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motris
motris
29 October 2009 @ 09:22 pm
Friday Puzzle #21 - Extra Region Sudoku  
My favorite current variation of Sudoku is Arrow Sudoku. Outside the realm of mathematical variants, my favorite geometric variant is the topic of this week's entry: Extra Region Sudoku. In addition to the standard 1-9 constraint in rows/columns/3x3 boxes, in these puzzles there are 4 more regions which also obey the 1-9 constraint and these are the contiguous groups of peach cells. I'm posting so many this week as I wrote these a long time ago and am unlikely to revisit this topic in the future; it should be noted that the last geometry is sometimes given its own name of Windoku and is syndicated in Dutch newspapers (and possibly elsewhere). The geometry of Windoku is less interesting to me than the others, but it has some hidden constraints to find if you've never looked at one before.





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(Anonymous) on October 30th, 2009 05:00 am (UTC)
More regions, less givens
Suppose that, in addition to the normal 3 ways to partition the grid into 9 pieces, each piece needing 9 different symbols, you find a fourth way to partition the grid (and again require each piece to have 9 different symbols). How many givens would you need to guarantee a unique solution?

I am aware of other variations which have smaller than the (so far unconfirmed) 17 needed for most sudoku, but I have not seen a variation which does 4 regular partitions of the grid. I suspect with four partitions, less than 10 numbers would need to be specified for a unique solution. Have you experienced a sudoku variation of this type ( with four or more partitions )?

Gerhard Paseman, 2009.10.29
motris[info]motris on October 30th, 2009 05:07 am (UTC)
Re: More regions, less givens
I've certainly seen puzzles like what you are describing; the closest in a minimal sense is probably this puzzle from Wei-Hwa although an 8 given version, the absolute minimum, might be possible.
[info]stigant on October 30th, 2009 09:02 pm (UTC)
These had some very nice deductions. As a side note, it's interesting that an error early in a puzzle can make the puzzle really difficult, but an error midway through usually makes the puzzle a lot "easier" while an error at the end has little effect on the difficulty of the solve.
Robert Hutchinson[info]ertchin on November 1st, 2009 03:57 am (UTC)
Having some trouble with the first two--I keep hopping back and forth between them. Probably just haven't had all the constraints seep thoroughly enough into my brain yet. Or maybe I should be making notes, which is hard to do in MS Paint.

BTW, just got your two sudoku books in the mail today! I've only spent a few minutes looking at each, but they're very nice, what with the introductions and the framing and all. (Oh, and I guess the puzzles are good too.)