Non-adjacent clues

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

Postby tso » Wed May 31, 2006 2:40 pm

Assuming adjacencies or connections in 8 directions (as opposed to 4),

Code: Select all
. . . . .
. 1 2 3 .
. . . . 4
. . . . .
. . . . .
Describing these four cells as "non-adjacent" would confuse everyone. I'd call them "connected".


Code: Select all
. . . . .
. 1 . 2 .
. . . . .
. . 3 . .
. . . . 4
These four are "non-adjacent" or "disconnected".


Code: Select all
. . . . .
. 1 2 . .
. 3 4 . .
. . . . .
. . . . .
These four are "adjacent".


The trouble is, without enough context, the reader might assume that any set of cells MUST be either "adjacent" OR "non-adjacent" -- it seems like binary choice. That's why I usually err on the side of redundancies and painfull over-specificity.


Code: Select all
. . . . .
. 1 . 2 .
. 3 . 4 .
. . . . .
. . . . .
These four are neither "adjacent" nor "non-adjacent'". They are therefore "not 'adjacent'" and "not 'non-adjacent'". This is ambiguous.
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Postby JPF » Wed May 31, 2006 10:09 pm

This discussion on semantic is interesting, but...

Can anybody help to find a puzzle with 23 clues ?

Suggested patterns :

23 clues, one empty group :
Code: Select all
 x . . | . x . | x . x
 . . x | . . . | . . .
 x . . | . x . | x . x
-------+-------+-------
 . . x | . . . | . . .
 x . . | . x . | x . x
 . . x | . . . | . . .
-------+-------+-------
 x . . | . x . | x . x
 . . . | . . . | . . .
 . x . | x . x | . x .


23 clues, two empty groups :
Code: Select all
 x . x | . . . | x . x
 . . . | . x . | . . .
 x . x | . . . | x . x
-------+-------+-------
 . . . | . x . | . . .
 x . x | . . . | x . x
 . . . | . . . | . . .
-------+-------+-------
 . x . | x . x | . x .
 . . . | . . . | . . .
 x . x | . x . | x . x


Thanks.

JPF

PS : about semantic...

Let G be the set of cells of the grid.

Each cell C is characterized by a row i and a column j (1<=i<=9 ; 1<=j<=9)

In G, we can define the distance between two cells A(i, j) and B(i’, j’) by:
d(A, B) = Max{ |i-i’|, |j-j’| }
d is a metric-distance and (G, d) is a metric-space.

I suggest the following definitions :

adjacent cells : two distinct cells A, B are adjacent if d(A, B)=1

Let Z be a set of cells : Z=(A, B, C,...) ; with at least 2 cells.

Connected set : a set Z of cells such that for every A of Z there exist B of Z such that d(A, B)=1.

Obviously, the set made by 2 adjacent cells is a connected set.

Non mutually adjacent set (of cells) : a set such as for every couple of distinct cells (A, B) : d(A, B)>1

Note that the exercise proposed by tso requires more than a non mutually adjacent set of clues. (who knows why ?)

Let's call the altitude between 2 cells A(i, j) and B(i', j') the number :
a(A, B)=|i-i'|

A "tso-set" is defined by the additional condition : if a(A, B)=1 then 1<d(A, B)<9
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Postby tso » Thu Jun 01, 2006 3:24 pm

JPF wrote:This discussion on semantic is interesting, but...

Can anybody help to find a puzzle with 23 clues ?


I found many with 22 clues; for example this one with vertical symmetry:

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



I found many with 23 clues that had two or three solutions.

(I don't have anywhere near the best search capability though.)
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Non-adjacent clues - a revival

Postby claudiarabia » Fri Mar 21, 2008 11:39 am

Let's give a little boost to this tiny but nevertheless nice thread. This sudoku is minimal. 21 clues. Full symmetry.
Code: Select all
8 . . 3 . 1 . . 2
. . . . . . . . .
. . 1 . 7 . 9 . .
4 . . . . . . . 8
. . 6 . 5 . 7 . .
3 . . . . . . . 1
. . 9 . 1 . 4 . .
. . . . . . . . .
2 . . 8 . 6 . . 3
ER 7.9

There surely exist sudokus with a likewise pattern without a clue in r5c5.

