## Sudokus with an original rare shape

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

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` . . . . . . . . . . . 1 2 . 3 4 . . . 5 . . . . . 6 . . 6 . . . . . 7 . . . 3 . . . 2 . . . . . 4 . 2 . . . . . 2 . . . 1 . . . . 8 . . . 3 . . . . . 7 9 6 . . .`
SE=3.2

JPF
JPF
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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

m_b_metcalf
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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.
Ocean

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Joined: 29 August 2005

### Re: Some diagonal stuff

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

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

How
udosuk

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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):
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` . . . . . . . . .  . . 1 2 . 3 4 . .  . 5 . . . . . 6 .  . 6 . . . . . 7 .  . . 3 . . . 2 . .  . . . 4 . 2 . . .  . . 8 . . . 1 . .  . . 2 . . . 3 . .  . . . 7 9 6 . . . `
Ocean

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Joined: 29 August 2005

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 . . . . .`

JPF
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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

m_b_metcalf
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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.
Ocean

Posts: 442
Joined: 29 August 2005

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 .|. . .|. . .`
Mauricio

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Joined: 22 March 2006

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 . . . . . .`

JPF
JPF
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dedicated to Håvard :

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` . . . 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

JPF
JPF
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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

JPF
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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 . .`
JPF
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### little route

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
claudiarabia

Posts: 288
Joined: 14 May 2006

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