very large empty edge

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very large empty edge

Postby claudiarabia » Mon Aug 07, 2006 1:28 am

I like the sudokus of ab and tso which have one empty frontier row/column at each side. I tried to enlarge this empty space to two empty columns and/or rows. The only thing that came out was this:
Code: Select all
. . . . . . . . .
. . . . . 8 . . .
. 6 5 . . 9 3 7 .
. 2 . 8 . 7 . 9 .
. . 8 . 3 . . 4 .
. . 4 . . 1 6 5 .
. 1 7 9 . 6 2 8
. . . 7 . . . . .
. . . . . . . . . 

:(Claudia
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Postby Ruud » Mon Aug 07, 2006 2:02 am

Claudia,

That's the best result you will get. 2 empty rows or columns in a chute would be fully exchangable and result in multiple solutions.

Ruud
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Postby udosuk » Mon Aug 07, 2006 6:25 am

How about this shape?
Code: Select all
 . . . . . . . . .
 . . . . # . . . .
 . . # # # # # . .
 . . # # # # # . .
 . # # # # # # # .
 . . # # # # # . .
 . . # # # # # . .
 . . . . # . . . .
 . . . . . . . . .

Or this (I believe 4 empty boxes are the maximum you could have)...:?:
Code: Select all
 . . . . . . . . .
 . . . . # . . . .
 . . . # # # . . .
 . . # # # # # . .
 . # # # # # # # .
 . . # # # # # . .
 . . . # # # . . .
 . . . . # . . . .
 . . . . . . . . .
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Postby JPF » Mon Aug 07, 2006 6:51 am

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




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



JPF
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what a nice star!

Postby claudiarabia » Mon Aug 07, 2006 1:47 pm

JPF wrote:
Code: Select all
 . . . . . . . . .
 . . 1 . . . 4 . .
 . . 9 7 8 6 2 . .
 . . 8 . 9 . 6 . .
 . 4 7 . 2 . 5 8 .
 . . 2 . 3 . 7 . .
 . . 5 4 7 2 9 . .
 . . 3 . . . 1 . .
 . . . . . . . . .
JPF
I like your star!

What fits this category surely with the lowest amount of numbers in the second rows/columns in e very elegant way I found in this 20-clue-puzzle (of tso?)
Code: Select all
. . . . . . . . .
. 1 . . . . . 2 .
. . 3 4 . 5 6 . .
. . 4 . 5 . 3 . .
. . . 2 . 7 . . .
. . 6 . 8 . 4 . .
. . 5 6 . 3 1 . .
. 7 . . . . . 9 .
. . . . . . . . .

Claudia
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Postby JPF » Mon Aug 07, 2006 3:11 pm

In that case, I propose this 20-clues , not easy.

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


JPF:)
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Postby kjellfp » Mon Aug 07, 2006 3:20 pm

udosuk wrote:Or this (I believe 4 empty boxes are the maximum you could have)...:?:
Code: Select all
 . . . . . . . . .
 . . . . # . . . .
 . . . # # # . . .
 . . # # # # # . .
 . # # # # # # # .
 . . # # # # # . .
 . . . # # # . . .
 . . . . # . . . .
 . . . . . . . . .

Impossible. The only possible shape with four empty boxes is

X0X
0X0
X0X

The shape

0X0
XXX
0X0

extends to

0X0
X0X
0X0

which is 5 empty boxes. No sudoku with 5 empty boxes exists, read this thread.
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Postby udosuk » Mon Aug 07, 2006 3:47 pm

Thanks kjellfp for clarifying the matter...:)

So I guess we're left with this:
Code: Select all
 . . . . . . . . .
 . . . . # . . . .
 . . # # # # # . .
 . . # # # # # . .
 . # # # # # # # .
 . . # # # # # . .
 . . # # # # # . .
 . . . . # . . . .
 . . . . . . . . .
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Postby JPF » Mon Aug 07, 2006 4:00 pm

udosuk wrote:So I guess we're left with this:
Code: Select all
 . . . . . . . . .
 . . . . # . . . .
 . . # # # # # . .
 . . # # # # # . .
 . # # # # # # # .
 . . # # # # # . .
 . . # # # # # . .
 . . . . # . . . .
 . . . . . . . . .

I haven't found any with less than 300 solutions, so far:(

JPF
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Postby RW » Mon Aug 07, 2006 4:15 pm

JPF wrote:In that case, I propose this 20-clues , not easy.
Code: Select all
 . . . . . . . . .
 . 3 . . 6 . . 1 .
 . . 2 7 . 5 4 . .
 . . 7 . . . 1 . .
 . 9 . . . . . 8 .
 . . 5 . . . 2 . .
 . . 6 2 . 7 5 . .
 . 1 . . 8 . . 9 .
 . . . . . . . . .


