The New Sudoku Players' Forum

[JPF]

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

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 1 . . . 2 . . . 3
 . 4 . . . . . 5 .
 . . 6 . . . 7 . .
 . . . 6 . 2 . . .
 8 . . . . . . . 9
 . . . 3 . 4 . . .
 . . 7 . . . 4 . .
 . 5 . . . . . 6 .
 3 . . . 1 . . . 2



SE=9.3

JPF

[coloin]

This one would appear to have only 2 near neighbours in sudoku space

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+---+---+---+
|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

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

[coloin]

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

Code: Select all

6 sol.
6 sol.
3 sol.
5 sol.
8 sol.
2 sol.
6 sol.
5 sol.

C

[RW]

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.

RW

[gsf]

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

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

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-f'%(required())#ph'


lists the number of solutions for each clue when omitted in pm grid style

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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

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 .  .  . | .  .  . | .  .  .
 .  .  . | .  .  . | .  .  .
 .  .  . | .  .  . | .  .  .
---------+---------+---------
 .  .  . | .  .  . | .  .  .
 .  .  . | .  .  . | .  .  .
 .  .  . |18  .  . | .  .  .
---------+---------+---------
 .  .  . | .  .  . | .  .  .
 .  .  . | .  .  . | .  .  .
 .  .  . | .  .  . | .  .  .


[JPF]

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.

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



JPF

[RW]

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:

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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:

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 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

[coloin]

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

To make up for my faux pas

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+---+---+---+
|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...

C

[RW]

Not bad coloin! Interesting feature with that grid, if you add the missing clue to box 1:

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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...]

RW

[m_b_metcalf]

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

Regards,

Mike Metcalf

[udosuk]

[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...

I'd be perfectly happy to share the Field Prize with a collaborator

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

[coloin]

No - I think there are 3 near neighbours - it is tricky this....

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1...2.....3.4.1.....5...6...1.....2.2.......7.4.....5...6...1.....7.8.9.....9...2 #1

non isomorphic neighbours

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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

C

[udosuk]

No - I think there are 3 near neighbours - it is tricky this....

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1...2.....3.4.1.....5...6...1.....2.2.......7.4.....5...6...1.....7.8.9.....9...2 #1

non isomorphic neighbours

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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...

[m_b_metcalf]

[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...

I'd be perfectly happy to share the Field Prize with a collaborator

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

Correct on all accounts. Sorry for my ineptitude!

Regards,

Mike Metcalf

[coloin]

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

C