very large empty edge

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

Postby udosuk » Wed Aug 09, 2006 7:59 am

Why are these patterns excluded?

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 x . x x . .
. x x . . . x x .
. . . . . . . . .
. x x . . . x x .
. . x x . x x . .
. . . x . x . . .
. . . . . . . . .
udosuk
 
Posts: 2698
Joined: 17 July 2005

Postby JPF » Wed Aug 09, 2006 8:50 am

Havard wrote:A statement like this is bound to attract some solvers!:) Can you post these "unsolved" puzzles for the likes of me to have a go at?:D
Havard
Sorry, these are "unsolved" patterns.

ab wrote:here's 7 patterns that match those criterion. Curiously they don't include the pattern for which we have a valid puzzle!
udosuk wrote: Why are these patterns excluded?

ab, udosuk, you are right.

Curiously, I was fascinated by ab's puzzle and had only considered pattern having a clue in r2c2.

Actually, there are 23 fully symmetrical patterns matching the conditions.

Code: Select all
 . . . | . . . | . . .
 . a b | c d . | . . .
 . . e | f g . | . . .
-------+-------+-------
 . . . | h i . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .
-------+-------+-------
 . . . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .


8(b+c+f)+4(a+d+e+g+h+i)=20
a+b+c+d=1
a+b+e>0
with a,b,c,d,e,f,g,h,i = 0 or 1.

Here is the list with the nomenclature used in this thread :
Code: Select all
0-1-5-3-0   
0-1-6-1-0   
0-1-6-2-0   
0-1-7-0-0   
0-2-4-3-0   udosuk
0-2-5-1-0   ab
0-2-5-2-0   ab
0-2-6-0-0   udosuk
0-4-1-3-0   ab
0-4-2-1-0   ab
0-4-2-2-0   ab
0-4-3-0-0   
0-4-4-3-0   
0-4-5-1-0   
0-4-5-2-0   
0-4-6-0-0   
0-8-2-3-0   JPF
0-8-3-1-0   JPF
0-8-3-2-0   JPF
0-8-5-3-0   JPF/ab
0-8-6-1-0   JPF
0-8-6-2-0   JPF/ab
0-8-7-0-0   JPF

The last 7 are those previously mentionned.

In addition of 0-8-6-1-0 (#12 by ab), two have been already "solved" :

0-4-2-1-0 (#06) by ab
0-2-5-1-0 (#34) by ab/Ocean

I will post these patterns as soon as I have some time.

JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

Postby JPF » Wed Aug 09, 2006 6:07 pm

Here are the full sym. patterns filling the conditions and the 3 puzzles already found (see here ).

There are actually only 22 non equivalent fully sym. patterns : 0-2-4-3-0 and 0-8-2-3-0 are equivalent.

Code: Select all
0-1-5-3-0
 . . . . . . . . .
 . . . . x . . . .
 . . x . x . x . .
 . . . x x x . . .
 . x x x . x x x .
 . . . x x x . . .
 . . x . x . x . .
 . . . . x . . . .
 . . . . . . . . .

0-1-6-1-0
 . . . . . . . . .
 . . . . x . . . .
 . . x x . x x . .
 . . x . x . x . .
 . x . x . x . x .
 . . x . x . x . .
 . . x x . x x . .
 . . . . x . . . .
 . . . . . . . . .

0-1-6-2-0
 . . . . . . . . .
 . . . . x . . . .
 . . x x . x x . .
 . . x x . x x . .
 . x . . . . . x .
 . . x x . x x . .
 . . x x . x x . .
 . . . . x . . . .
 . . . . . . . . .

0-1-7-0-0
 . . . . . . . . .
 . . . . x . . . .
 . . x x x x x . .
 . . x . . . x . .
 . x x . . . x x .
 . . x . . . x . .
 . . x x x x x . .
 . . . . x . . . .
 . . . . . . . . .
 
