Sudokus with an original rare shape

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

Postby JPF » Wed Apr 11, 2007 9:18 pm

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


SE=7.2
Code: Select all
 
 1 . . . 2 . . . 3
 . 4 . . . . . 5 .
 . . 6 . . . 7 . .
 . . . 6 . 2 . . .
 8 . . . . . . . 9
 . . . 3 . 4 . . .
 . . 7 . . . 4 . .
 . 5 . . . . . 6 .
 3 . . . 1 . . . 2


SE=9.3:)

JPF
Last edited by JPF on Wed Apr 11, 2007 7:08 pm, edited 1 time in total.
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Postby coloin » Wed Apr 11, 2007 9:53 pm

m_b_metcalf wrote:This one would appear to have only 2 near neighbours in sudoku space:!:
Code: Select all
+---+---+---+
|1..|.2.|...|
|.3.|4.1|...|
|..5|...|6..|
+---+---+---+
|.1.|...|.2.|
|2..|...|..7|
|.4.|...|.5.|
+---+---+---+
|..6|...|1..|
|...|7.8|.9.|
|...|.9.|..2|
+---+---+---+

I could only find one !
Code: Select all
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.....5...6...1.....7.8.9.....3...2

This r9c5 clue is termed mutable..... many puzzles dont have a single mutable clue and have been termed untouchable. [40% of Gordon's 17s didnt have mutable clues][level 1 untouchable]

Of course it depends how many clues you consider changing - but I tried several "remove -3 /add -3 and didnt get any more puzzles in that pattern- so you might well be right.

In general you would think that there would be less mutable clues in puzzles with less than 21 clues - but this appears not the case.
I dont know when this gets significant - bound to be more as you remove more clues - but see Nick70's collection of 851 different 19 clue puzzles of one pattern..........
Indeed
JPF wrote: I have checked the Nick70’s list.
25% Untouchables, 75% Volatiles
The most volatile puzzles (10 puzzles) have 5 mutable clues.

JPF did introduce a "level 2 untouchable" concept but this wasnt explored see untouchables and chameleons.......

It is an intriqing concept "the inner and outer regions of "sudoku space"" !

C
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Postby coloin » Thu Apr 12, 2007 12:16 am

Rather more on topic

here is an interesting one.........

Code: Select all
+---+---+---+
|1..|...|..2|
|.6.|...|.7.|
|..9|4..|5..|
+---+---+---+
|..5|942|...|
|...|5.7|...|
|...|136|4..|
+---+---+---+
|..4|..9|8..|
|.7.|...|.3.|
|2..|...|..1|
+---+---+---+  SE 9.1


Nice shape........but it is minimal - with 8 clues in a box - I wasnt aware this was possible - certainly rare enough not to be mentioned !

If you dont believe me these are the grid solution counts for the 8 clues in the central box:D
Code: Select all
6 sol.
6 sol.
3 sol.
5 sol.
8 sol.
2 sol.
6 sol.
5 sol.

C
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Postby RW » Thu Apr 12, 2007 4:34 am

Not at all that uncommon. I believe we don't see those very often because the shape is quite boring to solve with one box already filled. I've seen many of them while creating puzzles. Especially when creating for the 9+ thread I bumped into a lot of these. But is there a minimal puzzle with 8 clues in 2 boxes?? Or to make it easier, let's start with 8 clues in 2 units.

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Postby gsf » Thu Apr 12, 2007 5:24 am

coloin wrote:Rather more on topic

here is an interesting one.........

Code: Select all
+---+---+---+
|1..|...|..2|
|.6.|...|.7.|
|..9|4..|5..|
+---+---+---+
|..5|942|...|
|...|5.7|...|
|...|136|4..|
+---+---+---+
|..4|..9|8..|
|.7.|...|.3.|
|2..|...|..1|
+---+---+---+  SE 9.1


Nice shape........but it is minimal - with 8 clues in a box - I wasnt aware this was possible - certainly rare enough not to be mentioned !

If you dont believe me these are the grid solution counts for the 8 clues in the central box:D
Code: Select all
6 sol.
6 sol.
3 sol.
5 sol.
8 sol.
2 sol.
6 sol.
5 sol.

C

earlier this year I added mutable() and required() expression and formatting functions to my solver
this formatting option
Code: Select all
-f'%(required())#ph'

lists the number of solutions for each clue when omitted in pm grid style
Code: Select all
103  0   0  | 0   0   0  | 0   0   93
 0  121  0  | 0   0   0  | 0   92  0
 0   0   83 |153  0   0  |100  0   0
------------+------------+------------
 0   0  130 | 6   6   3  | 0   0   0
 0   0   0  | 5   0   8  | 0   0   0
 0   0   0  | 2   6   5  | 82  0   0
------------+------------+------------
 0   0  160 | 0   0   81 | 50  0   0
 0  118  0  | 0   0   0  | 0  102  0
 65  0   0  | 0   0   0  | 0   0  102

and this formatting option
Code: Select all
-f'%(mutable())#ph'

lists the mutable clue values in pm grid style
Code: Select all
 .  .  . | .  .  . | .  .  .
 .  .  . | .  .  . | .  .  .
 .  .  . | .  .  . | .  .  .
---------+---------+---------
 .  .  . | .  .  . | .  .  .
 .  .  . | .  .  . | .  .  .
 .  .  . |18  .  . | .  .  .
---------+---------+---------
 .  .  . | .  .  . | .  .  .
 .  .  . | .  .  . | .  .  .
 .  .  . | .  .  . | .  .  .
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Postby JPF » Thu Apr 12, 2007 6:56 am

