Maximum consecutive empty cells.

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

Maximum consecutive empty cells.

Postby tso » Sat Jun 03, 2006 9:37 pm

This trivial Sudoku, when represented as a string of 81 digits, has 34 consecutive empty cells, the maximum possible.

Code: Select all
+---+---+---+
|813|925|467|
|245|768|931|
|967|341|285|
+---+---+---+
|176|859|342|
|4..|...|...|
|...|...|...|
+---+---+---+
|...|...|...|
|...|...|..3|
|389|274|516|
+---+---+---+

8139254672457689319673412851768593424..................................3389274516


What is the maximum number of emtpy cells possible in exactly two strings?

Here's one with 50:

Code: Select all
+---+---+---+
|492|6..|...|
|...|...|...|
|...|...|..8|
+---+---+---+
|315|978|246|
|946|5..|...|
|...|...|...|
+---+---+---+
|...|...|...|
|...|..5|124|
|751|426|893|
+---+---+---+


4926......................83159782469465............................5124751426893
tso
 
Posts: 798
Joined: 22 June 2005

Be more precise?

Postby keith » Sat Jun 03, 2006 10:21 pm

Tso,

I presume you mean: "Empty substrings".

If the puzzle is a string, your first example has one empty substring and two populated substrings. The second has two empty, and three populated substrings.

What about the sequence

.......................nnnnnnnnnnnnnnnn........................

which also has two empty substrings?

If you reply with a clarification, or edit your original post, I will be happy to delete this message.

Keith
Last edited by keith on Sat Jun 03, 2006 9:41 pm, edited 1 time in total.
keith
2017 Supporter
 
Posts: 209
Joined: 03 April 2006

Postby JPF » Sat Jun 03, 2006 10:29 pm

Here's 51 :

Code: Select all

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



and one 52 :

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


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

Re: Be more precise?

Postby JPF » Sat Jun 03, 2006 11:22 pm

keith wrote:What about the sequence

.......................nnnnnnnnnnnnnnnn........................

which also has two empty substrings?



I'm sure tso will agree, but in that case the maximum is 34 empty cells.
example :

Code: Select all

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


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


Return to General