0-2-4-3-0 ~ 0-8-2-3-0
 . . . . . . . . .
 . . . x . x . . .
 . . x . . . x . .
 . x . x x x . x .
 . . . x . x . . .
 . x . x x x . x .
 . . x . . . x . .
 . . . x . x . . .
 . . . . . . . . .

0-2-5-1-0 (#34 by ab/Ocean)
 . . . . . . . . .
 . . . 6 . 5 . . .
 . . 1 . 3 . 2 . .
 . 5 . . 8 . . 9 .
 . . 8 3 . 2 7 . .
 . 9 . . 7 . . 4 .
 . . 2 . 1 . 8 . .
 . . . 4 . 9 . . .
 . . . . . . . . .

0-2-5-2-0
 . . . . . . . . .
 . . . x . x . . .
 . . x . x . x . .
 . x . x . x . x .
 . . x . . . x . .
 . x . x . x . x .
 . . x . x . x . .
 . . . x . x . . .
 . . . . . . . . .

0-2-6-0-0
 . . . . . . . . .
 . . . x . x . . .
 . . x x . x x . .
 . x x . . . x x .
 . . . . . . . . .
 . x x . . . x x .
 . . x x . x x . .
 . . . x . x . . .
 . . . . . . . . .

0-4-1-3-0
 . . . . . . . . .
 . . x . . . x . .
 . x . . x . . x .
 . . . x x x . . .
 . . x x . x x . .
 . . . x x x . . .
 . x . . x . . x .
 . . x . . . x . .
 . . . . . . . . .

0-4-2-1-0  (#06 by ab)
 . . . . . . . . .
 . . 7 . . . 9 . .
 . 2 . 5 . 8 . 1 .
 . . 5 . 6 . 4 . .
 . . . 3 . 2 . . .
 . . 6 . 9 . 3 . .
 . 8 . 2 . 1 . 3 .
 . . 9 . . . 7 . .
 . . . . . . . . .

0-4-2-2-0
 . . . . . . . . .
 . . x . . . x . .
 . x . x . x . x .
 . . x x . x x . .
 . . . . . . . . .
 . . x x . x x . .
 . x . x . x . x .
 . . x . . . x . .
 . . . . . . . . .

0-4-3-0-0
 . . . . . . . . .
 . . x . . . x . .
 . x . x x x . x .
 . . x . . . x . .
 . . x . . . x . .
 . . x . . . x . .
 . x . x x x . x .
 . . x . . . x . .
 . . . . . . . . .

0-4-4-3-0
 . . . . . . . . .
 . . x . . . x . .
 . x x . . . x x .
 . . . x x x . . .
 . . . x . x . . .
 . . . x x x . . .
 . x x . . . x x .
 . . x . . . x . .
 . . . . . . . . .

0-4-5-1-0
 . . . . . . . . .
 . . x . . . x . .
 . x x . x . x x .
 . . . . x . . . .
 . . x x . x x . .
 . . . . x . . . .
 . x x . x . x x .
 . . x . . . x . .
 . . . . . . . . .

0-4-5-2-0
 . . . . . . . . .
 . . x . . . x . .
 . x x . x . x x .
 . . . x . x . . .
 . . x . . . x . .
 . . . x . x . . .
 . x x . x . x x .
 . . x . . . x . .
 . . . . . . . . .

0-4-6-0-0
 . . . . . . . . .
 . . x . . . x . .
 . x x x . x x x .
 . . x . . . x . .
 . . . . . . . . .
 . . x . . . x . .
 . x x x . x x x .
 . . x . . . x . .
 . . . . . . . . .

0-8-2-3-0  ~  0-2-4-3-0

 . . . . . . . . .
 . x . . . . . x .
 . . . x . x . . .
 . . x x x x x . .
 . . . x . x . . .
 . . x x x x x . .
 . . . x . x . . .
 . x . . . . . x .
 . . . . . . . . .

