## very large empty edge

Everything about Sudoku that doesn't fit in one of the other sections
Why are these patterns excluded?

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`. . . . . . . . .. . . 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

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?
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.

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` . . . | . . . | . . . . 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 :
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`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   udosuk0-2-5-1-0   ab0-2-5-2-0   ab0-2-6-0-0   udosuk0-4-1-3-0   ab0-4-2-1-0   ab0-4-2-2-0   ab0-4-3-0-0   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   JPF0-8-3-1-0   JPF0-8-3-2-0   JPF0-8-5-3-0   JPF/ab0-8-6-1-0   JPF0-8-6-2-0   JPF/ab0-8-7-0-0   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: 3754
Joined: 06 December 2005
Location: Paris, France

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.

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`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: 3754
Joined: 06 December 2005
Location: Paris, France

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Eioru

Posts: 182
Joined: 16 August 2006

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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 :
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` . . . . . . . . . . . . . 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 :
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` . . . . . . . . . . . . . 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 :
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`. . . . . . . . . . . . . 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: 3754
Joined: 06 December 2005
Location: Paris, France

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