## Empty Boxes - I

Everything about Sudoku that doesn't fit in one of the other sections
Our minimum B159 with 95514sols
Code: Select all
`+---+---+---+|125|.7.|...||836|...|...||749|...|...|+---+---+---+|...|123|8..||..2|456|...||...|789|...|+---+---+---+|...|..8|134||...|...|287||...|...|596|+---+---+---+`
is solved with 4 additional clues

C
coloin

Posts: 1857
Joined: 05 May 2005

coloin wrote:Our minimum B159 with 95514sols
Code: Select all
`+---+---+---+|125|.7.|...||836|...|...||749|...|...|+---+---+---+|...|123|8..||..2|456|...||...|789|...|+---+---+---+|...|..8|134||...|...|287||...|...|596|+---+---+---+`
is solved with 4 additional clues

C

I change its number to
Code: Select all
`123.7....456......789.........1254....2836......749........4158......247......396`

and on the up&left box can delete number to 7 different kinds
{1,2,7} {2,3,7} {2,6} {2,9} {4} {5} {7,8}
Eioru

Posts: 182
Joined: 16 August 2006

This B1B5B9 has N solutions (N>=95514)
Code: Select all
` 9 5 2 | . . . | . . . 8 6 3 | . . . | . . . 7 4 1 | . . . | . . .-------+-------+------- . . . | 9 1 8 | . . . . . . | 5 4 2 | . . . . . . | 7 3 6 | . . .-------+-------+------- . . . | . . . | 8 2 7 . . . | . . . | 3 1 4 . . . | . . . | 9 5 6`

is solved with 3 additional clues :

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

JPF
JPF
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JPF wrote:This B1B5B9 has N solutions (N>=95514)

N=111559
gsf
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Thanks gsf.
JPF
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Joined: 06 December 2005
Location: Paris, France

### a wider slash

Eioru"][quote="coloin wrote:Our minimum B159 with 95514sols
Code: Select all
`+---+---+---+|125|.7.|...||836|...|...||749|...|...|+---+---+---+|...|123|8..||..2|456|...||...|789|...|+---+---+---+|...|..8|134||...|...|287||...|...|596|+---+---+---+`
is solved with 4 additional clues

If one can reach this with 4 additional clues, JPF's slash pattern is a much straighter example for this. There may be some slash-sudokus in which one can eliminate one clue to reach the JPF-posting previously:

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

Claudia
Last edited by claudiarabia on Fri Sep 15, 2006 7:19 pm, edited 1 time in total.
claudiarabia

Posts: 288
Joined: 14 May 2006

### to many empty rows and columns

Code: Select all
`*.*.*.*.*.........*.*.*.*.*.........*.*...*.*.........*.*.*.*.*.........*.*.*.*.*`

24-clue
there are 8 empty rows and 1 empty box

It is always a problem if you create sudokus with to many empty rows and columns. I don't know the minimum of rows resp. columns to be filled with at least one seed, but this here is definitely to empty.

The Non-adjacent-clue-thread is a good example for a minimal filled grid in this regard, I suppose.

[url=http://forum.enjoysudoku.com/viewtopic.php?t=4201[url]]http://forum.enjoysudoku.com/viewtopic.php?t=4201[url][/url]

Claudia
claudiarabia

Posts: 288
Joined: 14 May 2006

### Re: to many empty rows and columns

claudiarabia wrote:

Code: Select all
`*.*.*.*.*.........*.*.*.*.*.........*.*...*.*.........*.*.*.*.*.........*.*.*.*.*`

24-clue
there are 8 empty rows and 1 empty box

It is always a problem if you create sudokus with too many empty rows and columns. I don't know the minimum of rows resp. columns to be filled with at least one seed, but this here is definitely too empty.

Correct. Rows 4 and 6 are empty, and you can't generate from a template in which two rows (or columns) in the same chute are empty.

Regards,

Mike Metcalf

m_b_metcalf
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Posts: 10480
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Location: Berlin

Code: Select all
`*.*.*.*.*.........*.*.*.*.*.........*.*...*.*.........*.*.*.*.*.........*.*.*.*.*`

m_b_metcalf wrote:Correct. Rows 4 and 6 are empty, and you can't generate from a template in which two rows (or columns) in the same chute are empty.

