Sudokus with an original rare shape

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

Postby JPF » Wed May 09, 2007 6:24 pm

19 clues

Code: Select all
 . . . . . . . . .
 . . 1 2 . 3 4 . .
 . 5 . . . . . 6 .
 . 6 . . . . . 7 .
 . . 3 . . . 2 . .
 . . . 4 . 2 . . .
 . . 2 . . . 1 . .
 . . 8 . . . 3 . .
 . . . 7 9 6 . . .

SE=3.2

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Postby m_b_metcalf » Thu May 10, 2007 2:20 pm

JPF wrote:19 clues

Code: Select all
 . . . . . . . . .
 . . 1 2 . 3 4 . .
 . 5 . . . . . 6 .
 . 6 . . . . . 7 .
 . . 3 . . . 2 . .
 . . . 4 . 2 . . .
 . . 2 . . . 1 . .
 . . 8 . . . 3 . .
 . . . 7 9 6 . . .

SE=3.2

This appears to be a rare and beautiful urn, with, I think, only two d=2 near-neighbours in the same 19D sudoku space (r4c2 -> 9 and r4c8 -> 5, or r6c4 -> 1 and r4c8 -> 5). Well done.

Regards,

Mike Metcalf
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Postby Ocean » Thu May 10, 2007 4:03 pm

m_b_metcalf wrote:This appears to be a rare and beautiful urn, with, I think, only two d=2 near-neighbours in the same 19D sudoku space (r4c2 -> 9 and r4c8 -> 5, or r6c4 -> 1 and r4c8 -> 5). Well done.

Agree; beautiful puzzle, good design work, JPF!

Think (r7c3 -> 8 and r8c3 -> 2 [Edit: corrected]) gives still another non-isomorph. Also note that the puzzle is d=2 near-neighbour to three of its own isomorphs. (for instance, r8c3 -> 9 and r9c5 -> 8).
[Don't know if anybody formulated this (more or less useless?) conjecture: A puzzle which contains N digits with only 1 occurence each will have at least N(N-1)/2 d=2 near-neighbours which are isomorphic to the original puzzle.]

Here is a slightly more difficult (not so near) in the same pattern:
Code: Select all
 . . . . . . . . .
 . . 1 2 . 3 4 . .
 . 5 . . . . . 6 .
 . 6 . . . . . 7 .
 . . 3 . . . 2 . .
 . . . 1 . 2 . . .
 . . 2 . . . 1 . .
 . . 4 . . . 8 . .
 . . . 5 7 9 . . .
Last edited by Ocean on Fri May 11, 2007 4:09 am, edited 1 time in total.
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Re: Some diagonal stuff

Postby m_b_metcalf » Thu May 10, 2007 5:06 pm

claudiarabia wrote:
Code: Select all
1 . . . . 3 . . 7
. . . 5 . . 8 . .
. 4 . . 6 . . . .
5 . . . . 4 . 6 .
. . 8 . . . 5 . .
. 9 . 1 . . . . 2
. . . . 2 . . 4 .
. . 3 . . 9 . . .
7 . . 8 . . . . 1


SE 9.0

That's a mine of treasures, for instance a Pearl:
Code: Select all
 5 . . . . 2 . . 7
 . . . 5 . . 8 . .
 . 6 . . 3 . . . .
 4 . . . . 7 . 3 .
 . . 8 . . . 9 . .
 . 9 . 1 . . . . 4
 . . . . 2 . . 4 .
 . . 3 . . 9 . . .
 7 . . 8 . . . . 1 SE 6.7 Pearl -> 9.1

Regards,

Mike Metcalf
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Postby udosuk » Fri May 11, 2007 5:25 am

Ocean wrote:Think (r7c3 -> 8 and r7c4 -> 2) gives still another non-isomorph.

How:?:
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Postby Ocean » Fri May 11, 2007 8:08 am

udosuk wrote:
Ocean wrote:Think (r7c3 -> 8 and r7c4 -> 2) gives still another non-isomorph.