RW wrote:Not at all that uncommon. I believe we don't see those very often because the shape is quite boring to solve with one box already filled. I've seen many of them while creating puzzles. Especially when creating for the 9+ thread I bumped into a lot of these.
I agree.
RW wrote:But is there a minimal puzzle with 8 clues in 2 boxes?? Or to make it easier, let's start with 8 clues in 2 units.

yes , here's one :
Code: Select all
 1 2 3 | 4 5 . | . . .
 6 . 4 | . . . | . . .
 7 8 5 | . . . | . . .
-------+-------+-------
 3 . . | 5 . . | . . .
 . . . | . 9 . | . . 8
 . . . | . . . | . . 7
-------+-------+-------
 . . . | . . . | 1 5 4
 . . . | . . . | 7 . 2
 . . . | . 2 7 | 8 6 9


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Postby RW » Thu Apr 12, 2007 11:42 am

JPF, somehow I knew you would have a puzzle to answer this demand as well... It always amazes me how fast you find the most exotic puzzles! But, you could of course have made it symmetrical:

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

27 clues minimal, double diagonal symmetry. Here's the number of solutions for each given calculated with gsf's program:
Code: Select all
 47  14  73 | 25 380  0  | 0   0   0
 14  0   2  | 0   0   0  | 0   0   0
 27  3   16 | 0   0   0  | 0   0   0
------------+------------+------------
193  0   0  |120  0   0  | 0   0   0
137  0   0  | 0   15  0  | 0   0  495
 0   0   0  | 0   0  187 | 0   0  418
------------+------------+------------
 0   0   0  | 0   0   0  | 75  4  101
 0   0   0  | 0   0   0  | 63  0   32
 0   0   0  | 0   99 447 |141  27 102


RW
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Postby coloin » Thu Apr 12, 2007 12:38 pm

Quite good..........

To make up for my faux pas
Code: Select all
+---+---+---+
|952|...|...|
|863|...|...|
|.41|...|...|
+---+---+---+
|...|918|.7.|
|.1.|542|...|
|...|73.|...|
+---+---+---+
|...|...|827|
|...|.2.|314|
|...|...|95.|
+---+---+---+

Rearranged to

+---+---+---+
|592|...|...|
|4.1|...|...|
|683|...|...|
+---+---+---+
|...|981|..7|
|...|7.3|...|
|1..|524|...|
+---+---+---+
|...|...|872|
|...|...|9.5|
|...|..2|341|
+---+---+---+


Courtesy of JPF

Also courtesy of JPFs stretches
Code: Select all
+---+---+---+
|...|...|345|
|...|...|8.2|
|...|..3|679|
+---+---+---+
|...|728|9..|
|...|1.9|...|
|..1|435|...|
+---+---+---+
|845|2..|...|
|9.2|...|...|
|167|...|...|
+---+---+---+ very pleasing...


:D

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Postby RW » Thu Apr 12, 2007 1:20 pm

Not bad coloin! Interesting feature with that grid, if you add the missing clue to box 1:
Code: Select all
5 9 2|. . .|. . .
4 7 1|. . .|. . .
6 8 3|. . .|. . .
-----+-----+-----
. . .|9 8 1|. . 7
. . .|7 . 3|. . .
1 . .|5 2 4|. . .
-----+-----+-----
. . .|. . .|8 7 2
. . .|. . .|9 . 5
. . .|. . 2|3 4 1

There's five different clues you may remove to create a minimal puzzle:
5.2......471......683.........981..7...7.3...1..524.........872......9.5.....2341
59.......471......683.........981..7...7.3...1..524.........872......9.5.....2341
592......4.1......683.........981..7...7.3...1..524.........872......9.5.....2341
592......471......6.3.........981..7...7.3...1..524.........872......9.5.....2341
592......471......68..........981..7...7.3...1..524.........872......9.5.....2341

Is it possible to create an even more "unstable" box? Is there a box with 9 digits so that you can at most remove 1 digit or the puzzle would have multiple solutions?

And here's the double diagonal version of your puzzle::)
Code: Select all
5 7 2|. . 4|. . .
4 . 1|. . .|. . .
6 9 3|. . .|. . .
-----+-----+-----
. . .|1 8 9|. . 7
. . .|3 . 7|. . .
3 . .|4 2 5|. . .
-----+-----+-----
. . .|. . .|7 8 2
. . .|. . .|6 . 5
. . .|2 . .|4 3 1


[Edit: Sorry, you must have edited in your own double diagonal version while I was posting...]

