is a symertry missing from issomorphic variations

Everything about Sudoku that doesn't fit in one of the other sections

Postby StrmCkr » Sat Aug 16, 2008 2:31 am

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Postby StrmCkr » Sun Aug 17, 2008 1:21 am

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Postby coloin » Mon Aug 18, 2008 8:26 am

I think if you standardize your box operations and it is reproducable on other puzzles [with automorphic solutions], then I think you might have something here. I have lost that puzzle though - sorry.

I can almost see the effect on the puzzle of the "reflection" - which in effect is a row swap within a box. This is performed on the two boxes [B3&B4]. Then you say you perform a rotation on the 3rd box [B8] - this could be described as two reflections within the box.

To maintain the same puzzle a row swaps has to envolve the whole row,of course.

Partial row swaps may have an interaction,[provided it doesnt cause a conflict] which is compensated for by the double row swap within the third box. I cant visualize this as you can do !

The portrayal of the grid solution of an automorhphic grid with identical clues in diagonal boxes brings up an idea for a sudoku variant. Stormdoku

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Postby StrmCkr » Thu Aug 21, 2008 4:35 am

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Postby StrmCkr » Thu Aug 21, 2008 5:43 am

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Postby coloin » Thu Aug 21, 2008 6:51 am

I dont think there will be all that many essentially different grids with the feature. [Red Ed would tell us in a flash] Certainly it will be devided into ones which have 3 repeating minirows [MC] and those which have a 2:1 split.

Code: Select all
123|***|***
456|312|***
789|***|231

or

123|***|***
456|3*2|**1
789|*1*|23*


Going from puzzle 1 to each of the next 2 puzzles in your last examples
2 boxes are different in each puzzle
3 boxes are different
puzzle 3 to 4
2 boxes are different - not sure why this should be so....
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Postby Pat » Thu Aug 21, 2008 10:01 am

StrmCkr wrote:
a reflection/roation/ mirring in a box of clues held on a diagonal from one another. this change creates a knot in the bands of symertry to form a new solution grid based on that knot:) can be reversed to solve orgninal automorph....

original posted by ttt.

Code: Select all
 *-----------*
 |.2.|7..|.5.|
 |84.|...|6..|
 |1.5|.9.|...|
 |---+---+---|
 |.5.|.2.|7..|
 |6..|84.|...|
 |...|1.5|.9.|
 |---+---+---|
 |7..|.5.|.2.|
 |...|6..|84.|
 |.9.|...|1.5|
 *-----------*



new puzzle mirror clues in box 3 and 4.

Code: Select all
 *-----------*
 |.2.|7..|.5.|
 |84.|...|..6|
 |1.5|.9.|...|
 |---+---+---|
 |.5.|.2.|7..|
 |..6|84.|...|
 |...|1.5|.9.|
 |---+---+---|
 |7..|.5.|.2.|
 |...|6..|84.|
 |.9.|...|1.5|
 *-----------*



or box 2 ,6 ,7:) diagonally rotated.
Code: Select all
 *-----------*
 |.2.|...|.5.|
 |84.|...|6..|
 |1.5|79.|...|
 |---+---+---|
 |.5.|.2.|...|
 |6..|84.|...|
 |...|1.5|79.|
 |---+---+---|
 |...|.5.|.2.|
 |...|6..|84.|
 |79.|...|1.5|
 *-----------*




and a combination of the two:)

Code: Select all
 *-----------*
 |.2.|...|.5.|
 |84.|...|..6|
 |1.5|79.|...|
 |---+---+---|
 |.5.|.2.|...|
 |..6|84.|...|
 |...|1.5|79.|
 |---+---+---|
 |...|.5.|.2.|
 |...|6..|84.|
 |79.|...|1.5|
 *-----------*





these of course are not equivalent to each other
    and incidentally the 4th has more than one answer
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Postby StrmCkr » Thu Aug 21, 2008 3:31 pm

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Postby StrmCkr » Sat Aug 23, 2008 3:12 am

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Postby StrmCkr » Mon Aug 25, 2008 1:52 am

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Postby StrmCkr » Tue Aug 26, 2008 1:58 am

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Postby StrmCkr » Wed Aug 27, 2008 1:40 am

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Postby coloin » Wed Aug 27, 2008 8:40 am

coloin wrote:I dont think there will be all that many essentially different grids with the feature. [Red Ed would tell us in a flash]

There are only 3 different grids with the 3* property !

One with all of the 6 bands of repeating 3-tuple minirows - MC grid

Code: Select all
+---+---+---+
|123|...|.4.|
|456|231|.7.|
|789|...|.1.|
+---+---+---+
|.4.|123|...|
|.7.|456|231|
|.1.|789|...|
+---+---+---+
|...|.4.|123|
|231|.7.|456|
|...|.1.|789|
+---+---+---+  MC grid


One with all 6 bands of repeating 2+1 -tuple minirows -

Code: Select all
+---+---+---+
|123|...|.4.|
|456|238|.7.|
|789|...|.6.|
+---+---+---+
|.4.|123|...|
|.7.|456|238|
|.6.|789|...|
+---+---+---+
|...|.4.|123|
|238|.7.|456|
|...|.6.|789|
+---+---+---+


One with all 3 bands of 3-tuple minirows and 3 bands of 2+1 tupel-minirows

Code: Select all
+---+---+---+
|123|...|.4.|
|456|231|.9.|
|789|...|312|
+---+---+---+
|.4.|123|...|
|.9.|456|231|
|312|789|...|
+---+---+---+
|...|.4.|123|
|231|.9.|456|
|...|312|789|
+---+---+---+


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Postby coloin » Wed Aug 27, 2008 8:55 am

In a 9*9 puzzle, if you can continue to "see" the effect of removed clues.....and their reinsertion - in a different position - and see that a valid puzzle remains - you indeed have remarkable vision !

Is this really what you are doing ?

I still think your rotation in a box is effectivley a mini-row row-swap.


Code: Select all
+---+---+---+
|1..|...|..6|
|.2.|...|.5.|
|..3|...|4..|
+---+---+---+
|...|...|...|
|...|...|...|
|...|...|...|
+---+---+---+
|..4|...|...|
|.5.|...|...|
|6..|...|...|
+---+---+---+


with a complete r1/r3 swap and a complete c1/c3 column swap it becomes
Code: Select all
+---+---+---+
|3..|...|4..|
|.2.|...|.5.|
|..1|...|..6|
+---+---+---+
|...|...|...|
|...|...|...|
|...|...|...|
+---+---+---+
|4..|...|...|
|.5.|...|...|
|..6|...|...|
+---+---+---+


So two of your "reflections/90 deg. rotations/rowswaps" in B3 and B7 have an effect of a 180 deg. rotation in B1........I dont know if this contributes or not !

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Postby Red Ed » Wed Aug 27, 2008 12:51 pm

Could someone please give a concise description of what the heck you're trying to achieve here ...?
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