Square Patterns

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

Square Patterns

Postby udosuk » Fri Jun 06, 2008 2:29 pm

I suspect this must have been discussed before, and I trust the resourceful historians here will quickly point me to the correct thread (if there's one).

Is it possible for the following 24/20 clues patterns, and can they get very easy/hard?
Code: Select all
.........
.#######.
.#.....#.
.#.....#.
.#.....#.
.#.....#.
.#.....#.
.#######.
.........

.........
..#####..
.#.....#.
.#.....#.
.#.....#.
.#.....#.
.#.....#.
..#####..
.........

Thanks in advance.:)
udosuk
 
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Postby m_b_metcalf » Fri Jun 06, 2008 7:49 pm

The best I could do in five minutes was:
Code: Select all
 . . . . . . . . .
 . 9 1 2 4 3 5 6 .
 . 7 . . . . . 8 .
 . 2 . . . 6 . 9 .
 . 4 . . 2 . . 7 .
 . 8 . . 7 . . 1 .
 . 6 . . . . . 3 .
 . 3 7 5 1 9 6 2 .
 . . . . . . . . .


[edit after another five minutes]
Code: Select all
 . . . . . . . . .
 . . 1 2 4 8 5 . .
 . 7 . . . . . 4 .
 . 2 . . . 6 . 9 .
 . 4 . . 2 . . 7 .
 . 8 . . 7 . . 1 .
 . 6 . . . . . 3 .
 . . 7 5 1 9 6 . .
 . . . . . . . . .

These 'straight-line' patterns are typically very unyielding.

Regards,

Mike Metcalf
Last edited by m_b_metcalf on Fri Jun 06, 2008 6:37 pm, edited 1 time in total.
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Postby JPF » Fri Jun 06, 2008 10:02 pm

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


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

JPF
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Postby JPF » Fri Jun 06, 2008 10:54 pm

m_b_metcalf wrote:The best I could do in five minutes was:
Code: Select all
 . . . . . . . . .
 . 9 1 2 4 3 5 6 .
 . 7 . . . . . 8 .
 . 2 . . . 6 . 9 .
 . 4 . . 2 . . 7 .
 . 8 . . 7 . . 1 .
 . 6 . . . . . 3 .
 . 3 7 5 1 9 6 2 .
 . . . . . . . . .

[edit after another five minutes]
Code: Select all
 . . . . . . . . .
 . . 1 2 4 8 5 . .
 . 7 . . . . . 4 .
 . 2 . . . 6 . 9 .
 . 4 . . 2 . . 7 .
 . 8 . . 7 . . 1 .
 . 6 . . . . . 3 .
 . . 7 5 1 9 6 . .
 . . . . . . . . .


could be a new game:) :

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

JPF
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Postby udosuk » Sat Jun 07, 2008 5:53 am

After my first post I realised that with some row/column swapping I can convert those patterns to:
Code: Select all
#.#####.#
.........
#.......#
#.......#
#.......#
#.......#
#.......#
.........
#.#####.#

##.###.##
#.......#
.........
#.......#
#.......#
#.......#
.........
#.......#
##.###.##

..#####..
.........
#.......#
#.......#
#.......#
#.......#
#.......#
.........
..#####..

.#.###.#.
#.......#
.........
#.......#
#.......#
#.......#
.........
#.......#
.#.###.#.

Where it's been proven no puzzle exists. It's probably also impossible even if you add a clue @ r5c5 but I don't remember it's been proven explicitly.

So the best effort so far is 3 additional clues. Don't know if it's possible to get one with 1 or 2 additional clues? Carry on fighters!:)


Added later:

I wonder if these clover patterns are possible instead:
Code: Select all
.........
..##.##..
.#..#..#.
.#.....#.
..#...#..
.#.....#.
.#..#..#.
..##.##..
.........

.........
..##.##..
.#..#..#.
.#..#..#.
..##.##..
.#..#..#.
.#..#..#.
..##.##..
.........