Not easy, but not too hard either:

Code: Select all
 *--------------------------------------------------------------------------------------*
 | 145678   57       1489     | 13489    1234     123489   | 6789     2567     25678    |
 | 4578     3        489      | 489      6        2489     | 789      1        2578     |
 | 19       68       2        | 7        19       5        | 4        36       368      |
 |----------------------------+----------------------------+----------------------------|
 | 3468     2        7        | 345689   345      34689    | 1        3456     34569    |
 | 1346     9        134      | 13456    123457   12346    | 367      8        34567    |
 | 13468    468      5        | 134689   1347     134689   | 2        3467     34679    |
 |----------------------------+----------------------------+----------------------------|
 | 3489     48       6        | 2        1349     7        | 5        34       1348     |
 | 257      1        34       | 3456     8        346      | 367      9        23467    |
 | 257      57       3489     | 134569   1345     13469    | 3678     23467    1234678  |
 *--------------------------------------------------------------------------------------*

If r9c1=2 => r1c8=2 => r5c5=2 => r6c5=7 => r9c8=7 => r9c2=5 => r4c5=5 => r5c9=5 => no 5 in box 3 r9c1<>2

r8c1=2 => r8c4=5

If r2c9=5 => r4c8=5 => r5c5=5 => r5c6=2 => r1c5=2 => no 2 in box 3 => r2c9<>5

RW
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very large empty edge

Postby tso » Mon Aug 07, 2006 7:17 pm

claudiarabia wrote:
What fits this category surely with the lowest amount of numbers in the second rows/columns in e very elegant way I found in this 20-clue-puzzle (of tso?)
Code: Select all
. . . . . . . . .
. 1 . . . . . 2 .
. . 3 4 . 5 6 . .
. . 4 . 5 . 3 . .
. . . 2 . 7 . . .
. . 6 . 8 . 4 . .
. . 5 6 . 3 1 . .
. 7 . . . . . 9 .
. . . . . . . . .

Claudia


Unlikely that I generated this puzzle. I've made few with only 20 cells. The first 6 clues are 123456 -- that's practically DNA proof that someone else created it. It'll be hard to beat, with 56 orthogonally connected empty cells on the perimeter and only 4 in the second ring -- and maximum symmetry.
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Re: very large empty edge

Postby claudiarabia » Mon Aug 07, 2006 7:23 pm

tso wrote:
claudiarabia wrote:What fits this category surely with the lowest amount of numbers in the second rows/columns in e very elegant way I found in this 20-clue-puzzle (of tso?)
Code: Select all
. . . . . . . . .
. 1 . . . . . 2 .
. . 3 4 . 5 6 . .
. . 4 . 5 . 3 . .
. . . 2 . 7 . . .
. . 6 . 8 . 4 . .
. . 5 6 . 3 1 . .
. 7 . . . . . 9 .
. . . . . . . . .
Claudia
Unlikely that I generated this puzzle. .

I searched and found this thread:
[url=http://forum.enjoysudoku.com/viewtopic.php?t=4414&start=0[url]]http://forum.enjoysudoku.com/viewtopic.php?t=4414&start=0[url][/url]

It was Ocean, sorry.

Claudia
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Postby JPF » Tue Aug 08, 2006 4:28 pm

In the same thread :

Ocean wrote:
ab wrote:that's great Ocean. How about swordfish and jellyfish now:)

Here is a pattern you might recognize:
Code: Select all
# Swordfish
# Puzzle modified from 'ab':
 . . . | . . . | . . .
 . 4 . | . . . | . 1 .
 . . 9 | 2 . 6 | 3 . .
-------+-------+-------
 . . 6 | . 1 . | 7 . .
 . . . | 4 . 5 | . . .
 . . 7 | . 3 . | 2 . .
-------+-------+-------
 . . 2 | 7 . 9 | 6 . .
 . 3 . | . . . | . 5 .
 . . . | . . . | . . .



This pattern was posted by ab (#12) in the "Fully symmetrical puzzles" thread.

There are only 7 non equivalent full symmetrical patterns filling the following conditions :
-20 clues
-r1=r9=c1=c9=0
-2 clues in r2,r8,c2,c8.

To my knowledge, only one has been solved for the moment.

JPF
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Postby Havard » Tue Aug 08, 2006 11:15 pm

JPF wrote:
To my knowledge, only one has been solved for the moment.

JPF


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
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Postby ab » Wed Aug 09, 2006 12:22 am

here's 7 patterns that match those criterion. Curiously they don't include the pattern for which we have a valid puzzle!
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 . .
 . . . | . . . | . . .

 . . . | . . . | . . .
 . 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 . .
 . . . | . . . | . . .

 . . . | . . . | . . .
 . . 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 | . . .
 . . . | . . . | . . .

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