Symmetric Odd-Even Sudoku possible?

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Symmetric Odd-Even Sudoku possible?

Postby Pyrrhon » Fri May 12, 2006 3:30 pm

I want to make a symmetric odd/even sudoku, where not only the clues but also the colored grid is symmetric. (i. e. if R1C2 is an odd number then also R9C8 should be odd, and if R1C3 is even then also R9C7 should be. R5C5 must be odd of course. Or saying it in other way I look for a way to color a sudoku grid so that in every row, column and box are 4 green and 5 yellow cells.

Any other symmetry or a jigsaw variant would also be nice. But I can't find a possible grid. Any idea?
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Postby keith » Fri May 12, 2006 5:20 pm

Maybe your proposed symmetry is a deadly pattern?

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Postby Ruud » Fri May 12, 2006 5:51 pm

No deadly pattern in this puzzle.

Here is an example from the Superior Thread, by Red Ed. The colors are mine.

Image

This puzzle has a little extra, but it's a start, you can do a little scrambling and minimization.

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Postby Red Ed » Fri May 12, 2006 5:52 pm

You can do better than just symmetric odd/even: you can have opposite cells summing to 10.

Ah! I see Ruud's pipped me to it!:D

You can do odd/even symmetry for quarter turns, too:
Code: Select all
# 2 . 5 . . # . #
. # 1 3 . # . # 4
# . 9 # # # 3 7 .
. # # . 2 . # 2 5
. . # 6 . 4 # . .
5 9 # . 8 . # # .
. 3 7 # # # 1 . #
6 # . # . 7 9 # .
# . # . . 5 . 8 #

Key: . = odd
     # = even
(sorry about the bad graphics)
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Postby Pyrrhon » Fri May 12, 2006 6:41 pm

Thank,

nice extra idea.

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