## Maximum consecutive empty cells.

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

### Maximum consecutive empty cells.

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?

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: 216
Joined: 03 April 2006

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
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Location: Paris, France

### Re: Be more precise?

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
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Posts: 4022
Joined: 06 December 2005
Location: Paris, France