The New Sudoku Players' Forum

[JPF]

(Is 5x5 the largest possible empty rectangle as well?)

Here's a puzzle with a 7x4 rectangle...

Here's a puzzle with a 6x5 rectangle :

Code: Select all

 3 . . | 8 . . | 5 . .
 . 5 6 | 2 7 9 | 8 3 4
 . 8 . | . . . | . . 9
-------+-------+-------
 7 1 . | . . . | . . 3
 5 9 . | . . . | . . 8
 . 3 . | . . . | . . 1
-------+-------+-------
 2 4 . | . . . | . . 6
 . 6 1 | 3 5 4 | 9 7 2
 . . . | . . 6 | . . .

 

with one of its minimal :

Code: Select all

 3 . . | 8 . . | 5 . .
 . . 6 | 2 . 9 | 8 . 4
 . 8 . | . . . | . . 9
-------+-------+-------
 7 . . | . . . | . . 3
 5 9 . | . . . | . . 8
 . . . | . . . | . . 1
-------+-------+-------
 2 4 . | . . . | . . .
 . . 1 | . 5 4 | 9 7 .
 . . . | . . 6 | . . .


JPF

[Ruud]

This is the largest empty rectangle possible: 7x7

Code: Select all

8 . 9|2 4 3|6 . 7
. . .|. . .|. . .
3 . .|. . .|. . 4
-----+-----+-----
1 . .|. . .|. . 6
4 . .|. . .|. . 1
6 . .|. . .|. . 5
-----+-----+-----
5 . .|. . .|. . 8
. . .|. . .|. . .
9 . 8|7 1 4|5 . 3

It has a unique solution, but the diagonals must also contain digits 1-9. Sudoku-X boldly goes where no classic sudoku has gone before.

Here is a version with less clues, symmetry type I and it solves with singles only:

Code: Select all

. . 5|2 6 9|4 . .
. . .|. . .|. . .
8 . .|. . .|. . 5
-----+-----+-----
1 . .|. . .|. . 3
4 . .|. . .|. . 7
3 . .|. . .|. . 1
-----+-----+-----
6 . .|. . .|. . 2
. . .|. . .|. . .
. . 4|9 2 1|3 . .

Ruud.

[m_b_metcalf]

It has a unique solution, but the diagonals must also contain digits 1-9. Sudoku-X boldly goes where no classic sudoku has gone before.

Indeed. Here's one from my collection with a 5 x 7 hollow.

Code: Select all

  .  .  .  8  9  7  .  .  .  X-sudoku
  4  6  .  .  .  .  .  8  9
  .  .  .  .  .  .  .  .  .
  9  7  .  .  .  .  .  5  8
  8  .  .  .  .  .  .  .  7
  3  5  .  .  .  .  .  2  4
  .  .  .  .  .  .  .  .  .
  1  9  .  .  .  .  .  7  6
  .  .  .  7  5  6  .  .  .



Another interesting type is where a partial template is formed of predetermined values, like the digits 1-9 that snake (almost) in order around the perimter of this:

Code: Select all


  1  2  3  4  5  6  7  8  9
  6  .  7  .  .  .  .  .  1
  5  .  .  9  .  .  .  .  2
  4  .  .  .  7  9  .  .  3
  3  .  .  .  .  .  .  .  4
  2  .  .  .  .  .  .  .  5
  9  .  .  .  .  .  .  .  6
  8  3  .  .  .  5  .  .  7
  7  6  5  3  4  2  1  9  8


Regards,

Mike Metcalf

[tso]

Here's a puzzle with a 6x5 rectangle :

Excellent!

This is the largest empty rectangle possible: 7x7

Nice!

This is yet another reason that Sudoku X really should have been the standard puzzle to begin with. Other reasons: Magic Squares, which have common ancestors, always include the two main diagonals -- and every school kid knows that. Diagonals are easy to see, unlike other types of disjoint groups. The two additional groups allow for three cell forcing chains and other modified tactics, making solving potentially more interesting without making more complicated or opaque.

[JPF]

Here's a puzzle with a 8 x 4 empty rectangle :

Code: Select all

 . 3 . | . . 8 | . . .
 . . 4 | . . 2 | . . .
 . . 7 | . . 3 | . 4 .
-------+-------+-------
 2 9 5 | 1 6 4 | 8 7 3
 . . . | . . . | . . 1
 . . . | . . . | . . 9
-------+-------+-------
 . . . | . . . | . . 8
 . . . | . . . | . . 7
 6 1 8 | 7 3 5 | 9 2 4



and one minimal :

Code: Select all

 . 3 . | . . 8 | . . .
 . . 4 | . . 2 | . . .
 . . 7 | . . 3 | . 4 .
-------+-------+-------
 2 9 . | 1 6 . | . 7 3
 . . . | . . . | . . 1
 . . . | . . . | . . 9
-------+-------+-------
 . . . | . . . | . . 8
 . . . | . . . | . . 7
 . 1 8 | 7 . 5 | 9 2 .


any improvement on the Sudoku-X side ?

JPF

[ab]

here's a puzzle with a 39 square rectangle:

Code: Select all

 . 4 . | . 8 . | 9 . .
 8 . . | 6 . . | . 7 .
 . . 7 | . . . | . . 3
 ------+-------+------
 . 1 . | . . . | . . .
 6 . . | . . . | . . 5
 . . . | . . . | . 8 .
 ------+-------+------
 3 . . | . . . | 1 . .
 . 2 . | . . 3 | . . 4
 1 . 8 | . 2 . | . 5 .