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Postby m_b_metcalf » Thu Apr 12, 2007 1:54 pm

coloin wrote:
m_b_metcalf wrote:This one would appear to have only 2 near neighbours in sudoku space:!:
I could only find one !
Code: Select all
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.....5...6...1.....7.8.9.....3...2


Well, I looked again and found two more: in the original, r2c2 and r8c8 can swap values and also in your one above that swap is valid. That makes a tiny knot of four puzzles in sudoku space.

[Edit: whoops, that fourth one is an isomorph so we're back to two neighbours to the original.]
It is an intriqing concept "the inner and outer regions of "sudoku space"" !

Yes, but nobody seemed to take it up (or even rubbish it). I'd be perfectly happy to share the Fields Medal [edit] with a collaborator:D

Regards,

Mike Metcalf
Last edited by m_b_metcalf on Thu Apr 12, 2007 3:25 pm, edited 2 times in total.
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Postby udosuk » Thu Apr 12, 2007 3:32 pm

m_b_metcalf wrote:[Edit: whoops, that fourth one is an isomorph so we're back to two neighbours to the original.]

Correct me if I'm wrong, but ain't the 2nd & 3rd one isomorphic to each other? Which bring us back to only one neighbour to the original...:?:

m_b_metcalf wrote:I'd be perfectly happy to share the Field Prize with a collaborator:D

Good luck with the Fields Medal aspiration... It could be a good idea to join forces with a bright mind from Oxford...:D
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Postby coloin » Thu Apr 12, 2007 5:31 pm

No - I think there are 3 near neighbours - it is tricky this....
Code: Select all
1...2.....3.4.1.....5...6...1.....2.2.......7.4.....5...6...1.....7.8.9.....9...2 #1

non isomorphic neighbours
Code: Select all
1...2.....3.4.1.....5...6...1.....2.2.......7.4.....5...6...1.....7.8.9.....3...2 #2  level 1
1...2.....3.4.1.....5...6...1.....2.2.......7.4.....5...6...1.....7.8.3.....9...2 #3  level 1
1...2.....9.4.1.....5...6...1.....2.2.......7.4.....5...6...1.....7.8.9.....3...2 #4  level 2

isomorphs
Code: Select all
1...2.....9.4.1.....5...6...1.....2.2.......7.4.....5...6...1.....7.8.3.....3...2 #1
1...2.....9.4.1.....5...6...1.....2.2.......7.4.....5...6...1.....7.8.3.....9...2 #2

Simple isomorphs will occur if two clues values are swapped [9! per puzzle]

There might be a puzzle which has no [non-isomorphic] mutable clues at the 2 clue level - this would be an even more remote puzzle.

I will take "one small step for man....."

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

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Postby udosuk » Thu Apr 12, 2007 6:03 pm

coloin wrote:No - I think there are 3 near neighbours - it is tricky this....
Code: Select all
1...2.....3.4.1.....5...6...1.....2.2.......7.4.....5...6...1.....7.8.9.....9...2 #1

non isomorphic neighbours
Code: Select all
1...2.....3.4.1.....5...6...1.....2.2.......7.4.....5...6...1.....7.8.9.....3...2 #2  level 1
1...2.....3.4.1.....5...6...1.....2.2.......7.4.....5...6...1.....7.8.3.....9...2 #3  level 1
1...2.....9.4.1.....5...6...1.....2.2.......7.4.....5...6...1.....7.8.9.....3...2 #4  level 2

isomorphs
Code: Select all
1...2.....9.4.1.....5...6...1.....2.2.......7.4.....5...6...1.....7.8.3.....3...2 #1
1...2.....9.4.1.....5...6...1.....2.2.......7.4.....5...6...1.....7.8.3.....9...2 #2

Firstly, #3 & #4 are isomorphic to each other (permutation of symbols: 3<->9). Secondly, Simple Sudoku claims they each have 692 solutions... So unless we start accepting non-unique-solutional puzzles as "neighbours" I can only see 1 lonely neighbour for our original friend...:!:
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Postby m_b_metcalf » Thu Apr 12, 2007 6:57 pm

udosuk wrote:
m_b_metcalf wrote:[Edit: whoops, that fourth one is an isomorph so we're back to two neighbours to the original.]

Correct me if I'm wrong, but ain't the 2nd & 3rd one isomorphic to each other? Which bring us back to only one neighbour to the original...:?:

m_b_metcalf wrote:I'd be perfectly happy to share the Field Prize with a collaborator:D

Good luck with the Fields Medal aspiration... It could be a good idea to join forces with a bright mind from Oxford...:D


Correct on all accounts. Sorry for my ineptitude!

Regards,

Mike Metcalf
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Postby coloin » Thu Apr 12, 2007 8:46 pm

And sorry for mine too !

I reproduced my error, #3 and #4 do have multiple solutions.....

Only one neighbour for the puzzle then.

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

I suppose the neighbour may have some other neighbours:?:

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