0-8-3-1-0
 . . . . . . . . .
 . x . . . . . x .
 . . . x x x . . .
 . . x . x . x . .
 . . x x . x x . .
 . . x . x . x . .
 . . . x x x . . .
 . x . . . . . x .
 . . . . . . . . .

0-8-3-2-0
 . . . . . . . . .
 . x . . . . . x .
 . . . x x x . . .
 . . x x . x x . .
 . . x . . . x . .
 . . x x . x x . .
 . . . x x x . . .
 . x . . . . . x .
 . . . . . . . . .

0-8-5-3-0
 . . . . . . . . .
 . x . . . . . x .
 . . x . x . x . .
 . . . x x x . . .
 . . x x . x x . .
 . . . x x x . . .
 . . x . x . x . .
 . x . . . . . x .
 . . . . . . . . .

0-8-6-1-0  (#12 by ab)
. . . . . . . . .
 . 4 . . . . . 1 .
 . . 8 2 . 6 9 . .
 . . 6 . 1 . 7 . .
 . . . 4 . 5 . . .
 . . 7 . 3 . 2 . .
 . . 2 7 . 9 6 . .
 . 3 . . . . . 5 .
 . . . . . . . . .

0-8-6-2-0
 . . . . . . . . .
 . x . . . . . x .
 . . x x . x x . .
 . . x x . x x . .
 . . . . . . . . .
 . . x x . x x . .
 . . x x . x x . .
 . x . . . . . x .
 . . . . . . . . .

0-8-7-0-0
 . . . . . . . . .
 . x . . . . . x .
 . . x x x x x . .
 . . x . . . x . .
 . . x . . . x . .
 . . x . . . x . .
 . . x x x x x . .
 . x . . . . . x .
 . . . . . . . . .



It is probable that many of these patterns don't have a valid puzzle.

JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

Postby Eioru » Fri Aug 18, 2006 8:40 am

How about this pattern?

000000000
0000XX000
00XXXXX00
0XXXXXX00
0XXXXXXX0
00XXXXXX0
00XXXXX00
000XX0000
000000000
Eioru
 
Posts: 182
Joined: 16 August 2006

Postby JPF » Fri Aug 18, 2006 12:35 pm

Eioru wrote:How about this pattern?

000000000
0000XX000
00XXXXX00
0XXXXXX00
0XXXXXXX0
00XXXXXX0
00XXXXX00
000XX0000
000000000

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 x x x .
 . . x x x x x . .
 . . . x x . . . .
 . . . . . . . . .


It's a nice pattern too, but without full symmetry and with more than 20 clues.

Here is a 27 clues puzzle with 180° symmetry :
Code: Select all
 . . . . . . . . .
 . . . . 7 4 . . .
 . . 6 2 9 3 7 . .
 . 1 8 . . 2 9 . .
 . 7 3 . 5 . 2 1 .
 . . 9 1 . . 6 8 .
 . . 7 8 2 9 3 . .
 . . . 4 1 . . . .
 . . . . . . . . .

It should be possible to make a puzzle* with some symmetry, less clues and filling "the conditions" mentionned above (except maybe the 20 clues condition).

JPF

PS : It woud be nice if you could post your puzzles in using a standard form.
See this post

* [edit 1] : this one for example :
Code: Select all
 . . . . . . . . .
 . . . . 2 4 . . .
 . . 5 7 3 6 4 . .
 . 5 7 . . . 3 . .
 . 4 3 . 1 . 6 9 .
 . . 6 . . . 1 2 .
 . . 4 6 8 5 7 . .
 . . . 9 7 . . . .
 . . . . . . . . .

[edit 2] or better :
Code: Select all
. . . . . . . . .
 . . . . 2 9 . . .
 . . 4 3 8 7 1 . .
 . 8 6 . . . 7 . .
 . 9 1 . . . 4 2 .
 . . 3 . . . 5 8 .
 . . 7 4 1 5 3 . .
 . . . 2 6 . . . .
 . . . . . . . . .

JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

Previous

Return to General