## Sudokus with an original rare shape

Everything about Sudoku that doesn't fit in one of the other sections
coloin wrote:To qualify as a neighbour - a neighbouring puzzle has to
have a unique solution
be minimal
have the same pattern
be non-isomorphic puzzle of the other
share a variable and defined number of common clues

"neighbour" might be too general a term for puzzles with the same pattern
there was another thread where "neighboring" puzzles were genrated by dropping a clue and adding another
this technique can be used to generate a taxonomy of n-off puzzles

you can use mutable clues to get the "mutatble neighbors" of the given puzzle
for the given puzzle there is one mutable clue with two values
so the 2 mutable neighbors are
Code: Select all
`1...2.....3.4.1.....5...6...1.....2.2.......7.4.....5...6...1.....7.8.9.....9...2 #    22 FN C20.m/S4.da1...2.....3.4.1.....5...6...1.....2.2.......7.4.....5...6...1.....7.8.9.....3...2 #    22 FN C20.m/S4.da`
Last edited by gsf on Thu Apr 12, 2007 10:19 pm, edited 1 time in total.
gsf
2014 Supporter

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Joined: 21 September 2005
Location: NJ USA

Yes there will be many more puzzles if you diverge from the pattern.

Mutable clue = 1-off [one clue removed and a different one added in the same position]

Putting a clue somewhere else in the grid is possibly not what were thinking about - not sure how to coin this in neighbourly or galactic terms.
Code: Select all
`1...2.....3.4.1.....5...6...1.....2.2.......7.4.....5...6...1.....7.8.9.....3...21...2.....3.4.1.....5...6...1.....2.2.......7.4.....5...6...1.....7.8.9.....9...21...2.....3.4.1.....5...6...1.....2.2.......7.4..9..5...6...1.....7.8.9.........21...2.....3.4.1.....5...6...1.....2.2.......7.4.....5...6...1.....7.8.9......3..21...2.....3.4.1.....5...6...1...7.2.2.......7.4.....5...6...1.....7.8.9.........21...2.....3.4.1.....5..36...1.....2.2.......7.4.....5...6...1.....7.8.9.........2`

Im not particularly good at these rare patterns to order........the best I got was 64 solutions !
Code: Select all
`5...9.....1.8.6.....3...5...8.....4.9.......3.5.....9...6...1.....3.2.7.....7...9`

Are there really no more unique puzzles with this pattern ?

C
coloin

Posts: 1709
Joined: 05 May 2005

coloin wrote:
Code: Select all
`+---+---+---+ |...|...|345| |...|...|8.2| |...|..3|679| +---+---+---+ |...|728|9..| |...|1.9|...| |..1|435|...| +---+---+---+ |845|2..|...| |9.2|...|...| |167|...|...| +---+---+---+ very pleasing...`

Pleasing because it was symetrically minimal

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?

Regards,

Mike Metcalf

m_b_metcalf
2017 Supporter

Posts: 8983
Joined: 15 May 2006
Location: Berlin

### A fish-like shape

And here is a fish-like shape.
Code: Select all
`. . 6 . . . 9 . .. 3 . . . 2 . 6 .4 . . . 7 . . . 5. 2 . 9 . . . 7 .. . 9 . . . 8 . .. 8 . 1 . . . 4 .8 . . . 3 . . . 2. 7 . . . 6 . 3 .. . 5 . . . 1 . .`

SE 7-3

Claudia
claudiarabia

Posts: 288
Joined: 14 May 2006

### Re: A fish-like shape

claudiarabia wrote:And here is a fish-like shape.

And another. With its big belly, if ever it catches yours it will surely gobble it up!
Code: Select all
` . 8 . . . 4 . . . . . 3 . 1 . . 9 . 2 . . 7 . . . . 5 . 6 . 3 . . . . 9 . . . . . . . . . . 1 . 2 . . . . 3 6 . . 9 . . . . 7 . . . . 8 . . 1 . . 4 . . . 5 . . . SE 8.3`

Regards, and bon appétit,

Mike Metcalf

m_b_metcalf
2017 Supporter

Posts: 8983
Joined: 15 May 2006
Location: Berlin

### Re: A fish-like shape

Here are two more denizens of the deep:
Code: Select all
` . . 3 . . . . . 5 . 5 . 3 . . . 6 . 1 . . . 2 7 . . . 8 . . . . 6 2 . . . . . . 9 . . 1 . 3 . . . . 1 4 . . 7 . . . 5 3 . . . . 8 . 6 . . . 4 . . . 9 . . . . . 1    SE 6.6`