Yes, this pattern can't have a valid puzzle as daj already pointed it out above.

claudiarabia wrote:It is always a problem if you create sudokus with to many empty rows and columns. I don't know the minimum of rows resp. columns to be filled with at least one seed, but this here is definitely to empty.

JPF
JPF
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Location: Paris, France

### Re: a wider slash

claudiarabia wrote:
coloin wrote:Our minimum B159 with 95514sols
Code: Select all
`+---+---+---+|125|.7.|...||836|...|...||749|...|...|+---+---+---+|...|123|8..||..2|456|...||...|789|...|+---+---+---+|...|..8|134||...|...|287||...|...|596|+---+---+---+`
is solved with 4 additional clues

If one can reach this with 4 additional clues, JPF's slash pattern is a much straighter example for this. There may be some slash-sudokus in which one can eliminate one clue to reach the JPF-posting previously

There is no valid slash-puzzle compatible with the minimum B1B5B9 found by coloin :
Code: Select all
` 1 2 . . . . . . . 8 3 6 . . . . . . . 4 9 x . . . . . . . x 1 2 . . . . . . . 4 5 6 . . . . . . . 8 9 x . . . . . . . x 1 3 . . . . . . . 2 8 7 . . . . . . . 9 6`

JPF
JPF
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On analysying JPF's puzzle - the B159 with 3 additional clues - see below

I was impressed by the existance of the grid [I couldnt believe it was possible] and wondered how it was produced - I cant believe it was produced by random methods either !

How did he pick the B159 ? [main question]
How did he pick the whole grid fom the 111559 grid solutions ? [long winded but possible to try them all !]
Adding 3 clues is fairly easy !

The information that you need is that the solutions of B145789 is either 0 or more than 1 [ie cant be done]

But it is possible to solve it with a single clue in certain 3-box [e.g B236 in this case] arrangements of 27 cells.

This is not needed with the 4 clue [which are relatively common] that I posted.......but with 3 clues - JPF's brilliant example -

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

Boxes B238 B278 and B236 are solved with a single clue in each of these 3-box combinations.

I realise there is more than 1 way to fill up these 3 box combinations !
JPF wrote:can only have 0 or k solutions ; k=2,3,4,...,27,28*

If it has 2 solutions then the unavoidable sets within the 27 clues can be solved with a single clue in 1,2,3,4.... 6.... 12 ........and 27 ? ways

Suffice to say I think its an impossible ask to solve in 2 clues.....there would be need to be 6 3-box combinations. Each of the 2 clues would
need to simultaneously solve 3 of the 6 combinations.

Well here the 2 at r8c5 solves the 3 relevant 3-box combos
Code: Select all
`+---+---+---+|952|...|...||863|...|...||741|...|...|+---+---+---+|...|546|...||...|938|5..||...|712|.43|+---+---+---+|...|...|872||...|.2.|314||...|...|956|+---+---+---+`

But I couldnt get less than 3 clues in B6

I dont think it will happen even in sudoku !

C
coloin

Posts: 1857
Joined: 05 May 2005

coloin wrote:How did he pick the B159 ? [main question]

starting from your minimum B159 + 4 clues ...
the permutations :
col 2,3
col 5,6
row 7,8
col 7,8
give this equivalent puzzle :

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

I removed r1c6=7 and got a 168 solutions puzzle.
I have a program playing with the numbers in the cells to try to find a valid puzzle from a n-solutions puzzle when n is not too large.
Note that the puzzle I ended with, has the same B9 and 6 cells are the same in B1.

coloin wrote:How did he pick the whole grid fom the 111559 grid solutions ? [long winded but possible to try them all !]

It was the consequence of the new B'1B'5B9.

coloin wrote:.......but with 3 clues - JPF's brilliant example -

Thanks !

JPF
JPF
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Entertainment :

(can you prove that)

This puzzle :

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`

can only have 0 or 1 solution.

JPF
JPF
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Yes, it's just a long chain of naked singles.
Red Ed

Posts: 633
Joined: 06 June 2005

Red Ed wrote:Yes, it's just a long chain of naked singles.

r8c6-r8c2-r5c2-r4c1-r1c1-r3c3-r3c6-r1c4-r1c9-r2c7-r4c7-r5c9-r7c9-r9c8-r9c3-r7c3
Then it's a matter of proving an empty box is determined by 8 filled box...
(E.g. there is no possible deadly pattern left...)
udosuk

Posts: 2698
Joined: 17 July 2005

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