[fermat]

This is yet another reason that Sudoku X really should have been the standard puzzle to begin with.

Hello? This whole thing started with humans making grids. There would be. perhaps, one a month instead of several a day.

People are just human, you know?

[tso]

Could you give an example on how to use this program. (command lines, etc...)

Not appropriate to talk about here. I'll PM you. But all you need to know is in the manual in zip file.

[JPF]

Not appropriate to talk about here.

Sorry.

I'll PM you.

Thanks.

JPF

[Pyrrhon]

Wasn't there a 9x5 rectangle sudoku x in a japanese puzzle journal?

Pyrrhon

[JPF]

In this thread, tso and Nick70 posted these puzzles :

tso

Code: Select all

 . . . | . 5 4 | 6 8 3
 . . . | . . 9 | . . 1
 . . . | . . . | 2 . 9
-------+-------+------
 . . . | . . . | . 7 8
 8 . . | . . . | . . 5
 6 9 . | . . . | . . .
-------+-------+------
 5 . 6 | . . . | . . .
 2 . . | 8 . . | . . .
 3 4 7 | 5 6 . | . . .



Nick70

Code: Select all

 . . . | . 8 7 | 3 2 .
 . . . | . . 9 | . . 4
 . . . | . . . | 6 . 5
-------+-------+-------
 . . . | . . . | . 7 9
 1 . . | . . . | . . 8
 5 6 . | . . . | . . .
-------+-------+-------
 3 . 1 | . . . | . . .
 6 . . | 5 . . | . . .
 . 8 7 | 1 6 . | . . .



With the same idea, here is a puzzle with only 18 clues :

Code: Select all

 . . . | . 4 9 | . . .
 . . . | . . 8 | 1 . .
 . . . | . . . | 7 3 .
-------+-------+-------
 . . . | . . . | . 8 5
 7 . . | . . . | . . 4
 1 3 . | . . . | . . .
-------+-------+-------
 . 5 8 | . . . | . . .
 . . 4 | 7 . . | . . .
 . . . | 1 6 . | . . .



JPF

[claudiarabia]

Nick 70

Code: Select all

 . . . | . 8 7 | 3 2 .
 . . . | . . 9 | . . 4
 . . . | . . . | 6 . 5
-------+-------+-------
 . . . | . . . | . 7 9
 1 . . | . . . | . . 8
 5 6 . | . . . | . . .
-------+-------+-------
 3 . 1 | . . . | . . .
 6 . . | 5 . . | . . .
 . 8 7 | 1 6 . | . . .



JPF

You posted 3 nice puzzles. But this puzzle has more than one solution.

Claudia

[JPF]

Here is one solution :

Code: Select all

 4 9 5 | 6 8 7 | 3 2 1
 2 1 6 | 3 5 9 | 7 8 4
 7 3 8 | 4 2 1 | 6 9 5
-------+-------+-------
 8 4 3 | 2 1 6 | 5 7 9
 1 7 2 | 9 3 5 | 4 6 8
 5 6 9 | 7 4 8 | 1 3 2
-------+-------+-------
 3 5 1 | 8 7 2 | 9 4 6
 6 2 4 | 5 9 3 | 8 1 7
 9 8 7 | 1 6 4 | 2 5 3



what is the other one ?

JPF

[claudiarabia]

Here is one solution :what is the other one ?

JPF

Code: Select all

 . . 5 | 6 8 7 | 3 2 1
 2 1 6 | 3 5 9 | 7 8 4
 7 3 8 | . . 1 | 6 9 5
-------+-------+-------
 8 . 3 | . 1 6 | 5 7 9
 1 7 . | 9 3 5 | . 6 8
 5 6 9 | . . . | . . .
-------+-------+-------
 3 5 1 | . . . | . 4 6
 6 . . | 5 . . | . . 7
 . 8 7 | 1 6 . | . 5 .


Sorry, there is no other solution than yours. I wasn't able to solve it by logic. So I typed it into my program and it told me that there were several solutions. So I doubted at first. When I force it to guess then a (your) solution came but I can't force it to give me all the other solutions or even just the information of how many they are. I checked other machines then. The half-solved puzzle above is, what can be solved without guessing by other programs. And after more searching I got the statement that there is one solution only.

And thus I know finally the limits of my program. This really is a tricky one. Is there really a phase in which some Sudokus can't be solved by logic only?

Claudia

[JPF]

I checked other machines then. The half-solved puzzle above is, what can be solved without guessing by other programs.

Simple Sudoku , Sudo Cue solve this puzzle without a great deal of difficulty.
I’m sure almost all the solvers in the Net solve it easily as well.

Is there really a phase in which some Sudokus can't be solved by logic only?

I don’t want to enter into the endless philosophical debate “what is logic or not”.
You will find in this forum many threads and posts discussing this topic at length.

But this puzzle has more than one solution.

One can’t say that a puzzle has more than one solution only because it can't be solved by using a given set of techniques.
To my knowledge, the only cases we can prove that a puzzle has (at least) 2 solutions :

- there are only 7 different digits or less (e.g. no 8 and 9, for example)
- there is a deadly pattern
- or we can find and show 2 different solutions...

And thus I know finally the limits of my program. This really is a tricky one

I'm sure you are going to improve it.
We all started like that.

JPF