Code: Select all
` . . 3 . . . . . 2 . 5 . 3 . . . 6 . 1 . . . 2 7 . . . 8 . . . . 6 2 . . . . 7 . 9 . . 1 . . 3 . . . . 1 4 . . 7 . . . 5 3 . . . . 8 . 6 . . . 4 . . . 9 . . . . . 1     SE 8.3`

Regards,

Mike Metcalf

m_b_metcalf
2017 Supporter

Posts: 8983
Joined: 15 May 2006
Location: Berlin

### Some fully symmetrical stuff

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

ER 8,7

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

And here the same pattern ER 2,0
Both of them are minimal.
Last edited by claudiarabia on Wed May 02, 2007 4:44 pm, edited 1 time in total.
claudiarabia

Posts: 288
Joined: 14 May 2006

### Nice Jellyfish-puzzle

In reminiscence to tso's and m.b.metcalfs little rectangles a Jellyfish-puzzle.

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

Posts: 288
Joined: 14 May 2006

### Re: Some fully symmetrical stuff

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

And here the same pattern ER 2,0
Both of them are minimal and untouchable.

Actually, in this one you can change r6c9 to 8, which can unleash a whole string of changes, the least of which is r7c2 to 9.

Regards,

Mike Metcalf

m_b_metcalf
2017 Supporter

Posts: 8983
Joined: 15 May 2006
Location: Berlin

Code: Select all
`7...9...5.1.5.4.3.............9.3...6.......7.3.4.6.2...........4.1.2.6.9...6...8`

ER=7.1
Eioru

Posts: 182
Joined: 16 August 2006

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

Here is a 19 clues :

Code: Select all
` . . . 1 . 2 . . . . . 3 . 4 . 2 . . . 5 . . . . . 6 . 5 . . . . . . . 7 . 1 . . . . . 8 . 8 . . . . . . . 4 . 7 . . . . . 1 . . . 2 . . . 6 . . . . . 7 . 4 . . .   `
ER=6.6

JPF
JPF
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Location: Paris, France

20 clues, minimal :

Code: Select all
` . . . 1 . 2 . . . . . 3 . . . 1 . . . 4 . . . . . 5 . 6 . . . 5 . . . 7 7 . . . . . . . 1 8 . . . 9 . . . 2 . 9 . . . . . 3 . . . 5 . . . 8 . . . . . 7 . 6 . . .`
ER=8.3

JPF
JPF
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Posts: 3754
Joined: 06 December 2005
Location: Paris, France

[quote="Eioru"]
Code: Select all
`7 . . . 9 . . . 5. 1 . 5 . 4 . 3 .. . . . . . . . .. . . 9 . 3 . . .6 . . . . . . . 7. 3 . 4 . 6 . 2 .. . . . . . . . .. 4 . 1 . 2 . 6 .9 . . . 6 . . . 8`
quote end

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

ER=7.1

A nice Idea. For me it is more difficult to produce horizontal or vertical than diagonal or rotational Symmetry. I have changed you puzzle a bit to a minimal one and now the Swordfish is dominating where in yours the X-Wing rules.
claudiarabia

Posts: 288
Joined: 14 May 2006

Code: Select all
`9 . . . 2 . . . 1. . . 3 . . . 8 .. . 6 . . . 5 . .. 5 . . . 1 . . .7 . . . 8 . . . 2. . . 6 . . . 4 .. . 3 . . . 6 . .. 8 . . . 5 . . .1 . . . 7 . . . 9`
Slash-pattern-sudokus are a never-ending story.

Here is one with ER8,3

If you change r7c3 and r5c5 to 4 you will get a Sudoku ER 7,2

I leave it to JPF to eliminate r1c1 and r9c9 to make a perfect 19er.
claudiarabia

Posts: 288
Joined: 14 May 2006

claudiarabia wrote:Slash-pattern-sudokus are a never-ending story.

Here is one with ER8,3

And here's a slight variation with ER9.0:
Code: Select all
` 9 . . . 2 . . . 1 . . . 3 . . . 8 . . . 6 . . . 5 . . . 5 . . . 9 . . . 7 . . . 8 . . . 2 . . . 2 . . . 4 . . . 3 . . . 6 . . . 8 . . . 5 . . . 1 . . . 7 . . . 9 SE 9.0`

I leave it to JPF to eliminate r1c1 and r9c9 to make a perfect 19er.

I'll give him a hand by offering this:
Code: Select all
` 4 . . . 6 . . . 2  . . . 2 . . . 8 . . . 6 . . . 7 . . . 5 . . . 7 . . . 7 . . . 2 . . . 3 . . . 6 . . . 4 . . . 4 . . . 5 . . . 8 . . . 9 . . . 2 . . . 7 . . . .   SE 6.6`

Regards,

Mike Metcalf

m_b_metcalf
2017 Supporter

Posts: 8983
Joined: 15 May 2006
Location: Berlin

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