoku

Postby David P Bird » Wed May 14, 2014 9:51 pm

I wonder if perhaps you guys would like a little diversion? Suppose that we add a new rule to Sudoku:

Where a deadly pattern exists in a subset of cells that has two alternate solutions, the member cell in the lowest numbered row with the lowest number column will hold the lower of the two possible digits.

What is the minimum number of givens that would be needed to provide a valid puzzle?

This rule effectively allows solutions that contain non-overlapping 2-solution DPs as it provides a way to resolve them. I've got no idea of how many givens would be needed but would hazard a guess that it might drop to somewhere in the region of 12. A start point could be to check our existing collection of 17 clue Sudokus for redundant givens should this rule be applied.

DPB
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Re: Relaxed Rules Sudoku

Postby dobrichev » Thu May 15, 2014 3:12 am

Interesting idea.
In the low-clue ordinary puzzles any clue hits enormous number of UA sets. SF grid has a 16-clue puzzle with unhit bi-value U18. From memory there are < 20 17-1s with less than 20 solutions.
Maybe a better start would be the most canonical grid, along with the grids with large MCN and respectively large number of U4. I can give you the
If that doesn't work, I would the other corner - the 3 grids with U4+U6=3 and those with U18 published by blue in the programmers forum.
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