The New Sudoku Players' Forum

[tso]

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

[keith]

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

[JPF]

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]

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