:?:

Here are some related threads:

http://forum.enjoysudoku.com/viewtopic.php?t=4209

http://forum.enjoysudoku.com/viewtopic.php?t=4147

:idea:
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Postby JPF » Sat Jun 07, 2008 9:19 am

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


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

JPF
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Postby udosuk » Sat Jun 07, 2008 2:39 pm

Wow, thanks for the quick response!

You guys might continue the pattern searching if you like. For example, the original square patterns with 1 or 2 extra givens.

Good luck!:)
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Postby Pat » Tue Jun 10, 2008 1:48 pm

udosuk wrote:I wonder if these clover patterns are possible --

Code: Select all
.........
..##.##..
.#..#..#.
.#.....#.
..#...#..
.#.....#.
.#..#..#.
..##.##..
.........



Code: Select all
.........
..##.##..
.#..#..#.
.#..#..#.
..##.##..
.#..#..#.
.#..#..#.
..##.##..
.........





an example of the 24-clue pattern --

Code: Select all
...........97.54...3..1..8..2..9..1...51.68...4..8..6..6..3..2...79.86...........

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

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Postby udosuk » Wed Jun 11, 2008 3:28 am

Well thanks Para. I think that isn't a very hard pattern.

I'm still looking out for the square patterns (at the top of the thread) with 1 or 2 extra givens in the middle.
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Postby m_b_metcalf » Wed Jun 11, 2008 1:25 pm

udosuk wrote:I'm still looking out for the square patterns (at the top of the thread) with 1 or 2 extra givens in the middle.

Well, while you're waiting, here's a morsel to whet your appetite:
Code: Select all
 . . . . . . . . .
 . . 4 6 1 2 9 . .
 . 5 . . . . . 8 .
 . 2 . . . . . 7 .
 . 4 . . . . . 5 .
 . 8 . . . . . 9 .
 . 1 . . . . . 2 .
 . . 9 1 5 3 8 . .
 . . . . . . . . .   X-sudoku

Regards,

Mike Metcalf
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Postby coloin » Wed Jun 11, 2008 7:31 pm

udosuk wrote:I suspect this must have been discussed before

You might have deja vu here

Where Red Ed went on to confirm that this pattern
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
has more than 1 solution.

Red Ed wrote:I shouldn't bother: there are no puzzles with that template.

udosuk had the right idea: ignore the givens and just search for a way of filling in the blanks (the inner cross shape) such that there are no unavoidables. An exhaustive depth-first search, with some additional trimming by testing partial fills for isomorphism & unavoidables, finishes in less than 2 hours on my computer.

Of course this result means that there are no puzzles with the original template, sans central clue, either.


Other patterns without puzzles include
Trivially
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 |
+-------+-------+-------+

less trivially
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 |
+-------+-------+-------+

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


more ?
Code: Select all
+---+---+---+
|***|***|***|
|***|***|***|
|...|***|...|
+---+---+---+
|...|*.*|...|
|...|*.*|...|
|...|*.*|...|
+---+---+---+
|...|***|...|
|***|***|***|
|***|***|***|
+---+---+---+

and ?
Code: Select all
+---+---+---+         +---+---+---+
|*..|*.*|..*|         |*..|*.*|..*|
|...|*.*|...|         |...|*.*|...|
|...|*.*|...|         |...|*.*|...|
+---+---+---+         +---+---+---+
|***|***|***|         |***|***|***|
|...|***|...|         |*..|***|...|
|***|***|***|         |***|***|***|
+---+---+---+         +---+---+---+
|...|*.*|...|         |...|*.*|...|
|...|*.*|...|         |...|*.*|...|
|*..|*.*|..*|         |*..|*.*|..*|
+---+---+---+  or     +---+---+---+ !


If we could compile a list of these.

We might be able to approach the proof that clues[min] is 17 [ie not 16]

No combination of 16 clues with only clues from the above patterns can give a valid solution.

C
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