How:?:

Sorry for the mis-labeling.
I thought of this, which I think is different from those mentioned (r7c3 -> 8 and r8c3 -> 2):
Code: Select all
 . . . . . . . . .
 . . 1 2 . 3 4 . .
 . 5 . . . . . 6 .
 . 6 . . . . . 7 .
 . . 3 . . . 2 . .
 . . . 4 . 2 . . .
 . . 8 . . . 1 . .
 . . 2 . . . 3 . .
 . . . 7 9 6 . . .
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Postby JPF » Sat May 12, 2007 5:01 pm

Ocean wrote:
m_b_metcalf wrote:This appears to be a rare and beautiful urn... Well done.
Agree; beautiful puzzle, good design work, JPF!

Thanks, Mike and Ocean

Ocean wrote:[Don't know if anybody formulated this (more or less useless?) conjecture: A puzzle which contains N digits with only 1 occurence each will have at least N(N-1)/2 d=2 near-neighbours which are isomorphic to the original puzzle.]

It seems to me that it's not a conjecture : it's obviously true.

For The Ocean's Bicycle Collection:)
Code: Select all
 . . . . . 1 2 3 .
 . . . . 4 . . . 5
 . . . . 6 . . . 7
 . . . . . 8 1 7 .
 . . . . . . . . .
 . 6 5 9 . . . . .
 1 . . . 3 . . . .
 3 . . . 7 . . . .
 . 4 8 5 . . . . .


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Postby m_b_metcalf » Sat May 12, 2007 7:37 pm


Another, a bit harder to ride:
Code: Select all
 . . . . . 5 4 6 .
 . . . . 9 . . . 2
 . . . . 8 . . . 1
 . . . . . 6 5 7 .
 . . . . . . . . .
 . 3 2 1 . . . . .
 5 . . . 4 . . . .
 6 . . . 2 . . . .
 . 7 8 3 . . . . . .SE 2.6

Regards,

Mike Metcalf
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Postby Ocean » Sun May 13, 2007 7:31 pm

m_b_metcalf wrote:

Another, a bit harder to ride:

Thanks. Very nice design! I struggled hard to put in some x-cycles or y-cycles, but no success yet.
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Postby Mauricio » Wed May 16, 2007 10:57 pm

m_b_metcalf wrote:Modern models are even more pleasing when they are even more skinny. I tried that on your pattern and got
Code: Select all
 . . . . . . 2 1 4
 . . . . . . . . 6
 . . . . . 8 . 5 9
 . . . 6 . 5 3 . .
 . . . 3 8 4 . . .
 . . 2 1 . 9 . . .
 8 6 . 5 . . . . .
 3 . . . . . . . .
 4 1 7 . . . . . .   23 cells

(Another one had one cell less but was no longer rotationally symmetrical:( .)

Can anyone get skinnier still?


Here is one with 22 clues, minimal:
Code: Select all
. . .|. . .|1 2 3
. . .|. . .|4 . 5
. . .|. . 6|. 7 .
-----+-----+-----
. . .|3 4 .|8 . .
. . .|7 . 2|. . .
. . 7|. 5 9|. . .
-----+-----+-----
. 4 .|8 . .|. . .
2 . 3|. . .|. . .
1 6 9|. . .|. . .


Similar patterns:
Code: Select all
. . .|. . .|. 1 2
. . .|. . .|3 4 5
. . .|. . 5|6 7 .
-----+-----+-----
. . .|4 2 6|8 . .
. . .|9 . 7|. . .
. . 7|5 1 8|. . .
-----+-----+-----
. 3 8|2 . .|. . .
9 4 1|. . .|. . .
7 6 .|. . .|. . .


