## is a symertry missing from issomorphic variations

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

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StrmCkr

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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

C
coloin

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StrmCkr

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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|***|231or123|***|***456|3*2|**1789|*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....
coloin

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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

Pat

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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|+---+---+---+`

C
coloin

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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 !

C
coloin

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Joined: 05 May 2005

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

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