With best wishes

Claudia
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Re: Non-adjacent clues - a revival

Postby JPF » Fri Mar 21, 2008 12:26 pm

claudiarabia wrote:There surely exist sudokus with a likewise pattern without a clue in r5c5.

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

ER=9.0

JPF
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Re: Non-adjacent clues - a revival

Postby daj95376 » Fri Mar 21, 2008 5:02 pm

claudiarabia wrote:Let's give a little boost to this tiny but nevertheless nice thread. This sudoku is minimal. 21 clues. Full symmetry.

Wow, a rare 4444 Jellyfish!

Code: Select all
    b3  -  4567  Naked  Quad
r357    -  3     222 Swordfish
r357    -  8     222 Swordfish
    b7  -  38    Hidden Pair
r1469   -  5     4444 Jellyfish
        -  7     unfinned Franken Swordfish c19b8\r278
        -  9     unfinned Franken Jellyfish c1469\r258b5
                 etc.
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20 clues -- 0-9-6-0-0

Postby Pat » Sun Mar 23, 2008 1:50 pm

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

    [ minimal ]

    ER=9.0



this clue-pattern being fully-symmetrical,
it's no surprise to find that a puzzle has already been posted
with an equivalent clue-pattern --

Ocean (2006.May.5) wrote:
Code: Select all
 . . . . . . . . .
 . 1 . . 2 . . 3 .
 . . 4 5 . 6 7 . .
 . . 6 . . . 5 . .
 . 2 . . . . . 8 .
 . . 8 . . . 9 . .
 . . 5 4 . 7 6 . .
 . 8 . . 9 . . 1 .
 . . . . . . . . .

    minimal
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Postby JPF » Sun Mar 23, 2008 6:43 pm

Pat wrote:this clue-pattern being fully-symmetrical,
it's no surprise to find that a puzzle has already been posted
with an equivalent clue-pattern --

right, this pattern has already been posted by Ocean.
The pattern-code is :
Code: Select all
0-9-6-0-0  0-10-5-0-0  17-0-6-0-0 17-10-0-0-0  18-0-5-0-0  18-9-0-0-0

I only tried to give a puzzle with a higher SE rating (Ocean's ER=7.1)

By the way, this pattern would be a good candidate for the Patterns game.
There are not a lot of SE ratings, and I haven't found any singles-only puzzle for it.

Now, there are less than 67 non isomorphic fully-symmetrical patterns with 20 clues.
Only 16 have been "found".

Note that claudia's pattern has full symmetry too ; an isomorph was already posted by me here :

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


Too easy ; here' a new one :
Code: Select all
 1 . . | 2 . 3 | . . 4
 . . . | . . . | . . .
 . . 5 | . 6 . | 3 . .
-------+-------+-------
 7 . . | . . . | . . 1
 . . 1 | . 7 . | 6 . .
 2 . . | . . . | . . 8
-------+-------+-------
 . . 9 | . 5 . | 4 . .
 . . . | . . . | . . .
 4 . . | 8 . 7 | . . 2

ER=9.2

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re: 0-9-6-0-

Postby Pat » Mon Mar 24, 2008 4:47 pm

JPF wrote:this pattern [ 20 clues ]
would be a good candidate for the "patterns game"
    There are not a lot of SE ratings,
    and I haven't found any singles-only puzzle for it

seems too demanding for the "patterns game" --
they like clue-patterns where plenty of ratings can be found within a few days

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

    [ 21 clues ]

    [ minimal ]

    ER=9.2

yes, a "singles" example is too easy --
but then again, 9.2 may be too tough
    that's what i like in the "patterns game"
    -- we get a broad range of difficulties,
    something for everyone
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Postby Pat » Mon Apr 14, 2008 11:12 am

claudiarabia's pattern [ 21 clues ]
has now been used in the "patterns game"
    #24
    2008.Mar.31-Apr.4
    ( p.179-184 )
reducing it to just 20 clues may be too demanding---
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