Code: Select all
. . .|. . .|. 1 2
. . .|. . .|3 4 5
. . .|. . 4|6 7 .
-----+-----+-----
. . .|. 4 8|9 . .
. . .|7 1 5|. . .
. . 5|6 2 .|. . .
-----+-----+-----
. 4 7|1 . .|. . .
3 9 6|. . .|. . .
1 8 .|. . .|. . .
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Postby JPF » Thu May 17, 2007 8:04 pm

21 clues, minimal, diagonal symmetry :

Code: Select all
 . . . . . . . 1 2
 . . . . . . 3 4 5
 . . . . . 6 . . 7
 . . . . 1 . . 6 .
 . . . 4 . . 8 . .
 . . 5 . . 3 . . .
 . 6 . . 8 . . . .
 7 2 . 1 . . . . .
 8 9 3 . . . . . .


21 minimal, diagonal and anti-diagonal symmetry :

Code: Select all
 . . . . . . 1 2 .
 . . . . . 1 . 3 4
 . . . . 5 . . . 6
 . . . 3 . . . 6 .
 . . 6 . 7 . 5 . .
 . 1 . . . 2 . . .
 8 . . . 6 . . . .
 1 9 . 7 . . . . .
 . 3 4 . . . . . .


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Postby JPF » Fri May 18, 2007 7:58 pm

dedicated to Håvard :

Code: Select all
 . . . 1 2 3 . . .
 . . . . 4 . . . .
 . . 5 6 7 8 3 . .
 . 1 . . 8 . . 7 .
 . 8 . . . . . 2 .
 . . 7 . . . 5 . .
 . . . 5 . 2 . . .
 . . . . 1 . . . .
 . 2 6 7 9 4 1 8 .

SE=8.9, non minimal

This one is minimal :
Code: Select all
 . . . 1 2 3 . . .
 . . . . 4 . . . .
 . . 5 6 7 8 3 . .
 . 1 . . 8 . . 7 .
 . 4 . . . . . 2 .
 . . 3 . . . 8 . .
 . . . 8 . 2 . . .
 . . . . 1 . . . .
 . 2 6 7 3 5 1 4 .

SE=7.1

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Postby JPF » Mon May 21, 2007 6:41 am

Code: Select all
 . . . | . . . | . . .
 . 1 2 | . . . | 3 4 .
 . 4 . | 5 . 3 | . 6 .
-------+-------+-------
 . . . | . 3 . | . . .
 . . 3 | 2 7 8 | 9 . .
 . . . | . 6 . | . . .
-------+-------+-------
 . 6 . | 4 . 1 | . 5 .
 . 2 9 | . . . | 1 7 .
 . . . | . . . | . . .

SE=7.3

Code: Select all
 . . . | . . . | . . .
 . 1 2 | . . . | 3 4 .
 . 4 . | 5 . 6 | . 7 .
-------+-------+-------
 . . . | . 6 . | . . .
 . . 3 | . 8 . | 5 . .
 . . . | . 7 . | . . .
-------+-------+-------
 . 6 . | 7 . 3 | . 1 .
 . 5 9 | . . . | 8 2 .
 . . . | . . . | . . .

easy

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Postby JPF » Tue May 22, 2007 6:03 pm

Just a drop :

Code: Select all
 . . . . 1 . . . .
 . . . 2 . 3 . . .
 . . 4 . . . 5 . .
 . 2 . . . . . 6 .
 4 . . . . . . . 7
 5 . . . . . . . 3
 8 . . . . . . . 1
 . 3 . . . . . 7 .
 . . 2 5 9 7 4 . .

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little route

Postby claudiarabia » Thu May 24, 2007 2:32 pm

Again I tried to make a sudoku with the little route shape. This time it took me only 10 minutes while I worked for hours with my first and very easy result.

Code: Select all
4 . . . . . . . 9
. 8 . . 1 . . 7 .
. . . 3 . 6 . . .
. . 1 . . . 5 . .
. 6 . . 3 . . 9 .
. . 5 . . . 3 . .
. . . 5 . 2 . . .
. 7 . . 6 . . 8 .
9 . . . . . . . 4
SE 9.0
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