The New Sudoku Players' Forum

[gsf]

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.da
1...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


[coloin]

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...2
1...2.....3.4.1.....5...6...1.....2.2.......7.4.....5...6...1.....7.8.9.....9...2
1...2.....3.4.1.....5...6...1.....2.2.......7.4..9..5...6...1.....7.8.9.........2
1...2.....3.4.1.....5...6...1.....2.2.......7.4.....5...6...1.....7.8.9......3..2
1...2.....3.4.1.....5...6...1...7.2.2.......7.4.....5...6...1.....7.8.9.........2
1...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

[m_b_metcalf]

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

[claudiarabia]

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

[m_b_metcalf]

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]

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

[claudiarabia]

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.

[claudiarabia]

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 .
. . . . . . . . .


[m_b_metcalf]

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

[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

ER=7.1

[JPF]

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]

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

[claudiarabia]

[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]

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.

[m_b_metcalf]

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